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: Accepted)

x, y = gets.to_s.split.map { |s| s.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

len = [y, 2*y-x].max
fact = [1, 1]
invt = [1, 1]
finv = [1, 1]
2.upto(len) do |i|
  fact[i] = i * fact[i-1] % MOD
  invt[i] = MOD - invt[MOD % i] * (MOD / i) % MOD
  finv[i] = finv[i-1] * invt[i] % MOD
end

cnt = 0

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

p cnt % MOD