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 math
X,Y=list(map(int,input().split()))
mod=10**9+7


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))
if X>Y:
    big=X
    small=Y
else:
    big=Y
    small=X


if (small+big)%3!=0:
    print(0)
    exit()
if small*2==big:
    print(small%mod)
    exit()
    
    
diff=big-small
big-=diff*2
small-=diff
if big<0 or big!=small:
    print(0)
    exit()

num=big//3
tmp=1
for i in range(num+diff,num*2+diff):
    tmp=(tmp*(i+1))%mod
bunsi=tmp
bunbo=1
tmp=1
for i in range(num):
    tmp=(tmp*(i+1))%mod
bunbo=pow(tmp,mod-2,mod)
#ans=div(bunsi,bunbo)
ans=bunsi*bunbo
print(ans%mod)