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: Time Limit Exceeded)


def framod(n,mod,a=1):
    for i in range(1,n+1):
        a *= i % mod
    return a
def power(n,r,mod):
    if r == 0: return 1
    if r%2 == 0:
        return power(n*n, r//2, mod) % mod
    if r%2 == 1:
        return n * power(n, r-1, mod) % mod

def comb(n,k,mod):
    a = framod(n,mod)
    b = framod(k,mod)
    c = framod(n-k,mod)
    return (a * power(b, mod-2, mod) * power(c, mod-2, mod)) % mod



def main(X,Y,mod):
    if (X+Y)%3 != 0:
        print(0)
    else:
        #n枚とm枚
        n = int((2*X-Y)/3)
        m = int((2*Y-X)/3)

        if n < 0 or m < 0:
            print(0)
        elif n == 0 or m == 0:
            print(1)
        elif n >= m:
             #n+mCmを計算
             print(comb(n+m,m,mod))
        else:
            #n+mCnを計算
            print(comb(n+m,n,mod))


X,Y  = map(int,input().split())
mod = 10**6 + 7
main(X,Y,mod)