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 Julia (0.5.0) (judge verdict: Time Limit Exceeded)

parseInt(x) = parse(Int, x)
N_MAX = 1 * 10^6;fac = Array{Int}(N_MAX+1);inv = Array{Int}(N_MAX+1);MOD = 10^9 + 7;
#初期化
function COMINIT();fac[1] = 1;for i in 1:N_MAX-1;fac[i+1] = fac[i] * (i+1) % MOD;end;for i in 1:N_MAX;inv[i] = powermod(fac[i], MOD-2, MOD);end;end;
#nCk
function Comb(n, k);if n <= 0 || k < 0;return 0;end;if k > n;return 0;end;if k == 0 || n == k;return 1;end;return ((fac[n] * inv[k]) % MOD * inv[n-k])%MOD;end;
function H(n, m);return Comb(n + m, m);end;
function main()
    COMINIT()
    x, y = parseInt.(split(readline()))
    z = min(x, y)
    ans = 0
    if (x + y) % 3 == 0
        n = Int((x + y) / 3)
        l = z - n
        if l >= 0
            ans = Comb(n,l)
        end
    end
    println(ans)
end

main()