#include <bits/stdc++.h>
using namespace std;
int main() {
  int n, k;
  cin >> n >> k;
  long long int arr[n + 1][k + 1][4];
  for (int i = 0; i < n; i++)
    for (int j = 0; j < 4; j++) arr[i][0][j] = 0;
  for (int i = 0; i < n; i++) {
    arr[i][1][0] = arr[i][1][3] = 1;
    arr[i][1][1] = arr[i][1][2] = 0;
  }
  if (k >= 2) {
    arr[0][2][0] = arr[0][2][3] = 0;
    arr[0][2][1] = arr[0][2][2] = 1;
  }
  for (int i = 3; i <= k; i++)
    for (int j = 0; j < 4; j++) arr[0][i][j] = 0;
  for (int i = 1; i < n; i++) {
    for (int j = 2; j <= k; j++) {
      arr[i][j][0] = (arr[i - 1][j][0] + arr[i - 1][j - 1][3] +
                      arr[i - 1][j][1] + arr[i - 1][j][2]) %
                     998244353;
      arr[i][j][1] = (arr[i - 1][j - 1][0] + arr[i - 1][j - 1][3] +
                      arr[i - 1][j][1] + arr[i - 1][j - 2][2]) %
                     998244353;
      arr[i][j][2] = (arr[i - 1][j - 1][0] + arr[i - 1][j - 1][3] +
                      arr[i - 1][j][2] + arr[i - 1][j - 2][1]) %
                     998244353;
      arr[i][j][3] = (arr[i - 1][j - 1][0] + arr[i - 1][j][3] +
                      arr[i - 1][j][1] + arr[i - 1][j][2]) %
                     998244353;
    }
  }
  long long int total = 0;
  for (int i = 0; i < 4; i++) total = (total + arr[n - 1][k][i]) % 998244353;
  cout << total << endl;
}

### Prompt

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

You are given a grid, consisting of 2 rows and n columns. Each cell of this grid should be colored either black or white.

Two cells are considered neighbours if they have a common border and share the same color. Two cells A and B belong to the same component if they are neighbours, or if there is a neighbour of A that belongs to the same component with B.

Let's call some bicoloring beautiful if it has exactly k components.

Count the number of beautiful bicolorings. The number can be big enough, so print the answer modulo 998244353.

Input

The only line contains two integers n and k (1 ≤ n ≤ 1000, 1 ≤ k ≤ 2n) — the number of columns in a grid and the number of components required.

Output

Print a single integer — the number of beautiful bicolorings modulo 998244353.

Examples

Input

3 4


Output

12


Input

4 1


Output

2


Input

1 2


Output

2

Note

One of possible bicolorings in sample 1:

<image>

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int main() {
  int n, k;
  cin >> n >> k;
  long long int arr[n + 1][k + 1][4];
  for (int i = 0; i < n; i++)
    for (int j = 0; j < 4; j++) arr[i][0][j] = 0;
  for (int i = 0; i < n; i++) {
    arr[i][1][0] = arr[i][1][3] = 1;
    arr[i][1][1] = arr[i][1][2] = 0;
  }
  if (k >= 2) {
    arr[0][2][0] = arr[0][2][3] = 0;
    arr[0][2][1] = arr[0][2][2] = 1;
  }
  for (int i = 3; i <= k; i++)
    for (int j = 0; j < 4; j++) arr[0][i][j] = 0;
  for (int i = 1; i < n; i++) {
    for (int j = 2; j <= k; j++) {
      arr[i][j][0] = (arr[i - 1][j][0] + arr[i - 1][j - 1][3] +
                      arr[i - 1][j][1] + arr[i - 1][j][2]) %
                     998244353;
      arr[i][j][1] = (arr[i - 1][j - 1][0] + arr[i - 1][j - 1][3] +
                      arr[i - 1][j][1] + arr[i - 1][j - 2][2]) %
                     998244353;
      arr[i][j][2] = (arr[i - 1][j - 1][0] + arr[i - 1][j - 1][3] +
                      arr[i - 1][j][2] + arr[i - 1][j - 2][1]) %
                     998244353;
      arr[i][j][3] = (arr[i - 1][j - 1][0] + arr[i - 1][j][3] +
                      arr[i - 1][j][1] + arr[i - 1][j][2]) %
                     998244353;
    }
  }
  long long int total = 0;
  for (int i = 0; i < 4; i++) total = (total + arr[n - 1][k][i]) % 998244353;
  cout << total << endl;
}

```