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
#include <cstdio>
#include <iostream>
#include <algorithm>

using namespace std;

const int P=1e9+7;

int f[3010][3010][2];

inline void add(int &x,int y){ (x+=y)%=P; }

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