#include <iostream>
#include <cstdio>
#include <cmath>
#include <algorithm>
#define sqr(a) ((a)*(a))
using namespace std;

int X, Y, mod = 1e9+7;
int64_t tmp, res;

int64_t pw(int a,int n)
{
    if (n == 1) return a;
    tmp = pw(a, n>>1);
    return n&1 ? tmp * tmp % mod * a % mod : tmp * tmp % mod;
}
int64_t C(int n, int k)
{
    res = 1;
    for(int i=0; i<k; ++i) res = res * (n-i) % mod * pw(i+1, mod-2) % mod;
    return res;
}
int main()
{

    cin >> X >> Y; int64_t ans = 0;
    for(int a=X&1; a<=X; a+=2) if (a+a + (X-a)/2 == Y)
        ans = (ans + C((a+X)/2, a)) % mod;
    cout << ans;
}

### Prompt

Generate a cpp solution to 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 <iostream>
#include <cstdio>
#include <cmath>
#include <algorithm>
#define sqr(a) ((a)*(a))
using namespace std;

int X, Y, mod = 1e9+7;
int64_t tmp, res;

int64_t pw(int a,int n)
{
    if (n == 1) return a;
    tmp = pw(a, n>>1);
    return n&1 ? tmp * tmp % mod * a % mod : tmp * tmp % mod;
}
int64_t C(int n, int k)
{
    res = 1;
    for(int i=0; i<k; ++i) res = res * (n-i) % mod * pw(i+1, mod-2) % mod;
    return res;
}
int main()
{

    cin >> X >> Y; int64_t ans = 0;
    for(int a=X&1; a<=X; a+=2) if (a+a + (X-a)/2 == Y)
        ans = (ans + C((a+X)/2, a)) % mod;
    cout << ans;
}

```