排列组合lucas模板

//codeforces 559C|51nod1486 Gerald and Giant Chess(组合数学+逆元)

#include <bits/stdc++.h>
using namespace std;
#define LL long long
typedef pair<int,int> pii;
const int inf = 0x3f3f3f3f;
const int N =2e5+10;
#define clc(a,b) memset(a,b,sizeof(a))
const double eps = 1e-8;
const int MOD = 1e9+7;
void fre() {freopen("in.txt","r",stdin);}
void freout() {freopen("out.txt","w",stdout);}
inline int read() {int x=0,f=1;char ch=getchar();while(ch>'9'||ch<'0') {if(ch=='-') f=-1;ch=getchar();}while(ch>='0'&&ch<='9') {x=x*10+ch-'0';ch=getchar();}return x*f;}

struct Point{
    int x,y;
    Point(){}
    Point(int _x,int _y):x(_x),y(_y){}
    bool operator <(const Point &rhs) const{
        if(x==rhs.x) return y<rhs.y;
        return x<rhs.x;
    }
}p[N];

int f[N];
int invv[N];
int inv(int x){
  int ret=1,y=MOD-2;
  while(y){
    if(y&1)ret=1ll*ret*x%MOD;
    y>>=1;x=1ll*x*x%MOD;
  }
  return ret; 
}
int C(int n,int m){
  if(n<m)return 0;
  int ret=1ll*f[n]*invv[m]%MOD;
  ret=1ll*ret*invv[n-m]%MOD;
  return ret; 
}
int lucas(int n,int m){
   if(m == 0) return 1;
   return 1ll*C(n % MOD, m % MOD) * lucas(n / MOD, m / MOD) % MOD;
}

void init(int n,int m){
  f[0]=1;
  invv[0]=1;
  for(int i=1;i<=n+m+5;++i){
    f[i]=1ll*i*f[i-1]%MOD;
    invv[i]=inv(f[i]);
  }
}

int sum[N];
int main(){
    int n,m,q;
    scanf("%d%d%d",&n,&m,&q);
    init(n,m);
    for(int i=1;i<=q;i++){
        int x,y;
        x=read(),y=read();
        p[i]=Point(x,y);
    }
    p[++q]=Point(n,m);
    sort(p+1,p+1+q);
    for(int i=1;i<=q;i++){
        sum[i]=lucas(p[i].x-1+p[i].y-1,p[i].x-1);
        for(int j=1;j<i;j++){
            sum[i]=(sum[i]-1LL*sum[j]*lucas(p[i].x-p[j].x+p[i].y-p[j].y,p[i].x-p[j].x)%MOD+MOD)%MOD;
        }
    }
    printf("%d
",sum[q]);
    return 0;
}