Cod sursa(job #2054428)

Utilizator mlc_oficialBoris Barca mlc_oficial Data 1 noiembrie 2017 22:51:33
Problema Lowest Common Ancestor Scor 0
Compilator cpp Status done
Runda Arhiva educationala Marime 24.15 kb
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#include <iostream>
#include <vector>
#include <fstream>
#include <memory>
#include <cctype>

using namespace std;

#include <algorithm>
#include <cassert>
#include <complex>
#include <cstring>
#include <memory>
#include <string>
#include <vector>

using namespace std;

template <class T> struct is_iterator {
  template <class U, typename enable_if<!is_convertible<U, const char*>::value, int>::type = 0>
  constexpr static auto has_indirection(int) -> decltype(*declval<U>(), bool()) { return true; }
  template <class> constexpr static bool has_indirection(long) { return false; }
  constexpr static bool value = has_indirection<T>(0);
};

using uint = unsigned int;
// Buffer size should be 2^12 or 2^13 for optimal performance with files.
const uint BUFFER_SIZE = 1 << 12;
// Maximum possible length of a string representing primitive type
// assuming we won't encounter huge double values.
const uint MAX_LENGTH = 1 << 7;

namespace Detail {
  struct Width { uint value; };
  struct Fill { char value; };
  struct Base { uint value; };
  struct Precision { uint value; };
  struct Delimiter { const char* value; };
}  // namespace Detail

Detail::Width setWidth(uint value = 0) { return {value}; }
Detail::Fill setFill(char value = ' ') { return {value}; }
Detail::Base setBase(uint value = 10) { assert(2 <= value && value <= 36); return {value}; }
Detail::Precision setPrecision(uint value = 9) { assert(value < MAX_LENGTH); return {value}; }
Detail::Delimiter setDelimiter(const char* value = " ") { return {value}; }

/******************************* input classes ********************************/
class InputDevice {
protected:
  const char* head;
  const char* tail;

  InputDevice(const char* head, const char* tail) : head(head), tail(tail), base(setBase().value) {}

  virtual void fillInput() = 0;

  inline char nextChar() {
    if (__builtin_expect(head >= tail, false)) fillInput();
    return *head++;
  }

  template <class I> int readUnsignedIntGeneral(I& arg, char c) {
    I value = 0;
    int length = 0;
    for (;; ++length, c = nextChar()) {
      if (isDigit(c)) c -= '0';
      else if (isUpper(c)) c -= 'A' - 10;
      else if (isLower(c)) c -= 'a' - 10;
      else c = base;
      if (c >= base) break;
      value = base * value + c;
    }
    arg = value;
    return --head, length;
  }

  template <class I> inline int readUnsignedInt(I& arg, char c) {
    if (__builtin_expect(base > 10, false)) return readUnsignedIntGeneral(arg, c);
    I value = 0;
    int length = 0;
    for (; static_cast<unsigned char>(c - '0') < base; ++length, c = nextChar())
      value = base * value + c - '0';
    arg = value;
    return --head, length;
  }

  template <class I> inline bool readSignedInt(I& arg, char c) {
    bool negative = c == '-';
    if (negative) c = nextChar();
    typename make_unsigned<I>::type unsignedArg;
    if (readUnsignedInt(unsignedArg, c) == 0) return false;
    arg = negative ? ~static_cast<I>(unsignedArg - 1) : static_cast<I>(unsignedArg);
    return true;
  }

  template <class F> bool readFloatingPoint(F& arg, char c) {
    bool negative = c == '-';
    if (negative) c = nextChar();
    unsigned long long integerPart;
    if (readUnsignedInt(integerPart, c) == 0) return false;
    arg = static_cast<F>(integerPart);
    if (nextChar() == '.') {
      unsigned long long fractionalPart = 0;
      int fractionalLength = readUnsignedInt(fractionalPart, nextChar());
      if (fractionalLength > 0) {
        unsigned long long basePower = 1;
        for (; fractionalLength; --fractionalLength) basePower *= base;
        arg += static_cast<F>(fractionalPart) / basePower;
      }
    } else --head;
    if (negative) arg = -arg;
    return true;
  }

public:
  uint base;

