#include<bits/stdc++.h>
#define MOD 1000000007
using namespace std;
long long inv(long long x, int s){
    if(s==0) return 1;
    if(s%2==0) return inv((x*x)%MOD, s/2)%MOD;
    return (x*inv(x, s-1))%MOD;
}
int main(){
    int x, y;
    scanf("%d%d", &x, &y);
    long long a=(x+y)/3, b=(2*y-x)/3;
    long long res=1;
    if((2*x-y)<0 || (2*y-x)<0 || (x+y)%3!=0){
        printf("0");
        return 0;
    }
    if(a<b){
        long long c=b;
        b=a; a=c;
    }
    for(long long i=1; i<=b; ++i){
            res*=inv(i, MOD-2);
            res%=MOD;
    }
    for(long long i=a; i>=a-b+1; --i) {
            res*=i;
            res%=MOD;
    }
    printf("%I64d", res);
    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>
#define MOD 1000000007
using namespace std;
long long inv(long long x, int s){
    if(s==0) return 1;
    if(s%2==0) return inv((x*x)%MOD, s/2)%MOD;
    return (x*inv(x, s-1))%MOD;
}
int main(){
    int x, y;
    scanf("%d%d", &x, &y);
    long long a=(x+y)/3, b=(2*y-x)/3;
    long long res=1;
    if((2*x-y)<0 || (2*y-x)<0 || (x+y)%3!=0){
        printf("0");
        return 0;
    }
    if(a<b){
        long long c=b;
        b=a; a=c;
    }
    for(long long i=1; i<=b; ++i){
            res*=inv(i, MOD-2);
            res%=MOD;
    }
    for(long long i=a; i>=a-b+1; --i) {
            res*=i;
            res%=MOD;
    }
    printf("%I64d", res);
    return 0;
}

```