51nod1486 大大走格子

#include<cstdio>
#include<cstring>
#include<cctype>
#include<algorithm>
using namespace std;
#define rep(i,s,t) for(int i=s;i<=t;i++)
#define dwn(i,s,t) for(int i=s;i>=t;i--)
#define clr(x,c) memset(x,c,sizeof(x))
#define ll long long
int read(){
	int x=0;char c=getchar();
	while(!isdigit(c)) c=getchar();
	while(isdigit(c)) x=x*10+c-‘0‘,c=getchar();
	return x;
}
const int nmax=2e5+5;
const int maxn=2e3+5;
const int mod=1e9+7;
struct node{
	int a,b;
	bool operator<(const node&rhs)const{
	  return a<rhs.a||a==rhs.a&&b<rhs.b;}
};
node ns[maxn];
int h,w,n;ll fac[nmax],inv[nmax],sm[maxn];
ll pow(ll a,ll b){
	ll ans=a;--b;
	while(b){
		if(b&1) ans=ans*a%mod;
		a=a*a%mod;b>>=1;
	}
	return ans;
}
void init(){
	fac[0]=1;fac[1]=1;rep(i,2,h+w) fac[i]=fac[i-1]*i%mod;
	int t=max(h,w);inv[t]=pow(fac[t],mod-2);inv[0]=1;
	dwn(i,t-1,1) inv[i]=inv[i+1]*(i+1)%mod;
}
int main(){
	h=read(),w=read(),n=read();
	init();
	rep(i,1,n) ns[i].a=read(),ns[i].b=read();
	ns[++n].a=h,ns[n].b=w;
	sort(ns+1,ns+n+1);
	int ta,tb,ca,cb;
	rep(i,1,n){
		ta=ns[i].a;tb=ns[i].b;
		sm[i]=fac[ta+tb-2]*inv[ta-1]%mod*inv[tb-1]%mod;
		rep(j,1,i-1) {
			if(ns[j].a<=ta&&ns[j].b<=tb){
				ca=ta-ns[j].a;cb=tb-ns[j].b;
				sm[i]=(sm[i]-fac[ca+cb]*inv[ca]%mod*inv[cb]%mod*sm[j]%mod+mod)%mod;
			}
		}
	}
	printf("%lld\n",sm[n]);
	return 0;
}