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 (2.3.3) (judge verdict: Accepted)

MOD = 10**9 + 7

def fact(n)
  @facts ||= [1]
  (@facts.size).upto(n){|i| @facts << @facts[-1]*i % MOD}
  return @facts[n]
end

def modpow(x,n)
  ret = 1
  while n > 0
    ret = ret*x % MOD if n&1 == 1
    x = x*x % MOD
    n >>= 1
  end
  return ret
end

def modinv(x)
  return modpow(x,MOD-2)
end

def combin(n,k)
  return fact(n) * modinv(fact(n-k)) * modinv(fact(k)) % MOD
end

x,y = gets.split.map(&:to_i)
a = 0
while x < y * 2
  x -= 1
  y -= 2
  a += 1
end
#p [x,y]
if y * 2 != x || x < 0 || y < 0
  p 0
else
  p combin(a+y,a)
end