#include <bits/stdc++.h>
using namespace std;
long long int dp[1005][2005][2][2];
long long int count(long long int n, long long int k, long long int x1,
                    long long int x2) {
  if (n == 0) return (k == 0 ? 1 : 0);
  if (k < 0) return 0;
  if (dp[n][k][x1][x2] != -1) return dp[n][k][x1][x2];
  if (x1 == x2)
    return dp[n][k][x1][x2] = (count(n - 1, k - 1, !x1, !x2) % 998244353 +
                               count(n - 1, k, x1, x2) % 998244353 +
                               count(n - 1, k - 1, !x1, x2) % 998244353 +
                               count(n - 1, k - 1, x1, !x2) % 998244353) %
                              998244353;
  else
    return dp[n][k][x1][x2] = (count(n - 1, k - 2, !x1, !x2) % 998244353 +
                               count(n - 1, k, x1, x2) % 998244353 +
                               count(n - 1, k, !x1, x2) % 998244353 +
                               count(n - 1, k, x1, !x2) % 998244353) %
                              998244353;
}
int main() {
  long long int n, k;
  memset(dp, -1, sizeof(dp));
  cin >> n >> k;
  cout << (count(n - 1, k - 1, 0, 0) + count(n - 1, k - 1, 1, 1) +
           count(n - 1, k - 2, 1, 0) + count(n - 1, k - 2, 0, 1)) %
              998244353;
}

### 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;
long long int dp[1005][2005][2][2];
long long int count(long long int n, long long int k, long long int x1,
                    long long int x2) {
  if (n == 0) return (k == 0 ? 1 : 0);
  if (k < 0) return 0;
  if (dp[n][k][x1][x2] != -1) return dp[n][k][x1][x2];
  if (x1 == x2)
    return dp[n][k][x1][x2] = (count(n - 1, k - 1, !x1, !x2) % 998244353 +
                               count(n - 1, k, x1, x2) % 998244353 +
                               count(n - 1, k - 1, !x1, x2) % 998244353 +
                               count(n - 1, k - 1, x1, !x2) % 998244353) %
                              998244353;
  else
    return dp[n][k][x1][x2] = (count(n - 1, k - 2, !x1, !x2) % 998244353 +
                               count(n - 1, k, x1, x2) % 998244353 +
                               count(n - 1, k, !x1, x2) % 998244353 +
                               count(n - 1, k, x1, !x2) % 998244353) %
                              998244353;
}
int main() {
  long long int n, k;
  memset(dp, -1, sizeof(dp));
  cin >> n >> k;
  cout << (count(n - 1, k - 1, 0, 0) + count(n - 1, k - 1, 1, 1) +
           count(n - 1, k - 2, 1, 0) + count(n - 1, k - 2, 0, 1)) %
              998244353;
}

```