Cod sursa(job #3340503)

Utilizator BuzdiBuzdugan Rares Andrei Buzdi Data 14 februarie 2026 18:03:13
Problema Cowfood Scor 100
Compilator cpp-64 Status done
Runda Arhiva de probleme Marime 1.94 kb
#include <bits/stdc++.h>
#define ll long long
#define ld double

using namespace std;

ifstream fin("cowfood.in");
ofstream fout("cowfood.out");

const int NMAX = 20;
const int KMAX = 30;
const int SMAX = 2e4;
const int MOD = 3210121;

int k, s, n, answer;
int a[NMAX + 1][KMAX + 1];
int maxi[KMAX + 1];
int fact[SMAX + 1], invfact[SMAX + 1];

int power(int a, int b) {
    int rez = 1;
    while(b) {
        if(b % 2 == 1) {
            rez = (ll) rez * a % MOD;
        }
        a = (ll) a * a % MOD;
        b /= 2;
    }
    return rez;
}

int combinari(int n, int k) {
    if(n < 0 || k < 0 || n < k) {
        return 0;
    }
    return (ll) fact[n] * invfact[k] % MOD * invfact[n - k] % MOD;
}

void backtracking(int i = 1, int cnt = 0) {
    if(i == n + 1) {
        if(cnt) {
            int sum_here = 0;
            for(int j = 1; j <= k; j++) {
                sum_here += maxi[j];
            }
            int sign = (cnt % 2 == 1 ? 1 : -1);
            answer = (answer + sign * combinari(s - sum_here + k, k) % MOD + MOD) % MOD;
        }
        return;
    }

    backtracking(i + 1, cnt);

    int old_maxi[KMAX + 1];
    for(int j = 1; j <= k; j++) {
        old_maxi[j] = maxi[j];
        maxi[j] = max(maxi[j], a[i][j]);
    }

    backtracking(i + 1, cnt + 1);

    for(int j = 1; j <= k; j++) {
        maxi[j] = old_maxi[j];
    }
}

int main() {
    fin >> k >> s >> n;
    for(int i = 1; i <= n; i++) {
        for(int j = 1; j <= k; j++) {
            fin >> a[i][j];
        }
    }

    fact[0] = 1;
    for(int i = 1; i <= 2 * s; i++) {
        fact[i] = (ll) fact[i - 1] * i % MOD;
    }
    invfact[2 * s] = power(fact[2 * s], MOD - 2);
    for(int i = 2 * s - 1; i >= 0; i--) {
        invfact[i] = (ll) invfact[i + 1] * (i + 1) % MOD;
    }

    backtracking();
    fout << ((combinari(s + k, k) - answer - 1 - s * k) % MOD + MOD) % MOD << '\n';
    return 0;
}