#include <bits/stdc++.h>
using namespace std;
const int N = 1024;
const long long inf = 998244353;
int n, k;
long long dp[2][2][N][2 * N];
long long first(int c1, int c2, int n, int k) {
  if (n == 1) {
    if (k == 1 && c1 == c2) return 1;
    if (k == 1 && c1 != c2) return 0;
    if (k == 2 && c1 != c2) return 1;
    if (k == 2 && c1 == c2) return 0;
    return 0;
  }
  if (n == 0 && k == 0) return 1;
  if (n == 0) return 0;
  if (k == 0) return 0;
  if (k == 1) {
    if (c1 == c2) return 1;
    return 0;
  }
  if (dp[c1][c2][n][k] != -1) return dp[c1][c2][n][k];
  if (c1 != c2)
    dp[c1][c2][n][k] =
        first(1 - c1, c2, n - 1, k - 1) + first(c1, 1 - c2, n - 1, k - 1) +
        first(c1, c2, n - 1, k) + first(1 - c1, 1 - c2, n - 1, k - 2);
  else
    dp[c1][c2][n][k] = first(1 - c1, c2, n - 1, k) +
                       first(c1, 1 - c2, n - 1, k) + first(c1, c2, n - 1, k) +
                       first(1 - c1, 1 - c2, n - 1, k - 1);
  dp[c1][c2][n][k] %= inf;
  return dp[c1][c2][n][k];
}
int main() {
  cin >> n >> k;
  for (int i = 0; i <= n; i++)
    for (int j = 0; j <= k; j++)
      dp[0][0][i][j] = dp[1][1][i][j] = dp[1][0][i][j] = dp[0][1][i][j] = -1;
  long long ans = first(0, 0, n, k) + first(1, 1, n, k) + first(0, 1, n, k) +
                  first(1, 0, n, k);
  ans %= inf;
  cout << ans;
  return 0;
}

### Prompt

Your challenge is to write 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;
const int N = 1024;
const long long inf = 998244353;
int n, k;
long long dp[2][2][N][2 * N];
long long first(int c1, int c2, int n, int k) {
  if (n == 1) {
    if (k == 1 && c1 == c2) return 1;
    if (k == 1 && c1 != c2) return 0;
    if (k == 2 && c1 != c2) return 1;
    if (k == 2 && c1 == c2) return 0;
    return 0;
  }
  if (n == 0 && k == 0) return 1;
  if (n == 0) return 0;
  if (k == 0) return 0;
  if (k == 1) {
    if (c1 == c2) return 1;
    return 0;
  }
  if (dp[c1][c2][n][k] != -1) return dp[c1][c2][n][k];
  if (c1 != c2)
    dp[c1][c2][n][k] =
        first(1 - c1, c2, n - 1, k - 1) + first(c1, 1 - c2, n - 1, k - 1) +
        first(c1, c2, n - 1, k) + first(1 - c1, 1 - c2, n - 1, k - 2);
  else
    dp[c1][c2][n][k] = first(1 - c1, c2, n - 1, k) +
                       first(c1, 1 - c2, n - 1, k) + first(c1, c2, n - 1, k) +
                       first(1 - c1, 1 - c2, n - 1, k - 1);
  dp[c1][c2][n][k] %= inf;
  return dp[c1][c2][n][k];
}
int main() {
  cin >> n >> k;
  for (int i = 0; i <= n; i++)
    for (int j = 0; j <= k; j++)
      dp[0][0][i][j] = dp[1][1][i][j] = dp[1][0][i][j] = dp[0][1][i][j] = -1;
  long long ans = first(0, 0, n, k) + first(1, 1, n, k) + first(0, 1, n, k) +
                  first(1, 0, n, k);
  ans %= inf;
  cout << ans;
  return 0;
}

```