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;

#define rep(i, n) for(int i = 0; i < (int)n; ++i)
#define FOR(i, a, b) for(int i = a; i < (int)b; ++i)
#define rrep(i, n) for(int i = ((int)n - 1); i >= 0; --i)

typedef long long ll;

const double EPS = 1e-9;
const int MOD = 1e9 + 7;

ll calc(ll a, ll b, ll p) {
    if (b == 0) return 1;
    if (b % 2) {
        return (a * calc(a, b - 1, p)) % p;
    } else {
        ll t = calc(a, b / 2, p);
        return (t * t) % p;
    }
}

int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    int x, y;
    cin >> x >> y;
    int move = (x + y) / 3;
    int w, h;
    w = x - move;
    h = y - move;
    int remain = w + h;
    if (w < 0 || h < 0 || move != remain) {
        cout << 0 << endl;
        return 0;
    }
    ll res = 1;
    FOR (i, 1, w + h + 1) {
        res = (res * i) % MOD;
    }
    FOR (i, 1, w + 1) {
        res = (res * calc(i, MOD - 2, MOD)) % MOD;
    }
    FOR (i, 1, h + 1) {
        res = (res * calc(i, MOD - 2, MOD)) % MOD;
    }
    cout << res << endl;

    return 0;
}