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: Runtime Error)

# import numpy as np
import sys
sys.setrecursionlimit(10000)
e = 1000000000 + 7
N = 1000000 // 3
# dp = np.zeros((N, N))
memo = {}
for n in range(N):
	s = "n: {}, k: {}".format(n, 0)
	memo[s] = 1
	s = "n: {}, k: {}".format(n, n)
	memo[s] = 1
	# dp[n][0] = 1
	# dp[n][n] = 1

def pascal(n, k):
	# if dp[n][k] == 0:
	# 	dp[n][k] = pascal(n - 1, k - 1) % e + pascal(n - 1, k) % e
	# return dp[n][k] % e
	s = "n: {}, k: {}".format(n, k)
	if s not in memo:
		memo[s] = pascal(n - 1, k - 1) % e + pascal(n - 1, k) % e
	return memo[s] % e

# print(pascal(6, 3))

if __name__ == "__main__":
	X, Y = map(int, input().split())
	if (X + Y) % 3 != 0:
		print("0")
	else:
		n = (X + Y) // 3
		k = Y - n
		print(pascal(n, k))