#include <bits/stdc++.h>
using namespace std;
const int maxn = 2020;
const int mod = 998244353;
int f[4][maxn][maxn];
int solve(int ty, int row, int cmp) {
  if (cmp < 0) return 0;
  if (row == 0) {
    return cmp == 0;
  }
  if (~f[ty][row][cmp]) return f[ty][row][cmp];
  int ans = 0;
  for (int i = 0; i < 4; i++) {
    if (ty == 0) {
      ans += solve(i, row - 1, cmp - (i > 0));
    } else if (ty == 1) {
      if (i == 2) {
        ans += solve(i, row - 1, cmp - 2);
      } else {
        ans += solve(i, row - 1, cmp);
      }
    } else if (ty == 2) {
      if (i == 1) {
        ans += solve(i, row - 1, cmp - 2);
      } else {
        ans += solve(i, row - 1, cmp);
      }
    } else if (ty == 3) {
      ans += solve(i, row - 1, cmp - (i != 3));
    }
    if (ans >= mod) ans -= mod;
  }
  return f[ty][row][cmp] = ans;
}
int main() {
  int ans = 0;
  int n, k;
  cin >> n >> k;
  memset(f, -1, sizeof(f));
  for (int i = 0; i < 4; i++) {
    if (i == 0 || i == 3) {
      ans += solve(i, n - 1, k - 1);
    } else {
      if (k >= 2) ans += solve(i, n - 1, k - 2);
    }
    if (ans >= mod) ans -= mod;
  }
  cout << ans << endl;
  return 0;
}

### Prompt

Your task is to create 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 maxn = 2020;
const int mod = 998244353;
int f[4][maxn][maxn];
int solve(int ty, int row, int cmp) {
  if (cmp < 0) return 0;
  if (row == 0) {
    return cmp == 0;
  }
  if (~f[ty][row][cmp]) return f[ty][row][cmp];
  int ans = 0;
  for (int i = 0; i < 4; i++) {
    if (ty == 0) {
      ans += solve(i, row - 1, cmp - (i > 0));
    } else if (ty == 1) {
      if (i == 2) {
        ans += solve(i, row - 1, cmp - 2);
      } else {
        ans += solve(i, row - 1, cmp);
      }
    } else if (ty == 2) {
      if (i == 1) {
        ans += solve(i, row - 1, cmp - 2);
      } else {
        ans += solve(i, row - 1, cmp);
      }
    } else if (ty == 3) {
      ans += solve(i, row - 1, cmp - (i != 3));
    }
    if (ans >= mod) ans -= mod;
  }
  return f[ty][row][cmp] = ans;
}
int main() {
  int ans = 0;
  int n, k;
  cin >> n >> k;
  memset(f, -1, sizeof(f));
  for (int i = 0; i < 4; i++) {
    if (i == 0 || i == 3) {
      ans += solve(i, n - 1, k - 1);
    } else {
      if (k >= 2) ans += solve(i, n - 1, k - 2);
    }
    if (ans >= mod) ans -= mod;
  }
  cout << ans << endl;
  return 0;
}

```