dtoj1825. 放棋子(chess)

#include<cstdio>
#include<iostream>
#include<cstdlib>
#include<cstring>
#include<algorithm>
#include<cmath>
#define ll long long 
#define mod 1000000009
using namespace std;
int n,m,c,a[15],Max;
ll f[15][35][35],g[956][35][35],C[935][935];
void init(){
    int N=n*m;
    for(int i=0;i<=N;i++){
        C[i][0]=1;
        for(int j=1;j<=i;j++)C[i][j]=(C[i-1][j]+C[i-1][j-1])%mod;
    }
    for(int i=1;i<=Max;i++){
        for(int x=1;x<=n;x++){
            for(int y=1;y<=m;y++){
                if(x*y<i||x>i||y>i)continue;
                ll tmp=C[x*y][i];
                for(int j=1;j<=x;j++)
                for(int k=1;k<=y;k++){
                    if(j==x&&k==y)continue;
                    tmp=(tmp-g[i][j][k]*C[x][j]%mod*C[y][k]%mod)%mod;
                }
                g[i][x][y]=tmp;
                
            }
        }
    }
}
int main(){
    
    cin>>n>>m>>c;
    for(int i=1;i<=c;i++)scanf("%d",&a[i]),Max=max(Max,a[i]);
    init();
    f[0][0][0]=1;
    for(int i=0;i<c;i++){
        for(int j=0;j<=n;j++)
        for(int k=0;k<=m;k++){
            if(!f[i][j][k])continue;
            for(int x=1;x+j<=n;x++)
            for(int y=1;y+k<=m;y++){
                if(x*y>=a[i+1])
                (f[i+1][x+j][y+k]+=1LL*f[i][j][k]*g[a[i+1]][x][y]%mod*C[n-j][x]%mod*C[m-k][y]%mod)%=mod;
            }
        }
    }
    ll ans=0;
    for(int i=1;i<=n;i++)
    for(int j=1;j<=m;j++)ans=(ans+f[c][i][j])%mod;
    ans=(ans+mod)%mod;
    cout<<ans<<endl;
    return 0;
}