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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
const int mod = 1000000007;
int x, y;

const int MAX = 1000000;

long long fac[MAX], finv[MAX], inv[MAX];

void COMinit() {
    fac[0] = fac[1] = 1;
    finv[0] = finv[1] = 1;
    inv[1] = 1;
    for(int i = 2; i < MAX; i++) {
        fac[i] = fac[i-1] * i % mod;
        inv[i] = mod - inv[mod%i] * (mod/i) % mod;
        finv[i] = finv[i-1] * inv[i] % mod;
    }
}

long long COM(int n, int k) {
    if(n < k) return 0;
    if(n < 0 || k < 0) return 0;
    return fac[n] * (finv[k] * finv[n-k] % mod) % mod;
}

int main() {
    cin >> x >> y;
    COMinit();
    int k, l;
    bool flg = false;
    int judge = 2*x - y;
    if(judge >= 0 && judge % 3 == 0) {
        l = judge / 3;
        int check = x - 2*l;
        if(check >= 0) {
            k = check;
            flg = true;
        }
    }

    if(flg) {
        int les, gre;
        if(k > l) {
            les = l; gre = k;
        }else {
            les = k; gre = l;
        }

        int total = les + gre;
        long long ans = COM(total, les);
        cout << ans << endl;
    }else {
        cout << 0 << endl;
    }
}