#include <bits/stdc++.h>
using namespace std;
long long int memo[1001][2002][4];
long long int pd(int idx, int k, int fim) {
  if (k < 0 || idx < 0 || fim < 0) return 0;
  if (memo[idx][k][fim] != -1) return memo[idx][k][fim];
  if (idx == 1) {
    if (k > 2) {
      memo[idx][k][fim] = 0LL;
      return 0;
    }
    if (k == 2) {
      if (fim == 0 || fim == 3)
        memo[idx][k][fim] = 0LL;
      else
        memo[idx][k][fim] = 1LL;
      return memo[idx][k][fim];
    }
    if (k == 1) {
      if (fim == 1 || fim == 2)
        memo[idx][k][fim] = 0LL;
      else
        memo[idx][k][fim] = 1LL;
      return memo[idx][k][fim];
    }
  }
  if (fim == 0)
    memo[idx][k][fim] = pd(idx - 1, k, 0) + pd(idx - 1, k, 1) +
                        pd(idx - 1, k, 2) + pd(idx - 1, k - 1, 3);
  if (fim == 1)
    memo[idx][k][fim] = pd(idx - 1, k, 1) + pd(idx - 1, k - 1, 0) +
                        pd(idx - 1, k - 1, 3) + pd(idx - 1, k - 2, 2);
  if (fim == 2)
    memo[idx][k][fim] = pd(idx - 1, k, 2) + pd(idx - 1, k - 1, 0) +
                        pd(idx - 1, k - 1, 3) + pd(idx - 1, k - 2, 1);
  if (fim == 3)
    memo[idx][k][fim] = pd(idx - 1, k, 1) + pd(idx - 1, k, 2) +
                        pd(idx - 1, k, 3) + pd(idx - 1, k - 1, 0);
  while (memo[idx][k][fim] < 0) memo[idx][k][fim] += 998244353;
  memo[idx][k][fim] = memo[idx][k][fim] % 998244353;
  return memo[idx][k][fim];
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n, k;
  cin >> n >> k;
  for (int i = 0; i <= n; i++)
    for (int j = 0; j <= k; j++)
      for (int k = 0; k <= 3; k++) memo[i][j][k] = -1;
  long long int res =
      (pd(n, k, 0) + pd(n, k, 1) + pd(n, k, 2) + pd(n, k, 3)) % 998244353;
  cout << res << "\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;
long long int memo[1001][2002][4];
long long int pd(int idx, int k, int fim) {
  if (k < 0 || idx < 0 || fim < 0) return 0;
  if (memo[idx][k][fim] != -1) return memo[idx][k][fim];
  if (idx == 1) {
    if (k > 2) {
      memo[idx][k][fim] = 0LL;
      return 0;
    }
    if (k == 2) {
      if (fim == 0 || fim == 3)
        memo[idx][k][fim] = 0LL;
      else
        memo[idx][k][fim] = 1LL;
      return memo[idx][k][fim];
    }
    if (k == 1) {
      if (fim == 1 || fim == 2)
        memo[idx][k][fim] = 0LL;
      else
        memo[idx][k][fim] = 1LL;
      return memo[idx][k][fim];
    }
  }
  if (fim == 0)
    memo[idx][k][fim] = pd(idx - 1, k, 0) + pd(idx - 1, k, 1) +
                        pd(idx - 1, k, 2) + pd(idx - 1, k - 1, 3);
  if (fim == 1)
    memo[idx][k][fim] = pd(idx - 1, k, 1) + pd(idx - 1, k - 1, 0) +
                        pd(idx - 1, k - 1, 3) + pd(idx - 1, k - 2, 2);
  if (fim == 2)
    memo[idx][k][fim] = pd(idx - 1, k, 2) + pd(idx - 1, k - 1, 0) +
                        pd(idx - 1, k - 1, 3) + pd(idx - 1, k - 2, 1);
  if (fim == 3)
    memo[idx][k][fim] = pd(idx - 1, k, 1) + pd(idx - 1, k, 2) +
                        pd(idx - 1, k, 3) + pd(idx - 1, k - 1, 0);
  while (memo[idx][k][fim] < 0) memo[idx][k][fim] += 998244353;
  memo[idx][k][fim] = memo[idx][k][fim] % 998244353;
  return memo[idx][k][fim];
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n, k;
  cin >> n >> k;
  for (int i = 0; i <= n; i++)
    for (int j = 0; j <= k; j++)
      for (int k = 0; k <= 3; k++) memo[i][j][k] = -1;
  long long int res =
      (pd(n, k, 0) + pd(n, k, 1) + pd(n, k, 2) + pd(n, k, 3)) % 998244353;
  cout << res << "\n";
  return 0;
}

```