#include<cstdio>
#include<cstring>
#define rep(i,a,b) for(register int i=a;i<=b;++i)
using namespace std;
const int N=3500,mod=1e9+7;
int n,m,ans;
int f[N][N][2];
inline void inc(int &x,int y){
	x+=y;
	if(x>=mod)
		x-=mod;
}
int main(){
	scanf("%d%d",&n,&m);
	rep(i,1,n)
		f[0][i][0]=1;
	f[0][0][1]=1;
	rep(i,1,m)
		rep(j,0,n){
			if(j){
				inc(f[i][j-1][1],f[i-1][j][1]);
				if(j==1)inc(f[i][j-1][1],f[i-1][j][0]);
				else inc(f[i][j-1][0],f[i-1][j][0]);
				
				inc(f[i][j][1],f[i-1][j][1]);
				if(j==1)inc(f[i][j][1],f[i-1][j][0]);
				else inc(f[i][j][0],f[i-1][j][0]);
			}
			if(j<n){
				inc(f[i][j+1][1],f[i-1][j][1]);
				inc(f[i][j+1][0],f[i-1][j][0]);
				
				inc(f[i][j][1],f[i-1][j][1]);
				inc(f[i][j][0],f[i-1][j][0]);
			}
		}
	rep(i,0,n)
		inc(ans,f[m][i][1]);
	printf("%d\n",ans);
    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<cstdio>
#include<cstring>
#define rep(i,a,b) for(register int i=a;i<=b;++i)
using namespace std;
const int N=3500,mod=1e9+7;
int n,m,ans;
int f[N][N][2];
inline void inc(int &x,int y){
	x+=y;
	if(x>=mod)
		x-=mod;
}
int main(){
	scanf("%d%d",&n,&m);
	rep(i,1,n)
		f[0][i][0]=1;
	f[0][0][1]=1;
	rep(i,1,m)
		rep(j,0,n){
			if(j){
				inc(f[i][j-1][1],f[i-1][j][1]);
				if(j==1)inc(f[i][j-1][1],f[i-1][j][0]);
				else inc(f[i][j-1][0],f[i-1][j][0]);
				
				inc(f[i][j][1],f[i-1][j][1]);
				if(j==1)inc(f[i][j][1],f[i-1][j][0]);
				else inc(f[i][j][0],f[i-1][j][0]);
			}
			if(j<n){
				inc(f[i][j+1][1],f[i-1][j][1]);
				inc(f[i][j+1][0],f[i-1][j][0]);
				
				inc(f[i][j][1],f[i-1][j][1]);
				inc(f[i][j][0],f[i-1][j][0]);
			}
		}
	rep(i,0,n)
		inc(ans,f[m][i][1]);
	printf("%d\n",ans);
    return 0;
}
```