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

const int mod = 1e9+7, maxn = 2e6 + 15;

int x,y,fact[maxn];

int power(int a, int b){
	int ret = 1;
	while(b){
		if(b & 1)
			ret = 1ll * ret * a % mod;
		a = 1ll * a * a % mod;
		b >>= 1;
	}
	
	return ret;
}

int main(){
	
	scanf("%d%d",&x,&y);
	
	fact[0] = 1;
	for(int i = 1; i < maxn; i++)
		fact[i] = 1LL * fact[i-1] * i % mod;
	
	int cnt = 0;
	if(x < y) swap(x,y);
	
	while(x > y){
		cnt++;
		x -= 2;
		y--;
	}
	
	if(x < 0 || y < 0 || x % 3 != 0){
		puts("0");
		return 0;
	}
	int k = x / 3;
	printf("%lld\n",1ll*fact[k+k+cnt]*power(fact[k+cnt], mod-2)%mod*power(fact[k], mod-2)%mod);
	
	return 0;
}
### 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;

const int mod = 1e9+7, maxn = 2e6 + 15;

int x,y,fact[maxn];

int power(int a, int b){
	int ret = 1;
	while(b){
		if(b & 1)
			ret = 1ll * ret * a % mod;
		a = 1ll * a * a % mod;
		b >>= 1;
	}
	
	return ret;
}

int main(){
	
	scanf("%d%d",&x,&y);
	
	fact[0] = 1;
	for(int i = 1; i < maxn; i++)
		fact[i] = 1LL * fact[i-1] * i % mod;
	
	int cnt = 0;
	if(x < y) swap(x,y);
	
	while(x > y){
		cnt++;
		x -= 2;
		y--;
	}
	
	if(x < 0 || y < 0 || x % 3 != 0){
		puts("0");
		return 0;
	}
	int k = x / 3;
	printf("%lld\n",1ll*fact[k+k+cnt]*power(fact[k+cnt], mod-2)%mod*power(fact[k], mod-2)%mod);
	
	return 0;
}
```