#include <iostream>
#include <cstdio>
#define N 1000005
using namespace std;
typedef long long ll;

ll x, y, s, M=1e9+7;
ll fac[N]={1,1}, inv[N]={1,1}, fiv[N]={1,1};
int main() {
	cin >> x >> y;
	s = x + y;
	if(s%3) {puts("0"); return 0;}
	x -= s/3;
	y -= s/3;
	if(x<0 || y<0) {puts("0"); return 0;}
	for(int i=2; i<=x+y; i++) {
		fac[i] = fac[i-1] * i % M;
		inv[i] = inv[M%i] * (M-M/i) % M;
		fiv[i] = fiv[i-1] * inv[i] % M;
	}
	cout << fac[x+y] * fiv[x] % M * fiv[y] % M;
	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 <iostream>
#include <cstdio>
#define N 1000005
using namespace std;
typedef long long ll;

ll x, y, s, M=1e9+7;
ll fac[N]={1,1}, inv[N]={1,1}, fiv[N]={1,1};
int main() {
	cin >> x >> y;
	s = x + y;
	if(s%3) {puts("0"); return 0;}
	x -= s/3;
	y -= s/3;
	if(x<0 || y<0) {puts("0"); return 0;}
	for(int i=2; i<=x+y; i++) {
		fac[i] = fac[i-1] * i % M;
		inv[i] = inv[M%i] * (M-M/i) % M;
		fiv[i] = fiv[i-1] * inv[i] % M;
	}
	cout << fac[x+y] * fiv[x] % M * fiv[y] % M;
	return 0;
}

```