#include <bits/stdc++.h>
using namespace std;
int mod = 998244353, k, n, dp[5][1005][2005];
bool seen[5][1005][2005];
int sol(int p, int i, int c) {
  if (i == n) return (k == c);
  if (c > k || i > n) return 0;
  int &ans = dp[p][i][c];
  bool &f = seen[p][i][c];
  if (f) return ans;
  if (p == 0) {
    ans = ((sol(0, i + 1, c) + sol(3, i + 1, c + 1)) % mod +
           (2 * sol(1, i + 1, c + 1)) % mod) %
          mod;
  } else if (p == 1) {
    ans = ((sol(0, i + 1, c) + sol(3, i + 1, c)) % mod +
           (sol(1, i + 1, c) + sol(2, i + 1, c + 2)) % mod) %
          mod;
  } else if (p == 2) {
    ans = ((sol(0, i + 1, c) + sol(3, i + 1, c)) % mod +
           (sol(2, i + 1, c) + sol(1, i + 1, c + 2)) % mod) %
          mod;
  } else {
    ans = ((sol(3, i + 1, c) + sol(0, i + 1, c + 1)) % mod +
           (2 * sol(1, i + 1, c + 1)) % mod) %
          mod;
  }
  f = 1;
  return ans;
}
int main() {
  int t, m;
  scanf("%d %d", &n, &k);
  int aux = (sol(2, 1, 2) + sol(3, 1, 1)) % mod,
      ans = (sol(0, 1, 1) + sol(1, 1, 2)) % mod;
  printf("%d\n", (aux + ans) % mod);
}

### Prompt

Please formulate 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 mod = 998244353, k, n, dp[5][1005][2005];
bool seen[5][1005][2005];
int sol(int p, int i, int c) {
  if (i == n) return (k == c);
  if (c > k || i > n) return 0;
  int &ans = dp[p][i][c];
  bool &f = seen[p][i][c];
  if (f) return ans;
  if (p == 0) {
    ans = ((sol(0, i + 1, c) + sol(3, i + 1, c + 1)) % mod +
           (2 * sol(1, i + 1, c + 1)) % mod) %
          mod;
  } else if (p == 1) {
    ans = ((sol(0, i + 1, c) + sol(3, i + 1, c)) % mod +
           (sol(1, i + 1, c) + sol(2, i + 1, c + 2)) % mod) %
          mod;
  } else if (p == 2) {
    ans = ((sol(0, i + 1, c) + sol(3, i + 1, c)) % mod +
           (sol(2, i + 1, c) + sol(1, i + 1, c + 2)) % mod) %
          mod;
  } else {
    ans = ((sol(3, i + 1, c) + sol(0, i + 1, c + 1)) % mod +
           (2 * sol(1, i + 1, c + 1)) % mod) %
          mod;
  }
  f = 1;
  return ans;
}
int main() {
  int t, m;
  scanf("%d %d", &n, &k);
  int aux = (sol(2, 1, 2) + sol(3, 1, 1)) % mod,
      ans = (sol(0, 1, 1) + sol(1, 1, 2)) % mod;
  printf("%d\n", (aux + ans) % mod);
}

```