#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define fi first
#define se second
#define mp make_pair

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

ll mod=1000000007;
int main() {
	ll x,y;
	cin >> x >> y;
	if((x+y)%3!=0){
		cout << 0 << endl;
		return 0;
	}
	ll a,b;
	a=(2*x-y)/3;
	b=(2*y-x)/3;
	if(a<0||b<0){
		cout << 0 << endl;
		return 0;
	}
	ll res=1;
	for(ll i=a+b;i>=b+1;i--){
		res=res*i%mod;
	}
	for(ll i=a;i>=1;i--){
		res=res*modinv(i,mod)%mod;
	}
	cout << res%mod << endl;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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;
#define fi first
#define se second
#define mp make_pair

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

ll mod=1000000007;
int main() {
	ll x,y;
	cin >> x >> y;
	if((x+y)%3!=0){
		cout << 0 << endl;
		return 0;
	}
	ll a,b;
	a=(2*x-y)/3;
	b=(2*y-x)/3;
	if(a<0||b<0){
		cout << 0 << endl;
		return 0;
	}
	ll res=1;
	for(ll i=a+b;i>=b+1;i--){
		res=res*i%mod;
	}
	for(ll i=a;i>=1;i--){
		res=res*modinv(i,mod)%mod;
	}
	cout << res%mod << endl;
}

```