#include <bits/stdc++.h>
using namespace std;
long long dp[1001][2001][2][2], n, k;
long long DP(long long a, long long b, long long c, long long d) {
  if (b > k) return 0;
  if (a == n) {
    if (b == k)
      return 1;
    else
      return 0;
  }
  if (dp[a][b][c][d] != -1) return dp[a][b][c][d];
  long long value = 0;
  if (a == 0) {
    value += DP(a + 1, b + 1, 0, 0);
    value += DP(a + 1, b + 2, 0, 1);
    value += DP(a + 1, b + 2, 1, 0);
    value += DP(a + 1, b + 1, 1, 1);
  } else {
    for (int c1 = 0; c1 < 2; c1++) {
      for (int d1 = 0; d1 < 2; d1++) {
        if (c1 == d1) {
          if (c1 == c || d1 == d) {
            value += DP(a + 1, b, c1, d1);
          } else {
            value += DP(a + 1, b + 1, c1, d1);
          }
        } else {
          if (c1 == c && d1 == d) {
            value += DP(a + 1, b, c1, d1);
          } else if (c1 == c && d1 != d) {
            value += DP(a + 1, b + 1, c1, d1);
          } else if (c1 != c && d1 == d) {
            value += DP(a + 1, b + 1, c1, d1);
          } else {
            value += DP(a + 1, b + 2, c1, d1);
          }
        }
      }
    }
  }
  return dp[a][b][c][d] = value % 998244353;
}
int main() {
  cin >> n >> k;
  memset(dp, -1, sizeof(dp));
  cout << DP(0, 0, 0, 0) << endl;
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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;
long long dp[1001][2001][2][2], n, k;
long long DP(long long a, long long b, long long c, long long d) {
  if (b > k) return 0;
  if (a == n) {
    if (b == k)
      return 1;
    else
      return 0;
  }
  if (dp[a][b][c][d] != -1) return dp[a][b][c][d];
  long long value = 0;
  if (a == 0) {
    value += DP(a + 1, b + 1, 0, 0);
    value += DP(a + 1, b + 2, 0, 1);
    value += DP(a + 1, b + 2, 1, 0);
    value += DP(a + 1, b + 1, 1, 1);
  } else {
    for (int c1 = 0; c1 < 2; c1++) {
      for (int d1 = 0; d1 < 2; d1++) {
        if (c1 == d1) {
          if (c1 == c || d1 == d) {
            value += DP(a + 1, b, c1, d1);
          } else {
            value += DP(a + 1, b + 1, c1, d1);
          }
        } else {
          if (c1 == c && d1 == d) {
            value += DP(a + 1, b, c1, d1);
          } else if (c1 == c && d1 != d) {
            value += DP(a + 1, b + 1, c1, d1);
          } else if (c1 != c && d1 == d) {
            value += DP(a + 1, b + 1, c1, d1);
          } else {
            value += DP(a + 1, b + 2, c1, d1);
          }
        }
      }
    }
  }
  return dp[a][b][c][d] = value % 998244353;
}
int main() {
  cin >> n >> k;
  memset(dp, -1, sizeof(dp));
  cout << DP(0, 0, 0, 0) << endl;
}

```