// D - Knight
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define MOD 1000000007

ll modinv(ll a, ll m) {
	ll b = m, u = 1, v = 0;
	while(b){
		ll t = a / b;
		a -= t * b; swap(a, b);
		u -= t * v; swap(u, v);
	}
	u %= m;
	if(u < 0) u += m;
	return u;
}

int main(){
	int X,Y; cin>>X>>Y;
	if((X+Y)%3 != 0) puts("0");
	else{
		int r = (2*X-Y)/3;
		int n = (2*Y-X)/3;
		if(n<0 || r<0){puts("0"); return 0;}
		n += r;
		ll nPr = 1;
		for(int i=n; i>=n-r+1; --i) nPr = nPr * i % MOD;
		ll fact_r = 1;
		for(int i=r; i>=2; --i) fact_r = fact_r * i % MOD;
		cout<< nPr * modinv(fact_r, MOD) % MOD << endl;
	}
}
### Prompt

In cpp, your task is to solve 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
// D - Knight
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define MOD 1000000007

ll modinv(ll a, ll m) {
	ll b = m, u = 1, v = 0;
	while(b){
		ll t = a / b;
		a -= t * b; swap(a, b);
		u -= t * v; swap(u, v);
	}
	u %= m;
	if(u < 0) u += m;
	return u;
}

int main(){
	int X,Y; cin>>X>>Y;
	if((X+Y)%3 != 0) puts("0");
	else{
		int r = (2*X-Y)/3;
		int n = (2*Y-X)/3;
		if(n<0 || r<0){puts("0"); return 0;}
		n += r;
		ll nPr = 1;
		for(int i=n; i>=n-r+1; --i) nPr = nPr * i % MOD;
		ll fact_r = 1;
		for(int i=r; i>=2; --i) fact_r = fact_r * i % MOD;
		cout<< nPr * modinv(fact_r, MOD) % MOD << endl;
	}
}
```