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: Runtime Error)

import math
X, Y = map(int, input().split())
MOD = 10 ** 9 + 7



if (2 * Y - X) % 3 != 0:
	print(0)
elif (2 * X - Y) % 3 != 0:
	print(0)
else:
	a = (2 * Y - X) // 3
	b = (2 * X - Y) // 3
	print(a, b)
	factorial = [1]
	for i in range(1, a + b + 5):
		factorial.append(factorial[i-1] * i % MOD)
	# print(factsorial)
	print(factorial[a + b], factorial[a], factorial[b])
	print(int(factorial[a + b] // (factorial[a] * factorial[b])) % MOD)