#include <bits/stdc++.h>
using namespace std;
int dp[4][1005][2005];
int mod = 998244353;
int k, n;
int solve(int pre, int index, int tot) {
  if (index == n) {
    if (tot == k) {
      return 1;
    } else
      return 0;
  }
  if (dp[pre][index][tot] != -1) {
    return dp[pre][index][tot];
  }
  int ans = 0;
  if (pre == 0) {
    ans += solve(0, index + 1, tot);
    ans %= mod;
    ans += solve(1, index + 1, tot + 1);
    ans %= mod;
    ans += solve(2, index + 1, tot + 1);
    ans %= mod;
    ans += solve(3, index + 1, tot + 1);
  } else if (pre == 1) {
    ans += solve(0, index + 1, tot + 1);
    ans %= mod;
    ans += solve(1, index + 1, tot);
    ans %= mod;
    ans += solve(2, index + 1, tot + 1);
    ans %= mod;
    ans += solve(3, index + 1, tot + 1);
  } else if (pre == 2) {
    ans += solve(0, index + 1, tot);
    ans %= mod;
    ans += solve(1, index + 1, tot);
    ans %= mod;
    ans += solve(2, index + 1, tot);
    ans %= mod;
    ans += solve(3, index + 1, tot + 2);
  } else {
    ans += solve(0, index + 1, tot);
    ans %= mod;
    ans += solve(1, index + 1, tot);
    ans %= mod;
    ans += solve(2, index + 1, tot + 2);
    ans %= mod;
    ans += solve(3, index + 1, tot);
  }
  ans %= mod;
  dp[pre][index][tot] = ans;
  return ans;
}
int main() {
  ios_base::sync_with_stdio(false);
  int i, j, t, l, r, x;
  cin >> n >> k;
  memset(dp, -1, sizeof(dp));
  int ans = 0;
  ans += solve(0, 1, 1);
  ans %= mod;
  ans += solve(1, 1, 1);
  ans %= mod;
  ans += solve(2, 1, 2);
  ans %= mod;
  ans += solve(3, 1, 2);
  ans %= mod;
  cout << ans;
  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;
int dp[4][1005][2005];
int mod = 998244353;
int k, n;
int solve(int pre, int index, int tot) {
  if (index == n) {
    if (tot == k) {
      return 1;
    } else
      return 0;
  }
  if (dp[pre][index][tot] != -1) {
    return dp[pre][index][tot];
  }
  int ans = 0;
  if (pre == 0) {
    ans += solve(0, index + 1, tot);
    ans %= mod;
    ans += solve(1, index + 1, tot + 1);
    ans %= mod;
    ans += solve(2, index + 1, tot + 1);
    ans %= mod;
    ans += solve(3, index + 1, tot + 1);
  } else if (pre == 1) {
    ans += solve(0, index + 1, tot + 1);
    ans %= mod;
    ans += solve(1, index + 1, tot);
    ans %= mod;
    ans += solve(2, index + 1, tot + 1);
    ans %= mod;
    ans += solve(3, index + 1, tot + 1);
  } else if (pre == 2) {
    ans += solve(0, index + 1, tot);
    ans %= mod;
    ans += solve(1, index + 1, tot);
    ans %= mod;
    ans += solve(2, index + 1, tot);
    ans %= mod;
    ans += solve(3, index + 1, tot + 2);
  } else {
    ans += solve(0, index + 1, tot);
    ans %= mod;
    ans += solve(1, index + 1, tot);
    ans %= mod;
    ans += solve(2, index + 1, tot + 2);
    ans %= mod;
    ans += solve(3, index + 1, tot);
  }
  ans %= mod;
  dp[pre][index][tot] = ans;
  return ans;
}
int main() {
  ios_base::sync_with_stdio(false);
  int i, j, t, l, r, x;
  cin >> n >> k;
  memset(dp, -1, sizeof(dp));
  int ans = 0;
  ans += solve(0, 1, 1);
  ans %= mod;
  ans += solve(1, 1, 1);
  ans %= mod;
  ans += solve(2, 1, 2);
  ans %= mod;
  ans += solve(3, 1, 2);
  ans %= mod;
  cout << ans;
  return 0;
}

```