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: Accepted)

import math
MOD = 10 ** 9 + 7

X, Y = map(int, input().split())

if (X + Y) % 3 != 0:
    print (0)
    exit()

x = X - (X + Y) // 3
y = Y - (X + Y) // 3

if x < 0 or y < 0:
    print (0)
    exit()

if x < y:
    x, y = y, x

# tmp = math.factorial(y)
tmp = 1
for i in range(1, y + 1):
    tmp *= i
    tmp %= MOD

ans = 1
for i in range(x + 1, x + y + 1):
    ans *= i
    ans %= MOD

def modinv(a, m): #mod. m でのaの逆元 a^{-1}を計算する
    b = m
    u = 1
    v = 0
    while b:
        t = a//b
        a -= t * b
        a, b = b, a
        u -= t * v
        u, v = v, u
    
    u %= m
    if u < 0:
        u += m
    return u

tmp = modinv(tmp, MOD)

ans *= tmp

ans %= MOD

print (ans)

# print (x, y)