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>
using namespace std;

#define ll long long
#define mod 1000000007

ll bigmod(ll a, ll p)
{
	if(p==0) return 1;
	ll mul= bigmod(a,p/2);

	if(p&1) return ((mul*mul)%mod * a)%mod;
	return (mul*mul)%mod;
}

ll inv(ll x)
{
	return bigmod(x,mod-2);
}

ll f[2000007];

int main()
{
	f[0]=1;
	for(int i=1;i<2000007;i++)
	{
		f[i]=(f[i-1]%mod) * (i%mod);
		f[i]%=mod;
	}

	ll x,y;
	cin >> x >> y;

	ll r=0;
	for(int i=1;i<=1000000;i++, r++)
	{
		if(y<0 || x<0 || y<r) break;

		if(2*y == x)
		{
			ll k=y;

			cout << ((f[k]%mod*inv(f[r])%mod)%mod * (inv(f[k-r])%mod))%mod << endl;
			return 0;
		}

		x++,y--;
	}

	cout << 0 << endl;

	return 0;
}