codeforces #313 div1 C

#include<cstdio>
#include<cstring>
#include<iostream>
#include<cstdlib>
#include<algorithm>
using namespace std;

typedef long long LL;
const int maxn=100010;
const int mod=1e9+7;
int n,m,k,lim;
struct blo{
	int x,y;
}c[2010];
bool cmp(const blo &A,const blo &B){
	if(A.x==B.x)return A.y<B.y;
	return A.x<B.x;
}

LL fac[maxn<<1];
LL inv[maxn<<1];
LL pow_mod(LL v,int p){
	LL tmp=1;
	while(p){
		if(p&1)tmp=tmp*v%mod;
		v=v*v%mod;p>>=1;
	}return tmp;
}
LL C(int n,int m){return fac[n]*inv[m]%mod*inv[n-m]%mod;}

LL dp[2010];
void Get_DP(){
	for(int i=1;i<=k;++i){
		dp[i]=C(c[i].x+c[i].y,c[i].x);
		for(int j=1;j<i;++j){
			if(c[j].x<=c[i].x&&c[j].y<=c[i].y){
				dp[i]=dp[i]-dp[j]*C(c[i].x+c[i].y-c[j].x-c[j].y,c[i].x-c[j].x)%mod;
				if(dp[i]<0)dp[i]+=mod;
			}
		}
	}printf("%I64d\n",dp[k]);
}

int main(){
	scanf("%d%d%d",&n,&m,&k);lim=n+m-2;
	for(int i=1;i<=k;++i){
		scanf("%d%d",&c[i].x,&c[i].y);
		c[i].x--;c[i].y--;
	}
	fac[0]=1;k++;c[k].x=n-1;c[k].y=m-1;
	for(int i=1;i<=lim;++i)fac[i]=fac[i-1]*i%mod;
	inv[lim]=pow_mod(fac[lim],mod-2);
	for(int i=lim-1;i>=0;--i)inv[i]=inv[i+1]*(i+1)%mod;
	sort(c+1,c+k+1,cmp);Get_DP();
	return 0;
}