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)

a = list(map(int, input().split()))
import sys
sys.setrecursionlimit(100000)

if (2*a[0]- a[1])%3 != 0:
    print(0)
else:
    if (2*a[1] - a[0])%3 != 0:
        print(0)
    else:
        x = (2*a[1] - a[0])//3
        y = (2*a[0]- a[1])//3
        def cmb(n, r):
            if n - r < r: r = n - r
            if r == 0: return 1
            if r == 1: return n

            numerator = [n - r + k + 1 for k in range(r)]
            denominator = [k + 1 for k in range(r)]

            for p in range(2,r+1):
                pivot = denominator[p - 1]
                if pivot > 1:
                    offset = (n - r) % p
                    for k in range(p-1,r,p):
                        numerator[k - offset] /= pivot
                        denominator[k] /= pivot

            result = 1
            for k in range(r):
                if numerator[k] > 1:
                    result *= int(numerator[k])

            return result
        
        print((cmb(x+y,x))%(10**9 + 7))