#include <cstdio>
long long int mod = 1000000007;
long long int big(long long int b, long long int p){
	if (p == 1){
		return b;
	}
	long long int h = big(b, p / 2);
	if (p % 2 == 0){
		return (h * h) % mod;
	}else{
		return (((h * h) % mod) * b) % mod;
	}
}
int main(){
	int x, y;
	scanf("%d %d", &x, &y);
	if ((x + y) % 3 != 0){
		printf("0\n");
		return 0;
	}
	int n = (x + y) / 3;
	if (x < n || x > n * 2){
		printf("0\n");
		return 0;
	}
	int r = x - n;
	long long int ans = 1;
	while (r > 0){
		ans *= n;
		ans %= mod;
		ans *= big(r, mod - 2);
		ans %= mod;
		n--;
		r--;
	}
	printf("%lld\n", ans);
}
### Prompt

Your challenge is to write 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 <cstdio>
long long int mod = 1000000007;
long long int big(long long int b, long long int p){
	if (p == 1){
		return b;
	}
	long long int h = big(b, p / 2);
	if (p % 2 == 0){
		return (h * h) % mod;
	}else{
		return (((h * h) % mod) * b) % mod;
	}
}
int main(){
	int x, y;
	scanf("%d %d", &x, &y);
	if ((x + y) % 3 != 0){
		printf("0\n");
		return 0;
	}
	int n = (x + y) / 3;
	if (x < n || x > n * 2){
		printf("0\n");
		return 0;
	}
	int r = x - n;
	long long int ans = 1;
	while (r > 0){
		ans *= n;
		ans %= mod;
		ans *= big(r, mod - 2);
		ans %= mod;
		n--;
		r--;
	}
	printf("%lld\n", ans);
}
```