题解

#include<iostream>
using namespace std;
const int P = 1e9 + 7,N = 3e6 + 10;
int n,m,up,inv[N],jc[N],inj[N];
int Calc(int x,int y){
    return (x < 0 || y < 0) ? 0 : 1ll * jc[x + y] * inj[x] % P * inj[y] % P;
}
void flip1(int &x,int &y){
    swap(x,y);
    x--;
    y++;
}
void flip2(int &x,int &y){
    swap(x,y);
    x += m + 2;
    y -= m + 2;
}
void add(int &x,int y){
    x += y;
    if(x >= P){
        x -= P;
    }
}
int main(){
	cin >> n >> m;
    inv[0] = inv[1] = jc[0] = inj[0] = 1;
    up = max(n,m) * 3 + 1;
	for(int i = 2;i <= up;i++){
        inv[i] = (P - 1ll * P / i * inv[P % i] % P) % P;
    } 
	for(int i = 1;i <= up;i++){
        jc[i] = 1ll * jc[i - 1] * i % P;
        inj[i] = 1ll * inj[i - 1] * inv[i] % P;
    } 
	int x = n + m + 1,y = n,ans = Calc(x,y);
	while(x >= 0 && y >= 0){
		flip1(x,y);
        add(ans,P - Calc(x,y));
		flip2(x,y);
        add(ans,Calc(x,y));
	}
	x = n + m + 1,y = n;
	while(x >= 0 && y >= 0){
		flip2(x,y);
        add(ans,P - Calc(x,y));
		flip1(x,y);
        add(ans,Calc(x,y));
	}
	cout << ans << endl;
    return 0;
}