  InputDevice(InputDevice const&) = delete;
  InputDevice& operator = (InputDevice const&) = delete;

  static inline bool isSpace(char c) { return static_cast<unsigned char>(c - '\t') < 5 || c == ' '; }
  static inline bool isDigit(char c) { return static_cast<unsigned char>(c - '0') < 10; }
  static inline bool isUpper(char c) { return static_cast<unsigned char>(c - 'A') < 26; }
  static inline bool isLower(char c) { return static_cast<unsigned char>(c - 'a') < 26; }
  static inline bool isOneOf(char c, const char* str) { return strchr(str, c) != nullptr; }

  void putBack() { --head; }  // can be called only once directly after successfully reading a character

  inline bool readChar(char& arg) {
    if (__builtin_expect(head >= tail, false)) {
      fillInput();
      if (__builtin_expect(head >= tail, false)) return arg = '\0', false;
    }
    return arg = *head++, true;
  }

  template <class UnaryPredicate>
  inline char skipCharacters(UnaryPredicate isSkipped) {
    char c;
    do { c = nextChar(); } while (isSkipped(c));
    return c;
  }
  inline char skipCharacters() { return skipCharacters(isSpace); }

  template <class UnaryPredicate>
  inline int readString(char* arg, int limit, UnaryPredicate isTerminator) {
    skipCharacters(isTerminator);
    // put back first non-skipped character, reserve space for null character
    int charsRead = 0;
    for (--head, --limit; head < tail; fillInput()) {
      ptrdiff_t chunkSize = find_if(head, min(tail, head + limit - charsRead), isTerminator) - head;
      arg = copy_n(head, chunkSize, arg);
      head += chunkSize;
      charsRead += chunkSize;
      if (chunkSize == 0 || head < tail) break;
    }
    return *arg = '\0', charsRead;
  }

  inline int readString(char* arg, int limit, const char* terminators) {
    if (!*terminators) return readString(arg, limit, InputDevice::isSpace);
    return readString(arg, limit, [terminators](char c) { return InputDevice::isOneOf(c, terminators); });
  }

  // property setters
  inline bool read(Detail::Base newBase) { base = newBase.value; return true; }
  // primitive types
  inline bool read() { return true; }
  inline bool read(char& arg) { return readChar(arg); }
  template <class I> inline typename enable_if<is_integral<I>::value && is_unsigned<I>::value,
  bool>::type read(I& arg) { return readUnsignedInt(arg, skipCharacters()) > 0; }
  template <class I> inline typename enable_if<is_integral<I>::value && is_signed<I>::value,
  bool>::type read(I& arg) { return readSignedInt(arg, skipCharacters()); }
  template <class F> inline typename enable_if<is_floating_point<F>::value,
  bool>::type read(F& arg) { return readFloatingPoint(arg, skipCharacters()); }
  // characters skip
  inline bool read(const char& arg) { skipCharacters([arg](char c) { return arg != c; }); return true; }
  inline bool read(const char* arg) {
    if (*arg) skipCharacters([arg](char c) { return InputDevice::isOneOf(c, arg); });
    else skipCharacters();
    return putBack(), true;
  }
  inline bool read(bool (*isSkipped)(char)) { skipCharacters(isSkipped); putBack(); return true; }
  // strings
  template <class I, class Terminator, class... Ts> inline typename enable_if<is_integral<I>::value,
  bool>::type read(char* arg, I limit, Terminator terminator, Ts&&... args) {
    readString(arg, static_cast<int>(limit), terminator);
    return read(forward<Ts>(args)...);
  }
  template <class I> inline typename enable_if<is_integral<I>::value,
  bool>::type read(char* arg, I limit) { return read(arg, limit, ""); }
  template <class... Ts>
  inline bool read(char* first, char* last, Ts&&... args) {
    return read(first, static_cast<int>(last - first), forward<Ts>(args)...);
  }
  template <int N, class... Ts>
  inline bool read(char (&arg)[N], Ts&&... args) { return read(static_cast<char*>(arg), N, forward<Ts>(args)...); }
  template <class Terminator, class... Ts>
  inline bool read(string& arg, Terminator terminator, Ts&&... args) {
    for (int length = 16, last = 0;; last += length, length <<= 1) {
      arg.resize(last + length);
      int charsRead = readString(&arg[last], length + 1, terminator);
      if (charsRead < length) {
        arg.resize(last + charsRead);
        return read(forward<Ts>(args)...);
      }
    }
  }
  inline bool read(string& arg) { return read(arg, ""); }
  // complex types and ranges
  template <class T1, class T2>
  inline bool read(pair<T1, T2>& arg) { return read(arg.first, arg.second); }
  template <class T>
  inline bool read(complex<T>& arg) {
    T real, imag;
    if (!read(real, imag)) return false;
    arg.real(real), arg.imag(imag);
    return true;
  }
  template <class T>
  inline bool read(vector<T>& arg) {
    uint n;
    if (!read(n)) return false;
    arg.resize(n);
    return read(arg.begin(), arg.end());
  }
  template <class Iterator, class... Ts> inline typename enable_if<is_iterator<Iterator>::value,
  bool>::type read(Iterator first, Iterator last, Ts&&... args) {
    for (; first != last; ++first) if (!read(*first)) return false;
    return read(forward<Ts>(args)...);
  }
  template <class Iterator, class I, class... Ts>
  inline typename enable_if<is_iterator<Iterator>::value && is_integral<I>::value,
  bool>::type read(Iterator first, I count, Ts&&... args) { return read(first, first + count, forward<Ts>(args)...); }
  // generic forwarding
  template <class T>
  inline auto read(T& arg) -> decltype(arg.read(*this)) { return arg.read(*this); }
  template <class T0, class T1, class... Ts>
  inline typename enable_if<!is_iterator<T0>::value && !is_convertible<T0, char*>::value,
  bool>::type read(T0&& arg0, T1&& arg1, Ts&&... args) {
    return read(forward<T0>(arg0)) && read(forward<T1>(arg1), forward<Ts>(args)...);
  }
};

