RT，调了一晚上，不知道哪里错了，特来求助谷内大佬。本代码有两种方法求逆元，均经过ExLucas的验证是对的。

CF#4数据：

Input

100000 100000 4
50001 50001
50000 50000
50000 50001
50001 50000

Output

896312953

Answer

999612315

代码如下：

#include<iostream>
#include<cstdio>
#include<cmath>
#include<algorithm>
#include<cstring>
#define int long long 
using namespace std;
const int N=1e6+10;
const int mod=1e9+7;
struct node{
	int x,y;
}pos[N];
bool cmp(node a,node b){
	if(a.x==b.x){
		return a.x<b.x;
	}
	return a.x<b.x;
}
long long jc[N],ans,f[N],inv[N];
long long pow(long long y,long long z,long long p){
	long long res=1;
	while(z){
		if(z&1) res=(res*y)%p;
		y=(y*y)%p;
		z>>=1;
	}
	return (res%p+p)%p;
}
long long exgcd(long long a,long long b,long long &x,long long &y){
    if(b==0){
        x=1,y=0;
        return a;
    }
    long long gcd=exgcd(b,a%b,x,y);
    long long z=x;x=y;y=z-(a/b)*y;
    return gcd; 
}
long long inverse(long long n,long long p){
	long long x=0,y=0;
	exgcd(n,p,x,y);
	return (x%p+p)%p;
}
long long C(int m,int n){
	if(m>n){
		return 0;
	}
	return (long long)(1ll*jc[n]*inv[n-m]%mod*inv[m]%mod+mod)%mod;
}
signed main(){
	long long h,w,n;
	scanf("%lld%lld%lld",&h,&w,&n);
	for(int i=1;i<=n;i++){
		scanf("%lld%lld",&pos[i].x,&pos[i].y);
	}
	pos[n+1].x=h,pos[n+1].y=w;
	sort(pos+1,pos+n+2,cmp);
	jc[0]=1,inv[0]=1;
	for(int i=1;i<=h+w+h+w;i++){
		jc[i]=jc[i-1]*i%mod;
		inv[i]=pow(jc[i],mod-2,mod);
	}
	for(int i=1;i<=n+1;i++){
		f[i]=(C(pos[i].x-1,pos[i].x+pos[i].y-2)%mod+mod)%mod;
		for(int j=1;j<i;j++){
			f[i]-=f[j]*C((pos[i].x-pos[j].x),(pos[i].x+pos[i].y-pos[j].x-pos[j].y))%mod;
			f[i]=(f[i]%mod+mod)%mod;
		}
		f[i]=(f[i]%mod+mod)%mod;
	}
	printf("%lld\n",(f[n+1]%mod+mod)%mod);
}