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 sys
sys.setrecursionlimit(30000)
x,y = map(int, input().split())

dp = [[-1]*(x+1) for i in range(y+1)]
# dp[1][2]=1
# dp[2][1]=1
# dp[1][1]=0
# dp[1][0]=0
# dp[0][1]=0

def f(x,y):
    if (x,y)==(1,2):
        dp[y][x]=1
        return 1
    elif (x,y)==(2,1):
        dp[y][x]=1
        return 1
    elif (x,y)==(1,1):
        dp[y][x]=0
        return 0
    elif (x,y)==(0,1):
        dp[y][x]=0
        return 0
    elif (x,y)==(1,0):
        dp[y][x]=0
        return 0
    else:
        if dp[y][x]==-1:
            dp[y][x]=f(x-1,y-2)+f(x-2,y-1)
        return dp[y][x]

print(dp[y][x]%(10**9+7))