class InputFile : public InputDevice {
  FILE* file;
  bool lineBuffered;
  bool owner;
  char buffer[BUFFER_SIZE];

  void fillInput() override {
    head = buffer;
    *buffer = '\0';
    if (__builtin_expect(!lineBuffered, true)) {
      tail = head + fread(buffer, 1, BUFFER_SIZE, file);
    } else {
      tail = head;
      if (fgets(buffer, BUFFER_SIZE, file)) while (*tail) ++tail;
    }
  }

public:
  InputFile(FILE* file = stdin, bool lineBuffered = true, bool takeOwnership = false)
  : InputDevice(buffer, buffer) , file(file), lineBuffered(lineBuffered), owner(takeOwnership) {}
  InputFile(const char* fileName) : InputFile(fopen(fileName, "r"), false, true) {}
  ~InputFile() { if (owner) fclose(file); }
};

// Picks up data appended to the string but doesn't handle reallocation.
class InputString : public InputDevice {
  void fillInput() override { while (*tail) ++tail; }

public:
  InputString(const string& s) : InputDevice(s.data(), s.data() + s.size()) {}
  InputString(const char* s) : InputDevice(s, s + strlen(s)) {}
};

/******************************* output classes *******************************/
class OutputDevice {
protected:
  char buffer[BUFFER_SIZE + MAX_LENGTH];
  char* output;
  char* end;
  bool separate;

  OutputDevice() : output(buffer), end(buffer + BUFFER_SIZE + MAX_LENGTH), separate(false)
  , width(setWidth().value), fill(setFill().value), base(setBase().value), precision(setPrecision().value)
  , delimiter(setDelimiter().value) { computeBasePower(); }

  virtual void writeToDevice(uint count) = 0;

  inline void flushMaybe() {
    if (__builtin_expect(output >= buffer + BUFFER_SIZE, false)) {
      writeToDevice(BUFFER_SIZE);
      output = copy(buffer + BUFFER_SIZE, output, buffer);
    }
  }

  void computeBasePower() {
    basePower = 1;
    for (uint i = 0; i < precision; ++i) basePower *= base;
  }

  template <class I> inline char* writeUnsignedInt(I arg, char* last) {
    if (__builtin_expect(arg == 0, false)) *--last = '0';
    if (__builtin_expect(base == 10, true)) {
      for (; arg; arg /= 10) *--last = '0' + arg % 10;
    } else for (; arg; arg /= base) {
      I digit = arg % base;
      *--last = digit < 10 ? '0' + digit : 'A' - 10 + digit;
    }
    return last;
  }

  template <class I> inline char* writeSignedInt(I arg, char* last) {
    auto unsignedArg = static_cast<typename make_unsigned<I>::type>(arg);
    if (arg < 0) {
      last = writeUnsignedInt(~unsignedArg + 1, last);
      *--last = '-';
      return last;
    }
    return writeUnsignedInt(unsignedArg, last);
  }

