Gerald and Giant Chess -- 待补

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#include<iostream>
#include<cstring>
#include<cstdio>
#include<algorithm>
#define int long long
#define mod 1000000007
using namespace std;
inline int read(){
    int f=1,ans=0;char c=getchar();
    while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
    while(c>='0'&&c<='9'){ans=ans*10+c-'0';c=getchar();}
    return f*ans;
}
const int N=200011;
int inv[N],fac[N];
int ksm(int a,int b){
    int ans=1;
    while(b){
        if(b&1) ans*=a,ans%=mod;
        a*=a,a%=mod;
        b>>=1;
    }return ans%mod;
}
int n,m,k;
struct node{
    int x,y;
}a[N];
int C(int m,int n){if(n==0) return 1;return (fac[m]*((inv[n]*inv[m-n])%mod))%mod;}
bool cmp(node x1,node x2){
    if(x1.x==x2.x) return x1.y<x2.y;
    return x1.x<x2.x;
}
int f[N];
signed main(){
    inv[0]=1,fac[0]=1;
    for(int i=1;i<=200001;i++){
        fac[i]=(fac[i-1]*i)%mod;
        inv[i]=ksm(fac[i],mod-2);
    }
    n=read(),m=read(),k=read();
    for(int i=1;i<=k;i++) a[i].x=read(),a[i].y=read();
    sort(a+1,a+k+1,cmp);
    a[++k].x=n,a[k].y=m;
    for(int i=1;i<=k;i++){
        f[i]=C(a[i].x+a[i].y-2,a[i].x-1)%mod;
        for(int j=1;j<i;j++){
            if(a[j].x>a[i].x||a[j].y>a[i].y) continue;
            f[i]-=f[j]*C(a[i].x-a[j].x+a[i].y-a[j].y,a[i].x-a[j].x);
            f[i]=((f[i]%mod)+mod)%mod;
        }
    }
    printf("%lld",(f[k]%mod+2*mod)%mod);
}

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