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.chomp.split(" ").map(&:to_i)

n = (x + y) / 3
k = y - n

if (x + y) % 3 != 0
  puts 0
  exit
end

MOD = 10 ** 9 + 7
# 繰り返し二乗法(x.pow(n, mod)でもOK)
def pow(x, n, mod = MOD)
  ans = 1
  # 下位ビットから繰り返し計算を行う
  while n > 0 do
    ans = ans * x % mod if n.odd? # 下位ビットが1かどうか
    x = x * x % mod
    n >>= 1 # 右ビットシフト
  end
  return ans
end

# (mod p)下での逆元
# フェルマーの小定理より a^(p-1) = 1 (mod p) (aは整数, pは素数, aとpは互いに素)
# a * a^(p-2) = 1 なので, aの逆元が a^(p-2) となる
def inv(a, mod = MOD)
  pow(a, mod - 2, mod)
end

# 階乗
# 再利用できるようグローバル変数化
$fact = [1] # 0! = 1
def fact(n, mod = MOD)
  # 計算済ならそれを返す
  return $fact[n] unless $fact[n].nil?

  # 階乗を求めながら$factへ格納
  f = $fact[-1]
  ($fact.size).upto(n) do |i|
    f = (f * i) % mod
    $fact << f
  end
  return $fact[n]
end

# 順列
def perm(n, r, mod = MOD)
  # n*(n-1)*(n-2)*...*(n-r+1)
  return n.downto(n - r + 1).reduce(1) {|ans, x| (ans * x) % mod }
end

# 組み合わせ
def comb(n, r, mod = MOD)
  return 0 unless 0 <= r && r <= n
  return 1 if r == 0 || r == n
  # nCk = n!/(n-k)! * 1/k!
  return perm(n, r, mod) * inv(fact(r, mod) % mod, mod) % mod
end

puts comb(n, k)