  template <class F> char* writeFloatingPoint(F arg, char* last) {
    bool negative = signbit(arg);
    if (negative) arg = -arg;
    if (isnan(arg)) for (int i = 0; i < 3; ++i) *--last = i["NaN"];
    else if (isinf(arg)) for (int i = 0; i < 3; ++i) *--last = i["fnI"];
    else {
      auto integerPart = static_cast<unsigned long long>(arg);
      auto fractionalPart = static_cast<unsigned long long>((arg - integerPart) * basePower + F(0.5));
      if (fractionalPart >= basePower) ++integerPart, fractionalPart = 0;
      char* point = last - precision;
      if (precision > 0) {
        ::fill(point, writeUnsignedInt(fractionalPart, last), '0');
        *--point = '.';
      }
      last = writeUnsignedInt(integerPart, point);
    }
    if (negative) *--last = '-';
    return last;
  }

  inline int writeT(char* first) {
    int delimiterLenght = separate ? writeDelimiter() : 0;
    separate = true;
    uint charsWritten = static_cast<uint>(end - first);
    if (__builtin_expect(charsWritten < width, false))
      charsWritten += writeFill(width - charsWritten);
    output = copy(first, end, output);
    flushMaybe();
    return delimiterLenght + static_cast<int>(charsWritten);
  }

  inline int writeFill(uint count) {
    int charsWritten = static_cast<int>(count);
    if (__builtin_expect(output + count + MAX_LENGTH < end, true)) {
      if (count == 1) *output++ = fill;
      else output = fill_n(output, count, fill);
    } else for (uint chunkSize = static_cast<uint>(buffer + BUFFER_SIZE - output);; chunkSize = BUFFER_SIZE) {
      if (chunkSize > count) chunkSize = count;
      output = fill_n(output, chunkSize, fill);
      flushMaybe();
      if ((count -= chunkSize) == 0) break;
    }
    return charsWritten;
  }

public:
  uint width;
  char fill;
  uint base;
  uint precision;
  unsigned long long basePower;
  string delimiter;

  OutputDevice(OutputDevice const&) = delete;
  OutputDevice& operator = (OutputDevice const&) = delete;
  virtual ~OutputDevice() {};

  inline int writeChar(char arg) { separate = false; *output++ = arg; flushMaybe(); return 1; }

  inline int writeString(const char* arg, size_t length, bool checkWidth = true) {
    separate = false;
    uint count = static_cast<uint>(length);
    int charsWritten = static_cast<int>(count) + (checkWidth && count < width ? writeFill(width - count) : 0);
    if (__builtin_expect(output + count + MAX_LENGTH < end, true)) {
      if (count == 1) *output++ = *arg;
      else output = copy_n(arg, count, output);
    } else for (uint chunkSize = static_cast<uint>(buffer + BUFFER_SIZE - output);; chunkSize = BUFFER_SIZE) {
      if (chunkSize > count) chunkSize = count;
      output = copy_n(arg, chunkSize, output);
      flushMaybe();
      if ((count -= chunkSize) == 0) break;
      arg += chunkSize;
    }
    return charsWritten;
  }

  inline int writeDelimiter() { return writeString(delimiter.c_str(), delimiter.size(), false); }

  inline void flush() {
    writeToDevice(static_cast<uint>(output - buffer));
    output = buffer;
  }

