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Cod sursa(job #937153)
#include <cstring>
#include <fstream>
#include <algorithm>
using namespace std;
const int MOD = 3210121;
int K, S, N;
int A[22][32];
int fact[20002], invfact[20002];
int D[10002], E[10002];
int result;
int power(int x, int y)
{
if (y == 0) return 1;
if (y & 1) return 1LL * x * power(1LL * x * x % MOD, y >> 1) % MOD;
return power(1LL * x * x % MOD, y >> 1);
}
int COMB(int x, int y)
{
int resnow = fact[x];
resnow = 1LL * resnow * invfact[y] % MOD;
resnow = 1LL * resnow * invfact[x - y] % MOD;
return resnow;
}
int P[32];
void Back(int x, int y)
{
if (y != 0)
{
int sumnow = 0;
for (int i = 1; i <= K; ++i)
sumnow += P[i];
if (S - sumnow >= 0)
{
if (y & 1)
{
result -= D[S - sumnow];
if (result < 0) result += MOD;
}
else
{
result += D[S - sumnow];
if (result >= MOD) result -= MOD;
}
}
}
int aux[32];
for (int i = x + 1; i <= N; ++i)
{
for (int j = 1; j <= K; ++j)
{
aux[j] = P[j];
P[j] = max(P[j], A[i][j]);
}
Back(i, y + 1);
for (int j = 1; j <= K; ++j)
P[j] = aux[j];
}
}
int main()
{
ifstream fin("cowfood.in");
ofstream fout("cowfood.out");
fact[0] = 1;
invfact[0] = 1;
for (int i = 1; i <= 20000; ++i)
{
fact[i] = 1LL * fact[i - 1] * i % MOD;
invfact[i] = 1LL * invfact[i - 1] * power(i, MOD - 2) % MOD;
}
fin >> K >> S >> N;
for (int i = 1; i <= N; ++i)
for (int j = 1; j <= K; ++j)
fin >> A[i][j];
D[0] = 1;
E[0] = 0;
for (int i = 1; i <= S; ++i)
{
D[i] = D[i - 1] + COMB(i + K - 1, K - 1);
if (D[i] >= MOD) D[i] -= MOD;
E[i] = E[i - 1] + COMB(i + K - 1, K - 1);
if (E[i] >= MOD) E[i] -= MOD;
E[i] -= K;
if (E[i] < 0) E[i] += MOD;
}
result = E[S];
Back(0, 0);
fout << result << '\n';
fin.close();
fout.close();
}