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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define MOD 1000000007
#define int long long

using namespace std;

int Map[1000001];

signed main()
{
	int x=0,y=0;
	cin >> x >> y;
	if ((x+y)%3!=0)
	{
		cout << 0;
		return 0;
	}		
	int m = (2*y-x)/3;	
	if ((2*y-x)<0 || (2*y-x)%3!=0)
	{
		cout << 0;
		return 0;
	}
	int n = (x-m)/2;		
	if ((x-m)<0 || (x-m)%2!=0)
	{
		cout << 0;
		return 0;
	}
	for (int i=n+1; i<=n+m; i++)
	{
		int ii = i;
		while (ii%2==0)
		{
			ii/=2;
			Map[2]++;
		}
		int sqrtII = round(sqrt(ii));
		for (int j=3; j<=sqrtII; j+=2)
		{
			while (ii%j==0)
			{
				ii/=j;
				Map[j]++;
			}
		}
		if (ii!=1)
			Map[ii]++;
	}
	for (int i=2; i<=m; i++)
	{
		int ii = i;
		while (ii%2==0)
		{
			ii/=2;
			Map[2]--;
		}
		int sqrtII = round(sqrt(ii));
		for (int j=3; j<=sqrtII; j+=2)
		{
			while (ii%j==0)
			{
				ii/=j;
				Map[j]--;
			}
		}
		if (ii!=1)
			Map[ii]--;
	}
	int res=1;
	for (int i=2; i<=1000000; i++)
	{
		for (int j=1; j<=Map[i]; j++)
		{
			res = (res*i)%MOD;
		}
	}	
	cout << res;
	return 0;
}