#include <bits/stdc++.h>
using namespace std;
long long int mod = 998244353;
long long int n, k;
long long int dp[1005][2][2][2005];
long long int solve(long long int ind, long long int preva, long long int prevb,
                    long long int com) {
  if (ind >= n) {
    if (com == k) return 1;
    return 0;
  }
  if (dp[ind][preva][prevb][com] != -1) return dp[ind][preva][prevb][com];
  long long int ans = 0;
  if (ind == 0) {
    ans += solve(ind + 1, 0, 0, 1);
    ans %= mod;
    ans += solve(ind + 1, 1, 1, 1);
    ans %= mod;
    ans += solve(ind + 1, 1, 0, 2);
    ans %= mod;
    ans += solve(ind + 1, 0, 1, 2);
    ans %= mod;
  } else {
    if (preva == 1 && prevb == 1) {
      ans += solve(ind + 1, 1, 1, com);
      ans %= mod;
      ans += solve(ind + 1, 0, 0, com + 1);
      ans %= mod;
      ans += solve(ind + 1, 0, 1, com + 1);
      ans %= mod;
      ans += solve(ind + 1, 1, 0, com + 1);
      ans %= mod;
    } else if (preva == 0 && prevb == 0) {
      ans += solve(ind + 1, 1, 1, com + 1);
      ans %= mod;
      ans += solve(ind + 1, 0, 0, com);
      ans %= mod;
      ans += solve(ind + 1, 0, 1, com + 1);
      ans %= mod;
      ans += solve(ind + 1, 1, 0, com + 1);
      ans %= mod;
    } else if (preva == 1 && prevb == 0) {
      ans += solve(ind + 1, 1, 1, com);
      ans %= mod;
      ans += solve(ind + 1, 0, 0, com);
      ans %= mod;
      ans += solve(ind + 1, 0, 1, com + 2);
      ans %= mod;
      ans += solve(ind + 1, 1, 0, com);
      ans %= mod;
    } else {
      ans += solve(ind + 1, 1, 1, com);
      ans %= mod;
      ans += solve(ind + 1, 0, 0, com);
      ans %= mod;
      ans += solve(ind + 1, 0, 1, com);
      ans %= mod;
      ans += solve(ind + 1, 1, 0, com + 2);
      ans %= mod;
    }
  }
  dp[ind][preva][prevb][com] = ans % mod;
  return dp[ind][preva][prevb][com];
}
int main() {
  cin >> n >> k;
  memset(dp, -1, sizeof dp);
  cout << solve(0, 1, 1, 0) << endl;
  return 0;
}

### Prompt

Construct a cpp code solution to the problem outlined:

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 mod = 998244353;
long long int n, k;
long long int dp[1005][2][2][2005];
long long int solve(long long int ind, long long int preva, long long int prevb,
                    long long int com) {
  if (ind >= n) {
    if (com == k) return 1;
    return 0;
  }
  if (dp[ind][preva][prevb][com] != -1) return dp[ind][preva][prevb][com];
  long long int ans = 0;
  if (ind == 0) {
    ans += solve(ind + 1, 0, 0, 1);
    ans %= mod;
    ans += solve(ind + 1, 1, 1, 1);
    ans %= mod;
    ans += solve(ind + 1, 1, 0, 2);
    ans %= mod;
    ans += solve(ind + 1, 0, 1, 2);
    ans %= mod;
  } else {
    if (preva == 1 && prevb == 1) {
      ans += solve(ind + 1, 1, 1, com);
      ans %= mod;
      ans += solve(ind + 1, 0, 0, com + 1);
      ans %= mod;
      ans += solve(ind + 1, 0, 1, com + 1);
      ans %= mod;
      ans += solve(ind + 1, 1, 0, com + 1);
      ans %= mod;
    } else if (preva == 0 && prevb == 0) {
      ans += solve(ind + 1, 1, 1, com + 1);
      ans %= mod;
      ans += solve(ind + 1, 0, 0, com);
      ans %= mod;
      ans += solve(ind + 1, 0, 1, com + 1);
      ans %= mod;
      ans += solve(ind + 1, 1, 0, com + 1);
      ans %= mod;
    } else if (preva == 1 && prevb == 0) {
      ans += solve(ind + 1, 1, 1, com);
      ans %= mod;
      ans += solve(ind + 1, 0, 0, com);
      ans %= mod;
      ans += solve(ind + 1, 0, 1, com + 2);
      ans %= mod;
      ans += solve(ind + 1, 1, 0, com);
      ans %= mod;
    } else {
      ans += solve(ind + 1, 1, 1, com);
      ans %= mod;
      ans += solve(ind + 1, 0, 0, com);
      ans %= mod;
      ans += solve(ind + 1, 0, 1, com);
      ans %= mod;
      ans += solve(ind + 1, 1, 0, com + 2);
      ans %= mod;
    }
  }
  dp[ind][preva][prevb][com] = ans % mod;
  return dp[ind][preva][prevb][com];
}
int main() {
  cin >> n >> k;
  memset(dp, -1, sizeof dp);
  cout << solve(0, 1, 1, 0) << endl;
  return 0;
}

```