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 Python (3.4.3) (judge verdict: Wrong Answer)

import numpy as np
import math

def frac_mod(n, mod, f=1):
    for i in range(1, n + 1):
        f = (f * i) % mod
    return f

def ifrac_mod(n, mod, f_inv=1):
    for i in range(n, 1, -1):
        f_inv = (f_inv * pow(i, mod-2, mod)) % mod
    return f_inv

def cmb_mod(n, r, mod):
    n_frac = frac_mod(n, mod)
    n_r_ifrac = ifrac_mod(n-r, mod)
    r_ifrac = ifrac_mod(r, mod)
    
    return int((n_frac * n_r_ifrac * r_ifrac) % mod)
mod = 10**9+7
x,y = map(int, input().split())
a = np.array([[1,2], [2,1]])
b = np.array([x,y])
res = np.linalg.solve(a,b)
is_ok = True
if not (res[0].is_integer() and res[1].is_integer()):
    is_ok = False
    ans = 0
x_res = int(res[0])
y_res = int(res[1])
if is_ok:
    ans = cmb_mod(x_res+y_res, x_res, mod)
print(ans)