#include<bits/stdc++.h>
using namespace std;
using Int = long long;
//INSERT ABOVE HERE
const Int MOD=1e9+7;
Int calc(Int n,Int m){
  vector<Int> dp(n+1,1);
  for(Int i=0;i<m;i++){
    vector<Int> nx(n+1,0);
    for(Int j=0;j<=n;j++){
      if(j!=0){
	nx[j-1]+=dp[j];
	nx[j-0]+=dp[j];
	nx[j-1]%=MOD;
	nx[j-0]%=MOD;
      }
      if(j!=n){
	nx[j+1]+=dp[j];
	nx[j+0]+=dp[j];
	nx[j+1]%=MOD;
	nx[j+0]%=MOD;
      }
    }
    swap(dp,nx);
  }
  Int res=0;
  for(Int j=0;j<=n;j++)
    res=(res+dp[j])%MOD;
  return res;
}
signed main(){
  Int n,m;
  cin>>n>>m;
  Int ans=calc(n,m);
  ans+=MOD-calc(n-1,m);
  ans%=MOD;
  cout<<ans<<endl;
  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;
using Int = long long;
//INSERT ABOVE HERE
const Int MOD=1e9+7;
Int calc(Int n,Int m){
  vector<Int> dp(n+1,1);
  for(Int i=0;i<m;i++){
    vector<Int> nx(n+1,0);
    for(Int j=0;j<=n;j++){
      if(j!=0){
	nx[j-1]+=dp[j];
	nx[j-0]+=dp[j];
	nx[j-1]%=MOD;
	nx[j-0]%=MOD;
      }
      if(j!=n){
	nx[j+1]+=dp[j];
	nx[j+0]+=dp[j];
	nx[j+1]%=MOD;
	nx[j+0]%=MOD;
      }
    }
    swap(dp,nx);
  }
  Int res=0;
  for(Int j=0;j<=n;j++)
    res=(res+dp[j])%MOD;
  return res;
}
signed main(){
  Int n,m;
  cin>>n>>m;
  Int ans=calc(n,m);
  ans+=MOD-calc(n-1,m);
  ans%=MOD;
  cout<<ans<<endl;
  return 0;
}

```