#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
ll mod=1e9+7, mx=1e+7;
ll binpow(ll a, ll exp){
	ll res=1;
	while(exp>0){
		if(exp&1) res=res*a%mod;
		a = a*a%mod;
		exp>>=1;
	}
	return res;
}
int main(){
	ll x,y,k,xk,ans; cin>>x>>y;
	k=(x+y)/3;
	xk= x-k;
	if((x+y)%3||min(x,y)<k||max(x,y)>2*k) {cout<<0<<endl; return 0;}
	vector<ll>fact(mx);
	fact[0]=1;
	for(int i=1;i<mx;i++) fact[i]=(fact[i-1]*i)%mod;
	ans=fact[k];
	ans *= binpow(fact[xk], mod-2);
	ans %= mod;
	ans *= binpow(fact[k-xk], mod-2);
	ans %= mod;
	cout<<ans<<endl;
	return 0;
}
### Prompt

Your challenge is to write 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;
typedef long long ll;
ll mod=1e9+7, mx=1e+7;
ll binpow(ll a, ll exp){
	ll res=1;
	while(exp>0){
		if(exp&1) res=res*a%mod;
		a = a*a%mod;
		exp>>=1;
	}
	return res;
}
int main(){
	ll x,y,k,xk,ans; cin>>x>>y;
	k=(x+y)/3;
	xk= x-k;
	if((x+y)%3||min(x,y)<k||max(x,y)>2*k) {cout<<0<<endl; return 0;}
	vector<ll>fact(mx);
	fact[0]=1;
	for(int i=1;i<mx;i++) fact[i]=(fact[i-1]*i)%mod;
	ans=fact[k];
	ans *= binpow(fact[xk], mod-2);
	ans %= mod;
	ans *= binpow(fact[k-xk], mod-2);
	ans %= mod;
	cout<<ans<<endl;
	return 0;
}
```