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"

#if debug
#include "printer.hpp"
#define dump(a) cerr << #a << "(" << __LINE__ << ") = " << a << endl;
#else
#define dump(...)
#endif

#define rep(i, a, b) for (int i = (a); i < (b); i++)
#define repr(i, a, b) for (int i = (b)-1; i >= a; i--)
#define all(x) (x).begin(), (x).end()

using namespace std;
typedef long long ll;
typedef vector<ll> vi;
typedef vector<vi> vvi;
typedef pair<ll, ll> pii;
const ll mod = 1000000007;

ll pow(ll x, ll y) {
  ll ret = 1, tmp = x;
  while (y) {
    if (y % 2) ret = ret * tmp % mod;
    tmp = tmp * tmp % mod;
    y /= 2;
  }
  return ret;
}

ll inverse(ll x) { return pow(x, mod - 2); }

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(8);

  ll x, y;
  cin >> x >> y;
  if ((x + y) % 3) {
    cout << 0 << endl;
    return 0;
  }

  ll n = (x + y) / 3;
  x -= n;
  y -= n;

  if (x < 0 || y < 0) {
    cout << 0 << endl;
    return 0;
  }

  ll ans = 1;
  rep(i, 0, y) {
    ans = ans * (x + y - i) % mod;
    ans = ans * inverse(i + 1) % mod;
  }
  cout << ans << endl;
}