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)
    
    a = (2 * y) - x
    b = (2 * x) - y
    
    MOD = (10 ** 9) + 7
 
    
    if (a < 0) or (b < 0) or (a % 3 != 0) or (b % 3 != 0)
      puts 0
    else
        
      def kaijo(a, b)
        return (a..b).inject(1) {|i, j| (i * j) % MOD}
      end
   
      def joho_gyakugen(a, b)
        return ruijo(kaijo(a, b), MOD-2)
      end
      
      def ruijo(tei, bekisu)
        if bekisu == 0
          return 1
        elsif bekisu % 2 == 0
          return ruijo((tei ** 2) % MOD, bekisu / 2)
        else
          return tei * ruijo((tei ** 2) % MOD, bekisu / 2)
        end
      end
   
      n = [a, b].min / 3
      m = [a, b].max / 3
      total = n + m
      #if n == 0
        #puts 1
      #else
        result = (kaijo(m + 1, total) * joho_gyakugen(1, n))
        puts result % MOD
      #end
    end