#include <bits/stdc++.h>
using namespace std;
const int MOD = 998244353;
const int N = 1e5 + 7;
long long dp[1005][5][2005];
void add(long long& x, long long y) { x = (x + y) % MOD; }
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int n, k;
  cin >> n >> k;
  dp[1][1][1] = 1;
  dp[1][2][1] = 1;
  dp[1][3][2] = 1;
  dp[1][4][2] = 1;
  for (int i = 2; i <= n; i++) {
    for (int j = 1; j <= k; j++) {
      add(dp[i][1][j], dp[i - 1][1][j]);
      if (j > 1) add(dp[i][1][j], dp[i - 1][2][j - 1]);
      add(dp[i][1][j], dp[i - 1][3][j]);
      add(dp[i][1][j], dp[i - 1][4][j]);
      if (j > 1) add(dp[i][2][j], dp[i - 1][1][j - 1]);
      add(dp[i][2][j], dp[i - 1][2][j]);
      add(dp[i][2][j], dp[i - 1][3][j]);
      add(dp[i][2][j], dp[i - 1][4][j]);
      if (j > 1) add(dp[i][3][j], dp[i - 1][1][j - 1]);
      if (j > 1) add(dp[i][3][j], dp[i - 1][2][j - 1]);
      add(dp[i][3][j], dp[i - 1][3][j]);
      if (j > 2) add(dp[i][3][j], dp[i - 1][4][j - 2]);
      if (j > 1) add(dp[i][4][j], dp[i - 1][1][j - 1]);
      if (j > 1) add(dp[i][4][j], dp[i - 1][2][j - 1]);
      if (j > 2) add(dp[i][4][j], dp[i - 1][3][j - 2]);
      add(dp[i][4][j], dp[i - 1][4][j]);
    }
  }
  long long res = 0;
  add(res, dp[n][1][k]);
  add(res, dp[n][2][k]);
  add(res, dp[n][3][k]);
  add(res, dp[n][4][k]);
  cout << res << endl;
  return 0;
}

### Prompt

Your challenge is to write a CPP solution to the following problem:

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;
const int MOD = 998244353;
const int N = 1e5 + 7;
long long dp[1005][5][2005];
void add(long long& x, long long y) { x = (x + y) % MOD; }
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int n, k;
  cin >> n >> k;
  dp[1][1][1] = 1;
  dp[1][2][1] = 1;
  dp[1][3][2] = 1;
  dp[1][4][2] = 1;
  for (int i = 2; i <= n; i++) {
    for (int j = 1; j <= k; j++) {
      add(dp[i][1][j], dp[i - 1][1][j]);
      if (j > 1) add(dp[i][1][j], dp[i - 1][2][j - 1]);
      add(dp[i][1][j], dp[i - 1][3][j]);
      add(dp[i][1][j], dp[i - 1][4][j]);
      if (j > 1) add(dp[i][2][j], dp[i - 1][1][j - 1]);
      add(dp[i][2][j], dp[i - 1][2][j]);
      add(dp[i][2][j], dp[i - 1][3][j]);
      add(dp[i][2][j], dp[i - 1][4][j]);
      if (j > 1) add(dp[i][3][j], dp[i - 1][1][j - 1]);
      if (j > 1) add(dp[i][3][j], dp[i - 1][2][j - 1]);
      add(dp[i][3][j], dp[i - 1][3][j]);
      if (j > 2) add(dp[i][3][j], dp[i - 1][4][j - 2]);
      if (j > 1) add(dp[i][4][j], dp[i - 1][1][j - 1]);
      if (j > 1) add(dp[i][4][j], dp[i - 1][2][j - 1]);
      if (j > 2) add(dp[i][4][j], dp[i - 1][3][j - 2]);
      add(dp[i][4][j], dp[i - 1][4][j]);
    }
  }
  long long res = 0;
  add(res, dp[n][1][k]);
  add(res, dp[n][2][k]);
  add(res, dp[n][3][k]);
  add(res, dp[n][4][k]);
  cout << res << endl;
  return 0;
}

```