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)

# -*- coding: utf-8 -*-
import numpy as np
from collections import deque
import collections

mod = 10 ** 9 + 7
x, y = list(map(int, input().split()))
if ((2 * y - x) % 3 != 0 or (2 * x - y) % 3 != 0):
    print(0)
    exit()

# 合計 a + b回動かす
a = (2*y-x)//3  # a回
b = (2*x-y)//3  # b回
# (a+b)!/a!b!
ans = 1
for i in range(1, a+b+1):
    ans = (ans * i) % mod
a_func = 1
for i in range(1, a+1):
    a_func = (a_func * i) % mod

inv_a_func = pow(a_func, mod-2, mod)
b_func = 1
for i in range(1, b+1):
    b_func = (b_func * i) % mod
inv_b_func = pow(b_func, mod-2, mod)
ans = (ans * inv_b_func) % mod
ans = (ans * inv_a_func) % mod
print(ans)