#include <bits/stdc++.h>
using namespace std;
const double pi = acos(-1.0);
const int MAXN = 1010;
long long dp[MAXN][4][2 * MAXN];
const long long M = 998244353;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  int N, K;
  cin >> N >> K;
  memset(dp, (0), sizeof(dp));
  for (int i = 0; i < N; ++i) {
    dp[i][0][1] = 1;
    dp[i][3][1] = 1;
  }
  dp[0][1][2] = 1;
  dp[0][2][2] = 1;
  for (int i = 0; i < N - 1; ++i) {
    for (int k = 2; k <= K; ++k) {
      dp[i + 1][0][k] =
          (dp[i][0][k] + dp[i][1][k] + dp[i][2][k] + dp[i][3][k - 1]) % M;
      dp[i + 1][1][k] =
          (dp[i][0][k - 1] + dp[i][1][k] + dp[i][2][k - 2] + dp[i][3][k - 1]) %
          M;
      dp[i + 1][2][k] =
          (dp[i][0][k - 1] + dp[i][1][k - 2] + dp[i][2][k] + dp[i][3][k - 1]) %
          M;
      dp[i + 1][3][k] =
          (dp[i][0][k - 1] + dp[i][1][k] + dp[i][2][k] + dp[i][3][k]) % M;
    }
  }
  int ans = 0;
  for (int j = 0; j < 4; ++j) {
    ans += dp[N - 1][j][K];
    ans %= M;
  }
  cout << ans << endl;
  return 0;
}

### Prompt

In CPP, your task is to solve 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 double pi = acos(-1.0);
const int MAXN = 1010;
long long dp[MAXN][4][2 * MAXN];
const long long M = 998244353;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  int N, K;
  cin >> N >> K;
  memset(dp, (0), sizeof(dp));
  for (int i = 0; i < N; ++i) {
    dp[i][0][1] = 1;
    dp[i][3][1] = 1;
  }
  dp[0][1][2] = 1;
  dp[0][2][2] = 1;
  for (int i = 0; i < N - 1; ++i) {
    for (int k = 2; k <= K; ++k) {
      dp[i + 1][0][k] =
          (dp[i][0][k] + dp[i][1][k] + dp[i][2][k] + dp[i][3][k - 1]) % M;
      dp[i + 1][1][k] =
          (dp[i][0][k - 1] + dp[i][1][k] + dp[i][2][k - 2] + dp[i][3][k - 1]) %
          M;
      dp[i + 1][2][k] =
          (dp[i][0][k - 1] + dp[i][1][k - 2] + dp[i][2][k] + dp[i][3][k - 1]) %
          M;
      dp[i + 1][3][k] =
          (dp[i][0][k - 1] + dp[i][1][k] + dp[i][2][k] + dp[i][3][k]) % M;
    }
  }
  int ans = 0;
  for (int j = 0; j < 4; ++j) {
    ans += dp[N - 1][j][K];
    ans %= M;
  }
  cout << ans << endl;
  return 0;
}

```