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 Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.util.*;
import static java.lang.Math.*;
import java.math.BigInteger;

public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		
		// 入力
		int x = sc.nextInt();
		int y = sc.nextInt();
		int MOD = 1000000007;
		
		// 計算
		long result = 0;
		if((x + y)%3 != 0){
		    System.out.println(result);
		    return;
		}
		
		result = combination((x+y)/3, (2*x-y)/3, MOD);
		
		// 出力
		System.out.println(result);
	}
	
	public static long pow(long a, long n, long MOD) {
	    long res=1;
	    while (n>0) {
	        if ((n-n/2*2)==1) {
	            res=(res*a)%MOD;
	        }
	        a=(a*a)%MOD;
	        n>>=1;
	    }
	    return res%MOD;
	}
	
	public static long[] fact(int n, long MOD) {
	    long[] f = new long[n+1];
	    for(int i = 0; i < n+1; i++){
	        if(i == 0) f[i] = 1;
	        if(i > 0) f[i] = (f[i-1]*i)%MOD;
	    }
	    return f;
	}
	
	public static long combination(int n, int k, long MOD) {
	    if(n < k) return 0;
	    long[] f = fact(n, MOD);
	    long a = f[n];
	    long b = pow(f[k], MOD - 2, MOD);
	    long c = pow(f[n - k], MOD - 2, MOD);
	    return (((a*b)%MOD)*c)%MOD;
	}
}