Problem:
Score : 400 points

Problem Statement

There is a knight - the chess piece - at the origin (0, 0) of a two-dimensional grid.

When the knight is at the square (i, j), it can be moved to either (i+1,j+2) or (i+2, j+1).

In how many ways can the knight reach the square (X, Y)?

Find the number of ways modulo 10^9 + 7.

Constraints

1 \leq X \leq 10^6

1 \leq Y \leq 10^6

All values in input are integers.

Input

Input is given from Standard Input in the following format:

X Y

Output

Print the number of ways for the knight to reach (X, Y) from (0, 0), modulo 10^9 + 7.

Sample Input 1

3 3

Sample Output 1

2

There are two ways: (0,0) \to (1,2) \to (3,3) and (0,0) \to (2,1) \to (3,3).

Sample Input 2

2 2

Sample Output 2

0

The knight cannot reach (2,2).

Sample Input 3

999999 999999

Sample Output 3

151840682

Print the number of ways modulo 10^9 + 7.

Solution in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
using  LL = long long;
LL yhaa(LL x, LL n, LL mod){
    if (n == 0){
        return 1;
    }
    if (n%2 == 0){
        LL t = (yhaa(x,n/2, mod)) % mod;//偶数の時は半分
        return (t*t) % mod;
    }
    return (x * yhaa(x, n-1, mod)) % mod;
}

LL nCk(LL n,LL k,LL m){
    int K;
    if (2*k > n){
        K  = n - k;
    }
    else{
        K = k;
    }
    LL X = 1;
    for(int i = 0; i < K;i++){
        X = (X*(n-i)) % m;
    }
    LL Y = 1;
    for(int i = 1; i < K+1; i++){
        Y = (Y*i) % m;
    }
    LL YY = yhaa(Y,1000000005,m);
    return (X*YY) % m;

}
int main(){
    int X, Y;
    cin >> X >> Y;
    int a, b;
    LL ans; 
    ans = 0;
    if (X*Y != 0 & abs(X-Y) < min(X,Y)){
        if ((X+Y) % 3 == 0){
            a = (2*X - Y) / 3;
            b = Y - 2*a;
            if (a > 0){
                if(b > 0){
                    ans = nCk(a+b,min(a,b),1000000007);
                }
            }
            
        }
    }

    cout << ans << endl;

}