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 Ruby (2.7.1) (judge verdict: Time Limit Exceeded)

x, y = gets.split.map &:to_i
MOD = 1_000_000_007

def mod_pow(a, e, p)
  r = 1
  while e > 0
    r = r * a % p if (e & 1) == 1
    a = a * a % p
    e >>= 1
  end
  r
end

fact = [1, 1]
finv = [1, 1]
2.upto(y) do |i|
  fact[i] = i * fact[i-1] % MOD
  finv[i] = mod_pow(fact[i], MOD-2, MOD)
end

cnt = 0

(0..2*y-x).each do |b|
  a = y-b*2
  next unless a >= 0 and a*2+b == x and a+b*2 == y
  
  cnt = (cnt + fact[a+b] * finv[a] * finv[b]) % MOD
end

p cnt