#include <bits/stdc++.h>
using namespace std;
#define int long long

const int MOD = 1E9+7;

int a, b;
int x, y;
int u, v;

int cmod(int uu, int vv){
	if(vv == 0) return 1;
	int cc = cmod(uu, vv>>1);
	if(vv&1){
		return ((cc*cc)%MOD)*uu%MOD;
	}
	else return (cc*cc)%MOD;
}

int gt(int X){
	int XX = 1;
	for(int i=1; i <= X; ++i) XX = (XX*i)%MOD;
	return XX;
}

int C(int A, int B){
	return ((gt(A+B)*cmod(gt(A), MOD-2))%MOD)*cmod(gt(B), MOD-2)%MOD;
}

signed main(){
	cin >> x >> y;
	u = 2*y-x; v = 2*x-y;
	if(u < 0  || (u%3)!= 0 || v < 0 || (v%3)!=0){
		cout << "0";
		return 0;
	}
	a = u/3; b = v/3;
	cout << C(a, b);
}
### 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
#include <bits/stdc++.h>
using namespace std;
#define int long long

const int MOD = 1E9+7;

int a, b;
int x, y;
int u, v;

int cmod(int uu, int vv){
	if(vv == 0) return 1;
	int cc = cmod(uu, vv>>1);
	if(vv&1){
		return ((cc*cc)%MOD)*uu%MOD;
	}
	else return (cc*cc)%MOD;
}

int gt(int X){
	int XX = 1;
	for(int i=1; i <= X; ++i) XX = (XX*i)%MOD;
	return XX;
}

int C(int A, int B){
	return ((gt(A+B)*cmod(gt(A), MOD-2))%MOD)*cmod(gt(B), MOD-2)%MOD;
}

signed main(){
	cin >> x >> y;
	u = 2*y-x; v = 2*x-y;
	if(u < 0  || (u%3)!= 0 || v < 0 || (v%3)!=0){
		cout << "0";
		return 0;
	}
	a = u/3; b = v/3;
	cout << C(a, b);
}
```