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 <iostream>
#include <cstdio>
#include <cassert>
#include <bitset>
#include <string>
#include <sstream>
#include <algorithm>
#include <set>
#include <numeric>
#include <cmath>
#include <map>
#include <vector>
#include <queue>
#include <stack>
#include <cstring>
#include <queue>
#include <numeric>
#include <iomanip>
#define ll long long
using namespace std;
const int MAXN = 3005;
int r,c,n,yy,xx;
int mny,mxy,mnx,mxx;
long long fact[MAXN],dp[MAXN][MAXN],bino[MAXN][MAXN];
const long long mod = 1000000007;
void mul(long long &a,long long b){
a = (a*b) % mod;
}
long long go(int a,int b){
long long &ret = dp[a][b];
if(ret != -1) return ret;
if(a == r && b == c)return ret = 1;
ret = 1;
if(a < r){
mul(ret,go(a+1,b));
mul(ret,fact[b]);
}
if(b < c){
mul(ret,go(a,b+1));
mul(ret,fact[a]);
}
return ret;
}
int main(){
ios::sync_with_stdio(false); cin.tie(0);
cin >> r >> c >> n;
mny = mnx = 2e9;
mxy = mxx = -2e9;
for(int i = 0; i <= 3000; i++){
bino[i][0] = 1;
for(int j = 1; j <= 3000; j++){
bino[i][j] = bino[i-1][j-1] + bino[i-1][j];
bino[i][j] %= mod;
}
}
for(int i = 1; i <= n; i++){
cin >> yy >> xx;
mny = min(mny,yy);
mxy = max(mxy,yy);
mnx = min(mnx,xx);
mxx = max(mxx,xx);
}
long long tot = (mxy - mny + 1) * (mxx - mnx + 1) - n;
fact[0] = 1;
for(int i = 1; i <= 3000; i++) {fact[i] = fact[i-1] * i; fact[i] %= mod;}
memset(dp,-1,sizeof(dp));
long long ans = go(mxy-mny+1,mxx-mnx+1);
mul(ans,fact[tot]);
mul(ans,bino[mxy-mny+1][mny-1]);
mul(ans,bino[c-(mxx-mnx+1)][mnx-1]);
cout<<ans;
return 0;
}
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