#include <bits/stdc++.h>
using namespace std;
#define N 3100
#define mod 1000000007
int n,m,ans;
int f[N][N][2];
int main()
{
	//freopen("tt.in","r",stdin);
	scanf("%d%d",&n,&m);
	for(int i=0;i<=n;i++)
		f[0][i][0]=1;
	for(int i=0;i<m;i++)
		for(int j=0;j<=n;j++)
		{
			int k=n-j;
			if(j>=1)
			{
				//jj
				(f[i+1][j-1][j==1]+=f[i][j][0])%=mod;
		 		(f[i+1][j-1][1]+=f[i][j][1])%=mod;
				//jk
				(f[i+1][j][j==1]+=f[i][j][0])%=mod;
				(f[i+1][j][1]+=f[i][j][1])%=mod;
			}
			if(k>=1)
			{
				//kj
				(f[i+1][j][j==0]+=f[i][j][0])%=mod;
				(f[i+1][j][1]+=f[i][j][1])%=mod;
				//kk
				(f[i+1][j+1][j==0]+=f[i][j][0])%=mod;
				(f[i+1][j+1][1]+=f[i][j][1])%=mod;
			}
		}
	for(int i=0;i<=n;i++)
		(ans+=f[m][i][1])%=mod;
	printf("%d\n",ans);
	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>
using namespace std;
#define N 3100
#define mod 1000000007
int n,m,ans;
int f[N][N][2];
int main()
{
	//freopen("tt.in","r",stdin);
	scanf("%d%d",&n,&m);
	for(int i=0;i<=n;i++)
		f[0][i][0]=1;
	for(int i=0;i<m;i++)
		for(int j=0;j<=n;j++)
		{
			int k=n-j;
			if(j>=1)
			{
				//jj
				(f[i+1][j-1][j==1]+=f[i][j][0])%=mod;
		 		(f[i+1][j-1][1]+=f[i][j][1])%=mod;
				//jk
				(f[i+1][j][j==1]+=f[i][j][0])%=mod;
				(f[i+1][j][1]+=f[i][j][1])%=mod;
			}
			if(k>=1)
			{
				//kj
				(f[i+1][j][j==0]+=f[i][j][0])%=mod;
				(f[i+1][j][1]+=f[i][j][1])%=mod;
				//kk
				(f[i+1][j+1][j==0]+=f[i][j][0])%=mod;
				(f[i+1][j+1][1]+=f[i][j][1])%=mod;
			}
		}
	for(int i=0;i<=n;i++)
		(ans+=f[m][i][1])%=mod;
	printf("%d\n",ans);
	return 0;
}
```