
#include <bits/stdc++.h>
using namespace std;

using ll = long long;
#define f(i,a,b) for (int i = a; i < b; i++)

const ll mod = 1e9+7;

void add(ll &a, ll b) {
	if (b>=mod) b-=mod;
	a += b; if (a >= mod) a-=mod;
}

int main() {
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
#ifdef LOCAL
	freopen("input.txt", "r", stdin);
	freopen("output.txt", "w", stdout);
	clock_t start = clock();
#endif

	int n,m; cin>>m>>n;
	ll dp[n+1][m+1][2];
	f(i,0,n+1) f(j,0,m+1) f(k,0,2)
		dp[i][j][k] = 0;
	f(j,0,m+1) dp[0][j][!j]=1;
	f(i,0,n) f(j,0,m+1) f(k,0,2) if (dp[i][j][k]) {
		if (j) add(dp[i+1][j-1][k|(j==1)],dp[i][j][k]);	
		if (j) add(dp[i+1][j][k|(j==1)],dp[i][j][k]);
		if (j<m) add(dp[i+1][j][k],dp[i][j][k]);
		if (j<m) add(dp[i+1][j+1][k],dp[i][j][k]);
	}
	ll ans = 0;
	f(j,0,m+1) add(ans,dp[n][j][1]);
	cout << ans << endl;
	
	

#ifdef LOCAL
	cout << setprecision(12) << (long double)(clock()-start) / CLOCKS_PER_SEC << endl;
#endif
	
	return 0;
}


### Prompt

Your task is to create a Cpp solution to 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>
using namespace std;

using ll = long long;
#define f(i,a,b) for (int i = a; i < b; i++)

const ll mod = 1e9+7;

void add(ll &a, ll b) {
	if (b>=mod) b-=mod;
	a += b; if (a >= mod) a-=mod;
}

int main() {
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
#ifdef LOCAL
	freopen("input.txt", "r", stdin);
	freopen("output.txt", "w", stdout);
	clock_t start = clock();
#endif

	int n,m; cin>>m>>n;
	ll dp[n+1][m+1][2];
	f(i,0,n+1) f(j,0,m+1) f(k,0,2)
		dp[i][j][k] = 0;
	f(j,0,m+1) dp[0][j][!j]=1;
	f(i,0,n) f(j,0,m+1) f(k,0,2) if (dp[i][j][k]) {
		if (j) add(dp[i+1][j-1][k|(j==1)],dp[i][j][k]);	
		if (j) add(dp[i+1][j][k|(j==1)],dp[i][j][k]);
		if (j<m) add(dp[i+1][j][k],dp[i][j][k]);
		if (j<m) add(dp[i+1][j+1][k],dp[i][j][k]);
	}
	ll ans = 0;
	f(j,0,m+1) add(ans,dp[n][j][1]);
	cout << ans << endl;
	
	

#ifdef LOCAL
	cout << setprecision(12) << (long double)(clock()-start) / CLOCKS_PER_SEC << endl;
#endif
	
	return 0;
}


```