#include <bits/stdc++.h>
using namespace std;
const long long M = 998244353;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.precision(10);
  cout << fixed;
  int n, k;
  cin >> n >> k;
  vector<vector<vector<long long>>> dp(
      k + 1, vector<vector<long long>>(n, vector<long long>(4)));
  dp[1][0][0] = dp[1][0][3] = 1;
  if (k > 1) dp[2][0][1] = dp[2][0][2] = 1;
  for (int i = 1; i < n; ++i) {
    for (int j = 1; j <= k; ++j) {
      for (int curr = 0; curr < 4; ++curr) {
        for (int prev = 0; prev < 4; ++prev) {
          int bc = 0;
          if (min(prev, curr) == 0 && max(prev, curr) == 3)
            bc = 1;
          else if (min(prev, curr) == 1 && max(prev, curr) == 2)
            bc = 2;
          else if ((curr == 1 || curr == 2) && (prev == 0 || prev == 3))
            bc = 1;
          if (bc <= j)
            dp[j][i][curr] = (dp[j][i][curr] + dp[j - bc][i - 1][prev]) % M;
        }
      }
    }
  }
  long long ans = 0;
  for (int m = 0; m < 4; ++m) {
    ans = (ans + dp[k][n - 1][m]) % M;
  }
  cout << ans << "\n";
  return 0;
}

### Prompt

Generate 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 long long M = 998244353;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.precision(10);
  cout << fixed;
  int n, k;
  cin >> n >> k;
  vector<vector<vector<long long>>> dp(
      k + 1, vector<vector<long long>>(n, vector<long long>(4)));
  dp[1][0][0] = dp[1][0][3] = 1;
  if (k > 1) dp[2][0][1] = dp[2][0][2] = 1;
  for (int i = 1; i < n; ++i) {
    for (int j = 1; j <= k; ++j) {
      for (int curr = 0; curr < 4; ++curr) {
        for (int prev = 0; prev < 4; ++prev) {
          int bc = 0;
          if (min(prev, curr) == 0 && max(prev, curr) == 3)
            bc = 1;
          else if (min(prev, curr) == 1 && max(prev, curr) == 2)
            bc = 2;
          else if ((curr == 1 || curr == 2) && (prev == 0 || prev == 3))
            bc = 1;
          if (bc <= j)
            dp[j][i][curr] = (dp[j][i][curr] + dp[j - bc][i - 1][prev]) % M;
        }
      }
    }
  }
  long long ans = 0;
  for (int m = 0; m < 4; ++m) {
    ans = (ans + dp[k][n - 1][m]) % M;
  }
  cout << ans << "\n";
  return 0;
}

```