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)

def sq(a, b, mod):#aのb乗を剰余,kは初期値#20191116-D-Knight
    if b==0:
        return 1
    elif b%2==0:
        return sq(a, b//2, mod)**2%mod
    else:
        return sq(a, b-1, mod)*a%mod

def nCk(n, k, mod=10 ** 9 + 7):
    x=max(k, n-k)
    y=min(k, n-k)
    kkai=1
    for i in range(2, y+1):
        kkai=(kkai*i)%mod
    nkkai=1
    for i in range(x+1, n+1):
        nkkai=(nkkai*i)%mod
    answer=sq(kkai, mod-2, mod)*nkkai%mod
    return answer
    
import math
c    = [list(map(int, input().split())) for _ in range(1)]
aa=(2*c[0][1]-c[0][0])
bb=(2*c[0][0]-c[0][1])
k=10**9+7

if aa%3!=0 or bb%3!=0:
    print(0)
elif aa<=0 or bb<=0:
    print(0)
else:
    a=aa//3
    b=bb//3
    answer=nCk(a+b,a)%k
    print(answer)