#include <bits/stdc++.h>
#define X first
#define Y second
typedef long long ll;
using namespace std;

const int MOD = 1e9 + 7;
const ll INF = 1e18;

int n, m;
int dp[3002][3002][5];

int rek(int x, int y, int z) {
	if (x == 0) {
		return z;
	}
	
	int &ret = dp[x][y][z];
	if (ret != -1) return ret;
	ret = 0;
	
	for (int i = 0; i < 2; i ++) {
		for (int j = 0; j < 2; j ++) {
			if (y-i >= 0 && n-1-(y-i) >= 0 && y-i+1-j >= 0 && n-(y-i+1-j) >= 0) {
				if (y-i == 0 || y-i+1-j == 0) ret += rek(x-1, y-i+1-j, 1);
				else ret += rek(x-1, y-i+1-j, z);
				
				ret %= MOD;
			}
		}
	}
	
	return ret;
}

int main () {

	ios_base::sync_with_stdio(false);
	cin.tie(0);
	cin >> n >> m;
	int sol = 0;
	memset(dp, -1, sizeof dp);
	sol = rek(m, 0, 1);
	
	for (int i = 1; i <= n; i ++) {
		sol += rek(m, i, 0);
		sol %= MOD;
	}
	
	cout << sol;

	return 0;
}
### Prompt

In cpp, your task is to solve the following problem:

Joisino has a lot of red and blue bricks and a large box. She will build a tower of these bricks in the following manner.

First, she will pick a total of N bricks and put them into the box. Here, there may be any number of bricks of each color in the box, as long as there are N bricks in total. Particularly, there may be zero red bricks or zero blue bricks. Then, she will repeat an operation M times, which consists of the following three steps:

* Take out an arbitrary brick from the box.
* Put one red brick and one blue brick into the box.
* Take out another arbitrary brick from the box.



After the M operations, Joisino will build a tower by stacking the 2 \times M bricks removed from the box, in the order they are taken out. She is interested in the following question: how many different sequences of colors of these 2 \times M bricks are possible? Write a program to find the answer. Since it can be extremely large, print the count modulo 10^9+7.

Constraints

* 1 \leq N \leq 3000
* 1 \leq M \leq 3000

Input

Input is given from Standard Input in the following format:


N M


Output

Print the count of the different possible sequences of colors of 2 \times M bricks that will be stacked, modulo 10^9+7.

Examples

Input

2 3


Output

56


Input

1000 10


Output

1048576


Input

1000 3000


Output

693347555

### Response

```cpp
#include <bits/stdc++.h>
#define X first
#define Y second
typedef long long ll;
using namespace std;

const int MOD = 1e9 + 7;
const ll INF = 1e18;

int n, m;
int dp[3002][3002][5];

int rek(int x, int y, int z) {
	if (x == 0) {
		return z;
	}
	
	int &ret = dp[x][y][z];
	if (ret != -1) return ret;
	ret = 0;
	
	for (int i = 0; i < 2; i ++) {
		for (int j = 0; j < 2; j ++) {
			if (y-i >= 0 && n-1-(y-i) >= 0 && y-i+1-j >= 0 && n-(y-i+1-j) >= 0) {
				if (y-i == 0 || y-i+1-j == 0) ret += rek(x-1, y-i+1-j, 1);
				else ret += rek(x-1, y-i+1-j, z);
				
				ret %= MOD;
			}
		}
	}
	
	return ret;
}

int main () {

	ios_base::sync_with_stdio(false);
	cin.tie(0);
	cin >> n >> m;
	int sol = 0;
	memset(dp, -1, sizeof dp);
	sol = rek(m, 0, 1);
	
	for (int i = 1; i <= n; i ++) {
		sol += rek(m, i, 0);
		sol %= MOD;
	}
	
	cout << sol;

	return 0;
}
```