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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

import math
import time
from collections import deque
from collections import defaultdict
from copy import deepcopy

mod = 10 ** 9 + 7
t = time.time()

def iip():
    ret = [int(i) for i in input().split()]
    if len(ret) == 1:
        return ret[0]
    return ret

def power(n, p):
    if p == 0:
        return 1
    if p % 2 == 0:
        return (power(n, p//2) ** 2) % mod
    if p % 2 == 1:
        return (n * power(n, p-1)) % mod

def main():
    X, Y = iip()
    aa = (int(-X) + int(2*Y)) // 3
    bb = (int(-Y) + int(2*X)) // 3

    if (-X + 2*Y) % 3 != 0 or aa < 0:
        print(0)
        exit()

    if (-Y + 2*X) % 3 != 0 or aa < 0:
        print(0)
        exit()


    a = min(aa, bb)
    b = max(aa, bb)

    if a == 0:
        print(1)
        exit()
    #print(a)
    #print(b)

    npr = 1
    for i in range(a+1, a+b+1):
        npr *= i
        npr = npr % mod

    #print(npr)

    bunbo = 1
    for i in range(1, a+1):
        #print(f"i:{i}")
        bunbo *= i
        bunbo = bunbo % mod

    #print(bunbo)

    ans = npr * power(bunbo, mod-2)
    ans = ans % mod
    print(ans)





main()