#include <bits/stdc++.h>
using namespace std;
int n, k;
int dp[(1000 + 10)][4][(1000 + 10) + (1000 + 10)];
void add(int &target, int off) {
  if (off == -1) return;
  if (target == -1) {
    target = off;
  } else {
    target = (target + off) % 998244353;
  }
}
int main() {
  scanf("%d %d", &n, &k);
  memset(dp, 0xff, sizeof(dp));
  dp[0][0][1] = 1;
  dp[0][1][2] = 1;
  dp[0][2][2] = 1;
  dp[0][3][1] = 1;
  for (int i = 0; i < n - 1; i++) {
    for (int j = 1; j <= k; j++) {
      add(dp[i + 1][0][j], dp[i][0][j]);
      add(dp[i + 1][1][j + 1], dp[i][0][j]);
      add(dp[i + 1][2][j + 1], dp[i][0][j]);
      add(dp[i + 1][3][j + 1], dp[i][0][j]);
      add(dp[i + 1][0][j], dp[i][1][j]);
      add(dp[i + 1][1][j], dp[i][1][j]);
      add(dp[i + 1][2][j + 2], dp[i][1][j]);
      add(dp[i + 1][3][j], dp[i][1][j]);
      add(dp[i + 1][0][j], dp[i][2][j]);
      add(dp[i + 1][1][j + 2], dp[i][2][j]);
      add(dp[i + 1][2][j], dp[i][2][j]);
      add(dp[i + 1][3][j], dp[i][2][j]);
      add(dp[i + 1][0][j + 1], dp[i][3][j]);
      add(dp[i + 1][1][j + 1], dp[i][3][j]);
      add(dp[i + 1][2][j + 1], dp[i][3][j]);
      add(dp[i + 1][3][j], dp[i][3][j]);
    }
  }
  int ans = 0;
  for (int i = 0; i < 4; i++)
    if (dp[n - 1][i][k] != -1) {
      ans = ans + dp[n - 1][i][k];
      ans %= 998244353;
    }
  cout << ans << 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;
int n, k;
int dp[(1000 + 10)][4][(1000 + 10) + (1000 + 10)];
void add(int &target, int off) {
  if (off == -1) return;
  if (target == -1) {
    target = off;
  } else {
    target = (target + off) % 998244353;
  }
}
int main() {
  scanf("%d %d", &n, &k);
  memset(dp, 0xff, sizeof(dp));
  dp[0][0][1] = 1;
  dp[0][1][2] = 1;
  dp[0][2][2] = 1;
  dp[0][3][1] = 1;
  for (int i = 0; i < n - 1; i++) {
    for (int j = 1; j <= k; j++) {
      add(dp[i + 1][0][j], dp[i][0][j]);
      add(dp[i + 1][1][j + 1], dp[i][0][j]);
      add(dp[i + 1][2][j + 1], dp[i][0][j]);
      add(dp[i + 1][3][j + 1], dp[i][0][j]);
      add(dp[i + 1][0][j], dp[i][1][j]);
      add(dp[i + 1][1][j], dp[i][1][j]);
      add(dp[i + 1][2][j + 2], dp[i][1][j]);
      add(dp[i + 1][3][j], dp[i][1][j]);
      add(dp[i + 1][0][j], dp[i][2][j]);
      add(dp[i + 1][1][j + 2], dp[i][2][j]);
      add(dp[i + 1][2][j], dp[i][2][j]);
      add(dp[i + 1][3][j], dp[i][2][j]);
      add(dp[i + 1][0][j + 1], dp[i][3][j]);
      add(dp[i + 1][1][j + 1], dp[i][3][j]);
      add(dp[i + 1][2][j + 1], dp[i][3][j]);
      add(dp[i + 1][3][j], dp[i][3][j]);
    }
  }
  int ans = 0;
  for (int i = 0; i < 4; i++)
    if (dp[n - 1][i][k] != -1) {
      ans = ans + dp[n - 1][i][k];
      ans %= 998244353;
    }
  cout << ans << endl;
  return 0;
}

```