This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <cstdio>
#include <algorithm>
using namespace std;
int fact[9000005];
int dp[3005][3005];
int bino[3005][3005];
const int mod = 1e9 + 7;
int r,c,n;
int lx = 1e9, ly = 1e9, rx = -1, ry = -1;
int C(int x, int y){
if(x < y || y < 0) return 0;
if(y == 0 || x == y) return 1;
if(bino[x][y]) return bino[x][y];
return bino[x][y] = (C(x,y-1) + C(x-1,y))%mod;
}
int f(int x, int y){
if(x > r || y > c) return 0;
if(x == r && y == c) return 1;
if(dp[x][y]) return dp[x][y];
long long t = f(x,y+1) * fact[x] + 1ll * f(x+1,y) * fact[y];
t %= mod;
return dp[x][y] = t;
}
int main(){
scanf("%d %d",&r,&c);
fact[0] = 1;
for (int i=1; i<r*c; i++) {
fact[i] = 1ll * fact[i-1] * i % mod;
}
scanf("%d",&n);
for (int i=0; i<n; i++) {
int p,q;
scanf("%d %d",&p,&q);
lx = min(lx,p);
ly = min(ly,q);
rx = max(rx,p);
ry = max(ry,q);
}
long long res = fact[(ry-ly+1)*(rx-lx+1) - n];
res *= f(rx-lx+1,ry-ly+1);
res %= mod;
res *= C(r - rx + lx - 1,lx - 1);
res %= mod;
res *= C(c - ry + ly - 1,ly - 1);
res %= mod;
printf("%lld",res);
}
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