Submission #35242

#TimeUsernameProblemLanguageResultExecution timeMemory
35242wan2000마스코트 (JOI13_mascots)C++14
100 / 100
276 ms213844 KiB
#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

const int N = 3003;
const ll MOD = 1e9+7;

int row, col, n;
ll F[N][N], Fac[N*N], BC[N][N], res;

void init(){
    Fac[0] = 1;
    for(int i = 1; i <= row*col; i++) Fac[i] = (Fac[i-1]*(ll)i)%MOD;
    for(int i = 0; i <= max(row,col); i++) BC[0][i] = 1;
    for(int i = 1; i <= max(row,col); i++){
        BC[i][i] = 1;
        for(int j = i+1; j <= max(row,col); j++){
            BC[i][j] = (BC[i-1][j-1]+BC[i][j-1])%MOD;
        }
    }
}

ll f(int x, int y, int r, int c){
    if(F[x][y]) return F[x][y];
    if(x==r&&y==c) return 1;
    ll ret = 0;
    if(x>r) ret = (ret+f(x-1,y,r,c)*Fac[y])%MOD;
    if(y>c) ret = (ret+f(x,y-1,r,c)*Fac[x])%MOD;
    return F[x][y] = ret;
}

int main()
{
    ios_base::sync_with_stdio(0); cin.tie(0);
    cin>>row>>col;
    init();
    cin>>n;
    int u = N, v = N, p = 0, q = 0;
    for(int i = 1; i <= n; i++){
        int x, y;
        cin>>x>>y;
        u = min(u,x);
        v = min(v,y);
        p = max(p,x);
        q = max(q,y);
    }
    int x = p-u+1;
    int y = q-v+1;
    ll need = (Fac[x*y-n]*f(row,col,x,y))%MOD;
    res = (BC[u-1][row-x]*BC[v-1][col-y])%MOD;
    res = (res*need)%MOD;
    cout<<res<<endl;
    return 0;
}
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