#include<bits/stdc++.h>
using namespace std;
const int MOD = 1000000007;
const int MAX = 1000000;
long long fac[MAX], finv[MAX], inv[MAX];

void COMint(){
  fac[0] = fac[1] = 1;
  finv[0] = finv[1] = 1;
  inv[1] = 1;
  for(int i=2;i<MAX;i++){
    fac[i] = fac[i-1]*i%MOD;
    inv[i] = MOD - inv[MOD%i]*(MOD/i)%MOD;
    finv[i] = finv[i-1]*inv[i]%MOD;
  }
}

long long COM(int n, int r){
  if(n<r) return 0;
  if(n<0||r<0) return 0;
  return fac[n]*(finv[r]*finv[n-r]%MOD)%MOD;
}

int main(){
  int X,Y;
  cin >> X >> Y;
  COMint();
  if((X+Y)%3!=0){
    cout << 0 << endl;
    return 0;
  }
  int n = (X+Y)/3;
  int r = min(X-n,Y-n);
  cout << COM(n,r) << endl;
  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<bits/stdc++.h>
using namespace std;
const int MOD = 1000000007;
const int MAX = 1000000;
long long fac[MAX], finv[MAX], inv[MAX];

void COMint(){
  fac[0] = fac[1] = 1;
  finv[0] = finv[1] = 1;
  inv[1] = 1;
  for(int i=2;i<MAX;i++){
    fac[i] = fac[i-1]*i%MOD;
    inv[i] = MOD - inv[MOD%i]*(MOD/i)%MOD;
    finv[i] = finv[i-1]*inv[i]%MOD;
  }
}

long long COM(int n, int r){
  if(n<r) return 0;
  if(n<0||r<0) return 0;
  return fac[n]*(finv[r]*finv[n-r]%MOD)%MOD;
}

int main(){
  int X,Y;
  cin >> X >> Y;
  COMint();
  if((X+Y)%3!=0){
    cout << 0 << endl;
    return 0;
  }
  int n = (X+Y)/3;
  int r = min(X-n,Y-n);
  cout << COM(n,r) << endl;
  return 0;
}





```