  // property setters
  inline int write(Detail::Width newWidth) { width = newWidth.value; return 0; }
  inline int write(Detail::Fill newFill) { fill = newFill.value; return 0; }
  inline int write(Detail::Base newBase) { base = newBase.value; computeBasePower(); return 0; }
  inline int write(Detail::Precision newPrecision) {
    precision = newPrecision.value; computeBasePower(); return 0;
  }
  inline int write(Detail::Delimiter newDelimiter) { delimiter = newDelimiter.value; return 0; }
  // primitive types
  inline int write() { return 0; }
  inline int write(char arg) { return writeChar(arg); }
  template <class I> inline typename enable_if<is_integral<I>::value && is_unsigned<I>::value,
  int>::type write(I arg) { return writeT(writeUnsignedInt(arg, end)); }
  template <class I> inline typename enable_if<is_integral<I>::value && is_signed<I>::value,
  int>::type write(I arg) { return writeT(writeSignedInt(arg, end)); }
  template <class F> inline typename enable_if<is_floating_point<F>::value,
  int>::type write(F arg) { return writeT(writeFloatingPoint(arg, end)); }
  // complex types
  inline int write(const char* arg) { return writeString(arg, strlen(arg)); }
  template <int N>
  inline int write(char (&arg)[N]) { return writeString(arg, strlen(arg)); }
  inline int write(const string& arg) { return writeString(arg.c_str(), arg.size()); }
  template <class T1, class T2>
  inline int write(const pair<T1, T2>& arg) {
    int charsWritten = write(arg.first);
    charsWritten += writeDelimiter();
    return charsWritten + write(arg.second);
  }
  template <class T>
  inline int write(const complex<T>& arg) { return write(real(arg), imag(arg)); }
  // ranges
  template <class Iterator, class... Ts> inline typename enable_if<is_iterator<Iterator>::value,
  int>::type write(Iterator first, Iterator last, Ts&&... args) {
    int charsWritten = 0;
    for (; first != last; charsWritten += ++first == last ? 0 : writeDelimiter()) charsWritten += write(*first);
    return charsWritten + write(forward<Ts>(args)...);
  }
  template <class Iterator, class I, class... Ts>
  inline typename enable_if<is_iterator<Iterator>::value && is_integral<I>::value,
  int>::type write(Iterator first, I count, Ts&&... args) { return write(first, first + count, forward<Ts>(args)...); }
  // generic forwarding
  template <class T>
  inline auto write(const T& arg) -> decltype(arg.write(*this)) { return arg.write(*this); }
  template <class T0, class T1, class... Ts> inline typename enable_if<!is_iterator<T0>::value,
  int>::type write(T0&& arg0, T1&& arg1, Ts&&... args) {
    int charsWritten = write(forward<T0>(arg0));
    return charsWritten + write(forward<T1>(arg1), forward<Ts>(args)...);
  }
};

class OutputFile : public OutputDevice {
  FILE* file;
  bool owner;

  void writeToDevice(uint count) override {
    fwrite(buffer, 1, count, file);
    fflush(file);
  }

public:
  OutputFile(FILE* file = stdout, bool takeOwnership = false) : file(file), owner(takeOwnership) {}
  OutputFile(const char* fileName) : OutputFile(fopen(fileName, "w"), true) {}
  ~OutputFile() override { flush(); if (owner) fclose(file); }
};

class OutputString : public OutputDevice {
  string& str;

  void writeToDevice(uint count) override { str.append(buffer, count); }

public:
  OutputString(string& str) : OutputDevice(), str(str) {}
  ~OutputString() override { flush(); }
};

unique_ptr<InputDevice> input;
unique_ptr<OutputDevice> output;

template <class... Ts> inline bool read(Ts&&... args) { return input->read(forward<Ts>(args)...); }
template <class... Ts> inline int write(Ts&&... args) { return output->write(forward<Ts>(args)...); }
template <class... Ts> inline int writeln(Ts&&... args) { return write(forward<Ts>(args)..., '\n'); }
void flush() { output->flush(); }

class Graph {
private:
    struct Edge {
        int from, to;
        Edge() { }
        Edge(const int _from, const int _to) : from(_from), to(_to) { }
    };
     
    template<typename T>
    struct Range {
        struct Iterator {
            T& operator *() const { return *iter; }
            bool operator !=(const Iterator& rhs) const { return iter != rhs.iter; }
            void operator ++() { ++iter; }
            T* operator +(int i) const { return iter + i; }
            size_t operator -(const Iterator& rhs) const { return iter - rhs.iter; }
            T* iter;
        };
         
        Range(T* _first, T* _last) : first({_first}), last({_last}) { }
        T operator[] (const int i) { return *(first + i); }
        size_t size() const { return last - first; }
        Iterator& begin() { return first; }
        Iterator& end() { return last; }
        Iterator first, last;
    };
public:
    Range<int> operator [](int u) { 
        return Range<int>(&edges[offset[u]], &edges[offset[u + 1]]); 
    }
     
