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

const int Mod=1e9+7;

int N,M,Ans;
int F[3005][3005][2];

void Add(int &x,int y){
	if((x+=y)>=Mod)
		x-=Mod;
}

int main(){
	int i,j,k;
	scanf("%d%d",&N,&M);
	for(i=1;i<=N;i++)
		F[0][i][0]=1;
	F[0][0][1]=1;
	for(i=0;i<M;i++)
		for(j=0;j<=N;j++)
			for(k=0;k<2;k++)
				if(F[i][j][k]){
					if(j){
						Add(F[i+1][j][k|(j<2)],F[i][j][k]);
						Add(F[i+1][j-1][k|(j<2)],F[i][j][k]);
					}
					if(j<N){
						Add(F[i+1][j][k],F[i][j][k]);
						Add(F[i+1][j+1][k],F[i][j][k]);
					}
				}
	for(i=0;i<=N;i++)
		Add(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<bits/stdc++.h>
using namespace std;

const int Mod=1e9+7;

int N,M,Ans;
int F[3005][3005][2];

void Add(int &x,int y){
	if((x+=y)>=Mod)
		x-=Mod;
}

int main(){
	int i,j,k;
	scanf("%d%d",&N,&M);
	for(i=1;i<=N;i++)
		F[0][i][0]=1;
	F[0][0][1]=1;
	for(i=0;i<M;i++)
		for(j=0;j<=N;j++)
			for(k=0;k<2;k++)
				if(F[i][j][k]){
					if(j){
						Add(F[i+1][j][k|(j<2)],F[i][j][k]);
						Add(F[i+1][j-1][k|(j<2)],F[i][j][k]);
					}
					if(j<N){
						Add(F[i+1][j][k],F[i][j][k]);
						Add(F[i+1][j+1][k],F[i][j][k]);
					}
				}
	for(i=0;i<=N;i++)
		Add(Ans,F[M][i][1]);
	printf("%d\n",Ans);
	return 0;
}
```