#include<iostream>
#include<stdio.h>
#include<algorithm>
#include<math.h>
#include<string.h>
#include<fstream>
using namespace std;
const int mod=1000000007;
int n,m;
int f[3003][3003][2];
int dp(int tur,int num,int sta){
	int &ret=f[tur][num][sta];
	if(ret!=-1){
		return ret;
	}
	if(tur==m){
		if(sta==1){
			return ret=1;
		}
		return ret=0;
	}
	ret=0;
	if(num){
		ret=(ret+dp(tur+1,num-1,sta|(num==1)))%mod;//-1 red,+1 red,+1 blue,-1 red
	}
	if(num){
		ret=(ret+dp(tur+1,num,sta|(num==1)))%mod;//-1 red,+1 red,+1 blue,-1 blue
	}
	if(n-num){
		ret=(ret+dp(tur+1,num,sta))%mod;//-1 blue,+1 red,+1 blue,-1 red
	}
	if(n-num){
		ret=(ret+dp(tur+1,num+1,sta))%mod;//-1 blue,+1 red,+1 blue,-1 blue
	}
	return ret;
}
int main(){
	memset(f,-1,sizeof(f));
	cin>>n>>m;
	long long ans=0;
	ans=(ans+dp(0,0,1))%mod;
	for(int i=1;i<=n;i++){
		ans=(ans+dp(0,i,0))%mod;
	}
	cout<<ans<<endl;
	return 0;
}
/*

in:
2 3

out:
56

in:
1000 10

out:
1048576

*/
### Prompt

Please provide a CPP coded solution to the problem described below:

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<iostream>
#include<stdio.h>
#include<algorithm>
#include<math.h>
#include<string.h>
#include<fstream>
using namespace std;
const int mod=1000000007;
int n,m;
int f[3003][3003][2];
int dp(int tur,int num,int sta){
	int &ret=f[tur][num][sta];
	if(ret!=-1){
		return ret;
	}
	if(tur==m){
		if(sta==1){
			return ret=1;
		}
		return ret=0;
	}
	ret=0;
	if(num){
		ret=(ret+dp(tur+1,num-1,sta|(num==1)))%mod;//-1 red,+1 red,+1 blue,-1 red
	}
	if(num){
		ret=(ret+dp(tur+1,num,sta|(num==1)))%mod;//-1 red,+1 red,+1 blue,-1 blue
	}
	if(n-num){
		ret=(ret+dp(tur+1,num,sta))%mod;//-1 blue,+1 red,+1 blue,-1 red
	}
	if(n-num){
		ret=(ret+dp(tur+1,num+1,sta))%mod;//-1 blue,+1 red,+1 blue,-1 blue
	}
	return ret;
}
int main(){
	memset(f,-1,sizeof(f));
	cin>>n>>m;
	long long ans=0;
	ans=(ans+dp(0,0,1))%mod;
	for(int i=1;i<=n;i++){
		ans=(ans+dp(0,i,0))%mod;
	}
	cout<<ans<<endl;
	return 0;
}
/*

in:
2 3

out:
56

in:
1000 10

out:
1048576

*/
```