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 sys
import math
import numpy as np
import itertools
# いくつか入力
x,y = (int(i) for i in input().split())  

MOD = 1000000007

if (x+y) % 3 != 0:
    print(0)
    exit()

a = x - (x+y) // 3
b = y - (x+y) // 3

upper=1
lower=1

for i in range(1,a+b+1,1):
    upper *= i
    upper %= MOD

for i in range(1,a+1,1):
    lower *= i
    lower %= MOD

for i in range(1,b+1,1):
    lower *= i
    lower %= MOD

# karimono
# https://qiita.com/Yaruki00/items/fd1fc269ff7fe40d09a6
def mul(a, b):
    return ((a % MOD) * (b % MOD)) % MOD

def power(x, y):
    if   y == 0     : return 1
    elif y == 1     : return x % MOD
    elif y % 2 == 0 : return power(x, y//2)**2 % MOD
    else            : return power(x, y//2)**2 * x % MOD

def div(a, b):
    return mul(a, power(b, MOD-2))

answer = div(upper,lower)

print(answer)