#include <fstream>
#include <vector>

using namespace std;

class InParser {
private:
    FILE *fin;
    char *buff;
    int sp;

    char read_ch() {
        ++sp;
        if (sp == 4096) {
            sp = 0;
            fread(buff, 1, 4096, fin);
        }
        return buff[sp];
    }

public:
    InParser(const char* nume) {
        fin = fopen(nume, "r");
        buff = new char[4096]();
        sp = 4095;
    }

    InParser& operator >> (int &n) {
        char c;
        while (!isdigit(c = read_ch()) && c != '-');
        int sgn = 1;
        if (c == '-') {
            n = 0;
            sgn = -1;
        } else {
            n = c - '0';
        }
        while (isdigit(c = read_ch())) {
            n = 10 * n + c - '0';
        }
        n *= sgn;
        return *this;
    }

    InParser& operator >> (long long &n) {
        char c;
        n = 0;
        while (!isdigit(c = read_ch()) && c != '-');
        long long sgn = 1;
        if (c == '-') {
            n = 0;
            sgn = -1;
        } else {
            n = c - '0';
        }
        while (isdigit(c = read_ch())) {
            n = 10 * n + c - '0';
        }
        n *= sgn;
        return *this;
    }
};

class OutParser {
private:
    FILE *fout;
    char *buff;
    int sp;

    void write_ch(char ch) {
        if (sp == 50000) {
            fwrite(buff, 1, 50000, fout);
            sp = 0;
            buff[sp++] = ch;
        } else {
            buff[sp++] = ch;
        }
    }


public:
    OutParser(const char* name) {
        fout = fopen(name, "w");
        buff = new char[50000]();
        sp = 0;
    }
    ~OutParser() {
        fwrite(buff, 1, sp, fout);
        fclose(fout);
    }

    OutParser& operator << (int vu32) {
        if (vu32 <= 9) {
            write_ch(vu32 + '0');
        } else {
            (*this) << (vu32 / 10);
            write_ch(vu32 % 10 + '0');
        }
        return *this;
    }

    OutParser& operator << (long long vu64) {
        if (vu64 <= 9) {
            write_ch(vu64 + '0');
        } else {
            (*this) << (vu64 / 10);
            write_ch(vu64 % 10 + '0');
        }
        return *this;
    }

    OutParser& operator << (char ch) {
        write_ch(ch);
        return *this;
    }
    OutParser& operator << (const char *ch) {
        while (*ch) {
            write_ch(*ch);
            ++ch;
        }
        return *this;
    }
};

const int N=100000;
const int LG=18;

int n,q;
vector<int>v[N+5];
int g[N+5];

void dfs1(int nod) {
    for(auto nou:v[nod]) {
        g[nou]=g[nod]+1;
        dfs1(nou);
    }
}

int sol[3*N+5],cnt=0;
int lg[3*N+5];

void dfs2(int nod) {
    if(v[nod].size()==0)
        sol[++cnt]=nod;
    else {
        sol[++cnt]=nod;
        for(auto nou:v[nod]) {
            dfs2(nou);
            sol[++cnt]=nod;
        }
    }
}

int rmq[3*N+1][LG+1];
int who[3*N+1][LG+1];

int p[3*N+5];
int u[3*N+5];

int main() {
    InParser fin("lca.in");
    OutParser fout("lca.out");
    fin>>n>>q;
    for(int i=2;i<=n;i++) {
        int t;
        fin>>t;
        v[t].push_back(i);
    }
    g[1]=1;
    dfs1(1);
    dfs2(1);
    for(int i=1;i<=cnt;i++) {
        if(p[sol[i]]==0)
            p[sol[i]]=i;
        u[sol[i]]=i;
    }
    for(int i=1;(1<<i)<=cnt;i++)
        lg[(1<<i)]=i;
    for(int i=1;i<=cnt;i++)
        if(lg[i]==0)
            lg[i]=lg[i-1];
    for(int i=1;i<=cnt;i++) {
        rmq[i][0]=g[sol[i]];
        who[i][0]=sol[i];
    }
    int x,y;
    for(int j=1;j<=LG;j++)
        for(int i=1;i+(1<<j)-1<=cnt;i++) {
            x=rmq[i][j-1];
            y=rmq[i+(1<<(j-1))][j-1];
            if(x<y) {
                rmq[i][j]=x;
                who[i][j]=who[i][j-1];
            }
            else {
                rmq[i][j]=y;
                who[i][j]=who[i+(1<<(j-1))][j-1];
            }
        }
    int k,a,b;
    while(q--) {
        fin>>x>>y;
        x=p[x];
        y=u[y];
        k=lg[y-x+1];
        a=rmq[x][k];
        b=rmq[y-(1<<k)+1][k];
        if(a<b) {
            fout<<who[x][k]<<"\n";
        }
        else {
            fout<<who[y-(1<<k)+1][k]<<"\n";
        }
    }
    return 0;
}