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 sys

x,y = map(int,input().split())
MOD = 10**9+7
N = 10**6
if (x+y)%3 != 0:
    print(0)
    sys.exit()
else:
    m = (2*x-y)//3
    n = (2*y-x)//3
    if n < 0 or m < 0:
        print(0)
        sys.exit()
    else:
        A = [1,1]
        B = [1,1]
        Inv = [0,1]
        for i in range(2,N+1):
            A.append((A[-1]*i)%MOD)
            Inv.append((-Inv[MOD%i]*(MOD//i))%MOD)
            B.append((B[-1]*Inv[-1])%MOD)
print(A[m+n]*B[m]*B[n]%MOD)