#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int (i)=0; (i)<(n); (i)++)
typedef long long ll;

ll power(ll a, ll n, ll mod){
	if(a==1)return 1;
	ll p = 1;
	while(n>0){
		if(n&1){p *= a;}
		a = a*a % mod;
		p %= mod;
		n = n>>1;
	}
	return p;
}


int main(){
	const int MOD = 1e9+7;
	int X,Y;
	cin >> X >> Y;

	ll n = (2*Y-X)/3;
	ll m = (2*X-Y)/3;
	if((X+Y)%3 != 0 || n<0 || m<0){ cout<<0<<endl; return 0; }
	ll fact = 1;
	for(ll i=n+m; i>m; i--){
		fact = fact * i % MOD;
	}

	ll nume = 1;
	for(ll i=n; i>0; i--){
		nume = nume * i % MOD;
	}
	nume = power(nume,MOD-2,MOD);

	cout << fact * nume % MOD << endl;
}

### Prompt

Please formulate a CPP solution to the following problem:

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.

Examples

Input

3 3


Output

2


Input

2 2


Output

0


Input

999999 999999


Output

151840682

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int (i)=0; (i)<(n); (i)++)
typedef long long ll;

ll power(ll a, ll n, ll mod){
	if(a==1)return 1;
	ll p = 1;
	while(n>0){
		if(n&1){p *= a;}
		a = a*a % mod;
		p %= mod;
		n = n>>1;
	}
	return p;
}


int main(){
	const int MOD = 1e9+7;
	int X,Y;
	cin >> X >> Y;

	ll n = (2*Y-X)/3;
	ll m = (2*X-Y)/3;
	if((X+Y)%3 != 0 || n<0 || m<0){ cout<<0<<endl; return 0; }
	ll fact = 1;
	for(ll i=n+m; i>m; i--){
		fact = fact * i % MOD;
	}

	ll nume = 1;
	for(ll i=n; i>0; i--){
		nume = nume * i % MOD;
	}
	nume = power(nume,MOD-2,MOD);

	cout << fact * nume % MOD << endl;
}

```