#include <stdio.h>
#define mod 1000000007
typedef long long ll;

ll rev(ll a) {
  ll t = mod - 2, ans = 1;
  while(t) {
    if(t & 1) ans *= a, ans %= mod;
    a *= a, a %= mod, t >>= 1;
  }
  return ans;
}

int main(void) {
  ll i, j, x, y, sum, ans;
  scanf("%lld%lld", &x, &y);
  if((x + y) % 3) {
    printf("0");
    return 0;
  }
  sum = (x + y) / 3;
  if(x < sum || x > 2 * sum) {
    printf("0");
    return 0;
  }
  x -= sum;
  ll fact[sum + 1];
  fact[0] = 1;
  for(i = 1; i <= sum; ++i) fact[i] = (fact[i - 1] * i) % mod;
  ans = (fact[sum] * rev(fact[x])) % mod;
  ans *= rev(fact[sum - x]), ans %= mod;
  printf("%lld", ans);
  return 0;
}
### Prompt

Please create a solution in cpp 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 <stdio.h>
#define mod 1000000007
typedef long long ll;

ll rev(ll a) {
  ll t = mod - 2, ans = 1;
  while(t) {
    if(t & 1) ans *= a, ans %= mod;
    a *= a, a %= mod, t >>= 1;
  }
  return ans;
}

int main(void) {
  ll i, j, x, y, sum, ans;
  scanf("%lld%lld", &x, &y);
  if((x + y) % 3) {
    printf("0");
    return 0;
  }
  sum = (x + y) / 3;
  if(x < sum || x > 2 * sum) {
    printf("0");
    return 0;
  }
  x -= sum;
  ll fact[sum + 1];
  fact[0] = 1;
  for(i = 1; i <= sum; ++i) fact[i] = (fact[i - 1] * i) % mod;
  ans = (fact[sum] * rev(fact[x])) % mod;
  ans *= rev(fact[sum - x]), ans %= mod;
  printf("%lld", ans);
  return 0;
}
```