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: Accepted)

#!/usr/bin/env python3
import sys
import math
input = sys.stdin.readline
MOD = 10**9 + 7

def single_mod_nCr(n, r):
    if n < r or n < 0 or r < 0:
        return 0
    if r > n - r:
        r = n - r
    ret = 1
    for i in range(r):
        ret *= n - i
        ret *= pow(i+1, MOD-2, MOD)
        ret %= MOD
    return ret

x, y = [int(item) for item in input().split()]
if (x + y) % 3 != 0:
    print(0)
    exit()
step = (x + y) // 3
x -= step; y -= step
if x < 0 or y < 0:
    print(0)
    exit()

print(single_mod_nCr(x+y, x))