#include <bits/stdc++.h>
using namespace std;
const int N = 1000050;
const long long Mod = 998244353;
const int inf = 0x3f3f3f3f;
long long dp[1005][2005][4];
int main(int argc, const char* argv[]) {
  int n, k;
  scanf("%d%d", &n, &k);
  memset(dp, 0, sizeof dp);
  dp[1][1][0] = dp[1][1][3] = dp[1][2][1] = dp[1][2][2] = 1ll;
  for (int i = 2; i < ((n) + 1); i++) {
    for (int j = 1; j < ((k) + 1); j++) {
      dp[i][j][0] = dp[i - 1][j][0] + dp[i - 1][j][1] + dp[i - 1][j][2] +
                    dp[i - 1][j - 1][3];
      if (j > 1) {
        dp[i][j][1] = dp[i - 1][j - 1][0] + dp[i - 1][j][1] +
                      dp[i - 1][j - 2][2] + dp[i - 1][j - 1][3];
      } else {
        dp[i][j][1] =
            dp[i - 1][j - 1][0] + dp[i - 1][j][1] + dp[i - 1][j - 1][3];
      }
      if (j > 1) {
        dp[i][j][2] = dp[i - 1][j - 1][0] + dp[i - 1][j - 2][1] +
                      dp[i - 1][j][2] + dp[i - 1][j - 1][3];
      } else {
        dp[i][j][2] =
            dp[i - 1][j - 1][0] + dp[i - 1][j][2] + dp[i - 1][j - 1][3];
      }
      dp[i][j][3] = dp[i - 1][j - 1][0] + dp[i - 1][j][1] + dp[i - 1][j][2] +
                    dp[i - 1][j][3];
      dp[i][j][0] %= Mod;
      dp[i][j][1] %= Mod;
      dp[i][j][2] %= Mod;
      dp[i][j][3] %= Mod;
    }
  }
  long long ret = 0;
  for (int i = 0; i < ((3) + 1); i++) {
    ret += dp[n][k][i];
    ret %= Mod;
  }
  cout << ret << endl;
  return 0;
}

### Prompt

Construct a CPP code solution to the problem outlined:

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 N = 1000050;
const long long Mod = 998244353;
const int inf = 0x3f3f3f3f;
long long dp[1005][2005][4];
int main(int argc, const char* argv[]) {
  int n, k;
  scanf("%d%d", &n, &k);
  memset(dp, 0, sizeof dp);
  dp[1][1][0] = dp[1][1][3] = dp[1][2][1] = dp[1][2][2] = 1ll;
  for (int i = 2; i < ((n) + 1); i++) {
    for (int j = 1; j < ((k) + 1); j++) {
      dp[i][j][0] = dp[i - 1][j][0] + dp[i - 1][j][1] + dp[i - 1][j][2] +
                    dp[i - 1][j - 1][3];
      if (j > 1) {
        dp[i][j][1] = dp[i - 1][j - 1][0] + dp[i - 1][j][1] +
                      dp[i - 1][j - 2][2] + dp[i - 1][j - 1][3];
      } else {
        dp[i][j][1] =
            dp[i - 1][j - 1][0] + dp[i - 1][j][1] + dp[i - 1][j - 1][3];
      }
      if (j > 1) {
        dp[i][j][2] = dp[i - 1][j - 1][0] + dp[i - 1][j - 2][1] +
                      dp[i - 1][j][2] + dp[i - 1][j - 1][3];
      } else {
        dp[i][j][2] =
            dp[i - 1][j - 1][0] + dp[i - 1][j][2] + dp[i - 1][j - 1][3];
      }
      dp[i][j][3] = dp[i - 1][j - 1][0] + dp[i - 1][j][1] + dp[i - 1][j][2] +
                    dp[i - 1][j][3];
      dp[i][j][0] %= Mod;
      dp[i][j][1] %= Mod;
      dp[i][j][2] %= Mod;
      dp[i][j][3] %= Mod;
    }
  }
  long long ret = 0;
  for (int i = 0; i < ((3) + 1); i++) {
    ret += dp[n][k][i];
    ret %= Mod;
  }
  cout << ret << endl;
  return 0;
}

```