    Graph() = default;
    Graph(const int N, const int M=0) : n(N), offset(N + 1) {
        if (M > 0) { in.reserve(M); }
    } 
     
    void AddEdge(int x, int y) { in.emplace_back(x, y); }
     
    void Init() {
        edges.resize(in.size());
        for (auto&& e : in) { offset[e.from] += 1; }
        for (int i = 1; i <= n; i += 1) { 
            offset[i] += offset[i - 1]; 
        }
        for (auto&& e : in) { 
            edges[--offset[e.from]] = e.to; 
        }
        in.clear();
    }
     
    size_t size() const {
        return (size_t)n;
    }
private:    
    int n;
    vector<int> offset, edges;
    vector<Edge> in;
};
 
class SchieberVishkinLCA {
private:
    static inline int lsb(int value) {
        return value & -value;
    }
     
    static inline int msb(int v) {
        v |= v >> 1;
        v |= v >> 2;
        v |= v >> 4;
        v |= v >> 8;
        v |= v >> 16;
        return v >> 1;
    }
public:
    SchieberVishkinLCA() = default;
    SchieberVishkinLCA(Graph& G, int root) : idx(G.size()), max_idx(G.size()), ancestor_height(G.size()), path_parent(G.size()) {
        int n = G.size();
        vector<int> parent(n), vertices(n);
         
        auto Dfs = [&]() {
            int stack_size = 1, euler_idx = 1;
            vertices[0] = root;
            parent[root] = -1;
            while (stack_size > 0) {
                const int node = vertices[--stack_size];
                idx[node] = euler_idx++;
                for (auto&& son : G[node]) {
                    if (parent[node] != son) {
                        parent[son] = node;
                        vertices[stack_size++] = son;
                    }
                }
            }
        };
         
        auto Bfs = [&]() {
            int q_front = 0, q_end = 1;
            vertices[0] = root;
            parent[root] = -1;
            while (q_front != q_end) {
                const int node = vertices[q_front++];
                for (auto&& son : G[node]) {
                    if (parent[node] != son) {
                        parent[son] = node;
                        vertices[q_end++] = son;
                    }
                }
            }
        };
         
        Dfs(); Bfs();
        max_idx = idx;
        for (int i = n - 1; i > 0; i -= 1) {
            const int node = vertices[i];
            if (lsb(max_idx[parent[node]]) < lsb(max_idx[node])) {
                max_idx[parent[node]] = max_idx[node];
            }
        }
         
        ancestor_height[root] = 0;
        for (int i = 1; i < n; i += 1) {
            const int node = vertices[i];
            ancestor_height[node] = ancestor_height[parent[node]] | lsb(max_idx[node]);
        }
         
        path_parent[idx[root] - 1] = root;
        for (int i = 0; i < n; i += 1) {
            const int node = vertices[i];
            for (auto&& son : G[node]) {
                if (parent[node] == son) {
                    continue;
                }
                 
                path_parent[idx[son] - 1] = (max_idx[node] == max_idx[son]) ? path_parent[idx[node] - 1] : node;
            }
        }
    }
     
    int Query(int x, int y) const {
        const int Ix = max_idx[x], Iy = max_idx[y];
        const int hIx = lsb(Ix), hIy = lsb(Iy);
        const int msb_mask = msb((Ix ^ Iy) | hIx | hIy);
        const int mask = lsb(ancestor_height[x] & ancestor_height[y] & ~msb_mask);
         
        int left, right;
         
        if (mask == hIx) {
            left = x;
        } else {
            const int kMask = msb(ancestor_height[x] & (mask - 1));
            left = path_parent[((idx[x] & ~kMask) | (kMask + 1)) - 1];
        }
         
        if (mask == hIy) {
            right = y;
        } else {
            const int kMask = msb(ancestor_height[y] & (mask - 1));
            right = path_parent[((idx[y] & ~kMask) | (kMask + 1)) - 1];
        }
        return (idx[left] < idx[right]) ? left : right;
    }
private:
    vector<int> idx, max_idx, ancestor_height, path_parent;
};
 
int main() {
    #ifdef INFOARENA
    input.reset(new InputFile("lca.in", false));
    output.reset(new OutputFile("lca.out"));
    #else
    input.reset(new InputFile(stdin, false));
    output.reset(new OutputFile());
    #endif
    
    int n, m; read(n, m);
    Graph G(n, n - 1);
    for (int i = 1; i < n; i += 1) {
        int parent; read(parent); parent -= 1;
        G.AddEdge(parent, i);
    }
    G.Init();
     
    SchieberVishkinLCA LcaSolver(G, 0);
    for (int i = 0; i < m; i += 1) {
        int x, y; read(x, y); x -= 1; y -= 1;
        writeln(1 + LcaSolver.Query(x, y));
    }
}