#include <bits/stdc++.h>

using namespace std;

typedef unsigned long long ull;
typedef long long ll;

#define mod ((ll)(1e9)+7)

ll pmod(ll n, ll p){
	ll m=n%mod;
	if(p==0) return 1;
	ll rtn=pmod((m*m)%mod, p/2)%mod;
	if(p%2==1) rtn=rtn*m%mod;
	return rtn;
}

ll binom(ll n, ll k){
	if(n<k || n<0 || k<0) return 0;
	ll a=1, b=1;
	for(ll i=0; i<k; i++){
		a=a*(n-i)%mod;
		b=b*(k-i)%mod;
	}
	return a*pmod(b, mod-2)%mod;
}

int main(){
	ll x, y;
	cin >> x >> y;
	if((2*x-y)%3!=0){
		cout << 0 << endl;
		return 0;
	}else{
		ll p=(-x+2*y)/3, q=(2*x-y)/3;
		cout << binom(p+q, p) << endl;
	}

	return 0;
}
### Prompt

Develop a solution in cpp to the problem described below:

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;

typedef unsigned long long ull;
typedef long long ll;

#define mod ((ll)(1e9)+7)

ll pmod(ll n, ll p){
	ll m=n%mod;
	if(p==0) return 1;
	ll rtn=pmod((m*m)%mod, p/2)%mod;
	if(p%2==1) rtn=rtn*m%mod;
	return rtn;
}

ll binom(ll n, ll k){
	if(n<k || n<0 || k<0) return 0;
	ll a=1, b=1;
	for(ll i=0; i<k; i++){
		a=a*(n-i)%mod;
		b=b*(k-i)%mod;
	}
	return a*pmod(b, mod-2)%mod;
}

int main(){
	ll x, y;
	cin >> x >> y;
	if((2*x-y)%3!=0){
		cout << 0 << endl;
		return 0;
	}else{
		ll p=(-x+2*y)/3, q=(2*x-y)/3;
		cout << binom(p+q, p) << endl;
	}

	return 0;
}
```