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: Time Limit Exceeded)

MOD = 1000000007
INV = []

def conv(a,b)
  if b > a/2
    b = a - b
  end
  ans = 1
  for i in 1..b
    ans = ((ans * (a - (i - 1))) * INV[i]) % MOD
  end
  ans % MOD
end

def pow(x,n)
  if n == 0
    1
  elsif n % 2 == 0
    pow(x*x%MOD, n/2) % MOD
  else
    x * pow(x, n-1) % MOD
  end
end

def calc_fact(n)
  INV[0] = pow(1, MOD-2)
  for i in 1..n
    INV[i] = pow(i, MOD-2)
  end
end

x,y=gets.chomp.split(" ").map(&:to_i)

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

n = (x + y) / 3
x = x - n
y = y - n
if x < 0 || y < 0
  puts "0"
  exit
end

calc_fact(x > y ? x : y)
puts conv(x + y, x)