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;
#define ms(x,y) memset(x, y, sizeof(x))
#define lowbit(x) ((x)&(-x))
#define sqr(x) ((x)*(x))
typedef long long LL;
typedef pair<int,int> pii;
typedef pair<LL,LL> pll;

const int maxn = 2e6+5;
const LL MOD = 1e9+7;
LL inv[maxn], f[maxn], invf[maxn];

void init() {
    inv[1] = 1;
    for(int i = 2; i < maxn; ++i)
        inv[i] = (MOD - MOD / i) - inv[MOD % i] % MOD;
    f[0] = invf[0] = 1;
    for(int i = 1; i < maxn; ++i) {
        f[i] = f[i-1] * 1LL * i % MOD;
        invf[i] = invf[i-1] * inv[i] % MOD;
    }
}

LL comb(int a, int b) {
    if(b < 0 || b > a) return 0;
    return f[a]*invf[a-b]%MOD*invf[b]%MOD;
}

void run_case() {
    int n, m;
    init();
    cin >> n >> m;
    if((n+m)%3) cout << "0\n";
    else {
        cout << (comb((n+m)/3, n-(n+m)/3) + MOD) % MOD;
    }
}


int main() {
    ios::sync_with_stdio(false), cin.tie(0);
    cout.flags(ios::fixed);cout.precision(9);
    //int t; cin >> t;
    //while(t--)
    run_case();
    cout.flush();
    return 0;
}