#include <stdio.h>
#define M 1000000007
typedef long long LL;

LL qpow(LL x, int y)
{
	if(!y) return 1;
	LL t = qpow(x, y >> 1);
	t = t * t % M;
	if(y & 1) t = t * x % M;
	return t;
}

int main()
{		
	int x, y, a, b, c, t, i, j;
	LL f1 = 1, f2 = 1;
		
	scanf("%d%d", &x, &y);
	c = x + y;
	if(c % 3){
		puts("0");
		return 0;
	}
	c /= 3;
	b = x - c, a = y - c;
	if(b < 0 || a < 0){
		puts("0");
		return 0;
	}
	if(a < b) t = a;
	else t = b;
	for(i = 1, j = c; i <= t; i++, j--){
		f1 = f1 * (LL)j % M;
		f2 = f2 * (LL)i % M;
	}
	printf("%lld\n", f1 * qpow(f2, M - 2) % M);
		
	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 M 1000000007
typedef long long LL;

LL qpow(LL x, int y)
{
	if(!y) return 1;
	LL t = qpow(x, y >> 1);
	t = t * t % M;
	if(y & 1) t = t * x % M;
	return t;
}

int main()
{		
	int x, y, a, b, c, t, i, j;
	LL f1 = 1, f2 = 1;
		
	scanf("%d%d", &x, &y);
	c = x + y;
	if(c % 3){
		puts("0");
		return 0;
	}
	c /= 3;
	b = x - c, a = y - c;
	if(b < 0 || a < 0){
		puts("0");
		return 0;
	}
	if(a < b) t = a;
	else t = b;
	for(i = 1, j = c; i <= t; i++, j--){
		f1 = f1 * (LL)j % M;
		f2 = f2 * (LL)i % M;
	}
	printf("%lld\n", f1 * qpow(f2, M - 2) % M);
		
	return 0;
}
```