#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e3 + 2;
const int mod = 998244353;
int n, k;
long long dp[4][maxn][maxn << 1];
void DP() {
  dp[0][1][1] = 1;
  dp[1][1][2] = 1;
  dp[2][1][2] = 1;
  dp[3][1][1] = 1;
  for (int i = 2; i <= n; i++)
    for (int j = 1; j <= (i << 1); j++) {
      dp[0][i][j] = (dp[0][i][j] + dp[0][i - 1][j] + dp[1][i - 1][j] +
                     dp[2][i - 1][j] + dp[3][i - 1][j - 1]) %
                    mod;
      dp[1][i][j] = (dp[1][i][j] + dp[0][i - 1][j - 1] + dp[1][i - 1][j] +
                     dp[2][i - 1][j - 2] + dp[3][i - 1][j - 1]) %
                    mod;
      dp[2][i][j] = (dp[2][i][j] + dp[0][i - 1][j - 1] + dp[1][i - 1][j - 2] +
                     dp[2][i - 1][j] + dp[3][i - 1][j - 1]) %
                    mod;
      dp[3][i][j] = (dp[3][i][j] + dp[0][i - 1][j - 1] + dp[1][i - 1][j] +
                     dp[2][i - 1][j] + dp[3][i - 1][j]) %
                    mod;
    }
}
int main() {
  scanf("%d%d", &n, &k);
  DP();
  printf("%I64d",
         (dp[0][n][k] + dp[1][n][k] + dp[2][n][k] + dp[3][n][k]) % mod);
  return 0;
}

### Prompt

Develop a solution in CPP to the problem described below:

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 = 1e3 + 2;
const int mod = 998244353;
int n, k;
long long dp[4][maxn][maxn << 1];
void DP() {
  dp[0][1][1] = 1;
  dp[1][1][2] = 1;
  dp[2][1][2] = 1;
  dp[3][1][1] = 1;
  for (int i = 2; i <= n; i++)
    for (int j = 1; j <= (i << 1); j++) {
      dp[0][i][j] = (dp[0][i][j] + dp[0][i - 1][j] + dp[1][i - 1][j] +
                     dp[2][i - 1][j] + dp[3][i - 1][j - 1]) %
                    mod;
      dp[1][i][j] = (dp[1][i][j] + dp[0][i - 1][j - 1] + dp[1][i - 1][j] +
                     dp[2][i - 1][j - 2] + dp[3][i - 1][j - 1]) %
                    mod;
      dp[2][i][j] = (dp[2][i][j] + dp[0][i - 1][j - 1] + dp[1][i - 1][j - 2] +
                     dp[2][i - 1][j] + dp[3][i - 1][j - 1]) %
                    mod;
      dp[3][i][j] = (dp[3][i][j] + dp[0][i - 1][j - 1] + dp[1][i - 1][j] +
                     dp[2][i - 1][j] + dp[3][i - 1][j]) %
                    mod;
    }
}
int main() {
  scanf("%d%d", &n, &k);
  DP();
  printf("%I64d",
         (dp[0][n][k] + dp[1][n][k] + dp[2][n][k] + dp[3][n][k]) % mod);
  return 0;
}

```