#include <bits/stdc++.h>
using namespace std;
long long x, y, mod=1000000007, a, b, q, ans[1000005];
void build(){
	ans[0]=1;
	for (long long i=1; i<1000003; i++){
		ans[i]=ans[i-1]*i; 
		ans[i]%=mod;
	}
}
long long div(long long a){
	long long b=mod-2, sol=1;
	while (b){
		if (b&1) sol*=a; a*=a; b>>=1; sol%=mod; a%=mod;
	}
	return sol;
}
int main (){
ios::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
cin >> x >> y; 
if ((x+y)%3) {cout << 0; return 0;}
if (x>2*y or y>2*x){cout << 0; return 0;}
	a=(x+y)/3; b=(x+y)/3*2 - max(x, y); build();
	cout << ((((ans[a]*div(ans[b]))%mod)*div(ans[a-b]))%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;
long long x, y, mod=1000000007, a, b, q, ans[1000005];
void build(){
	ans[0]=1;
	for (long long i=1; i<1000003; i++){
		ans[i]=ans[i-1]*i; 
		ans[i]%=mod;
	}
}
long long div(long long a){
	long long b=mod-2, sol=1;
	while (b){
		if (b&1) sol*=a; a*=a; b>>=1; sol%=mod; a%=mod;
	}
	return sol;
}
int main (){
ios::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
cin >> x >> y; 
if ((x+y)%3) {cout << 0; return 0;}
if (x>2*y or y>2*x){cout << 0; return 0;}
	a=(x+y)/3; b=(x+y)/3*2 - max(x, y); build();
	cout << ((((ans[a]*div(ans[b]))%mod)*div(ans[a-b]))%mod);
return 0;
}
```