#include <bits/stdc++.h>
using namespace std;
const long long N = 1005;
const long long mod = 998244353;
long long m, n, dp[2][N * 2][2][2];
inline long long min(long long s1, long long s2) { return s1 < s2 ? s1 : s2; }
signed main() {
  scanf("%lld%lld", &m, &n);
  dp[1][1][0][0] = dp[1][2][0][1] = dp[1][2][1][0] = dp[1][1][1][1] = 1;
  for (long long i = 2; i <= m; i++) {
    long long now = i & 1, last = i + 1 & 1;
    memset(dp[now], 0, sizeof(dp[now]));
    for (long long j = 1; j <= min(n, i * 2); j++) {
      dp[now][j][0][0] = dp[last][j][0][0] + dp[last][j][1][0] +
                         dp[last][j][0][1] + dp[last][j - 1][1][1];
      dp[now][j][0][0] %= mod;
      dp[now][j][1][1] = dp[last][j][1][1] + dp[last][j][1][0] +
                         dp[last][j][0][1] + dp[last][j - 1][0][0];
      dp[now][j][1][1] %= mod;
      dp[now][j][0][1] =
          dp[last][j][0][1] + dp[last][j - 1][1][1] + dp[last][j - 1][0][0];
      if (j > 1) dp[now][j][0][1] += dp[last][j - 2][1][0];
      dp[now][j][0][1] %= mod;
      dp[now][j][1][0] =
          dp[last][j][1][0] + dp[last][j - 1][1][1] + dp[last][j - 1][0][0];
      if (j > 1) dp[now][j][1][0] += dp[last][j - 2][0][1];
      dp[now][j][1][0] %= mod;
    }
  }
  long long s = m & 1;
  printf("%lld",
         (dp[s][n][0][0] + dp[s][n][0][1] + dp[s][n][1][0] + dp[s][n][1][1]) %
             mod);
  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;
const long long N = 1005;
const long long mod = 998244353;
long long m, n, dp[2][N * 2][2][2];
inline long long min(long long s1, long long s2) { return s1 < s2 ? s1 : s2; }
signed main() {
  scanf("%lld%lld", &m, &n);
  dp[1][1][0][0] = dp[1][2][0][1] = dp[1][2][1][0] = dp[1][1][1][1] = 1;
  for (long long i = 2; i <= m; i++) {
    long long now = i & 1, last = i + 1 & 1;
    memset(dp[now], 0, sizeof(dp[now]));
    for (long long j = 1; j <= min(n, i * 2); j++) {
      dp[now][j][0][0] = dp[last][j][0][0] + dp[last][j][1][0] +
                         dp[last][j][0][1] + dp[last][j - 1][1][1];
      dp[now][j][0][0] %= mod;
      dp[now][j][1][1] = dp[last][j][1][1] + dp[last][j][1][0] +
                         dp[last][j][0][1] + dp[last][j - 1][0][0];
      dp[now][j][1][1] %= mod;
      dp[now][j][0][1] =
          dp[last][j][0][1] + dp[last][j - 1][1][1] + dp[last][j - 1][0][0];
      if (j > 1) dp[now][j][0][1] += dp[last][j - 2][1][0];
      dp[now][j][0][1] %= mod;
      dp[now][j][1][0] =
          dp[last][j][1][0] + dp[last][j - 1][1][1] + dp[last][j - 1][0][0];
      if (j > 1) dp[now][j][1][0] += dp[last][j - 2][0][1];
      dp[now][j][1][0] %= mod;
    }
  }
  long long s = m & 1;
  printf("%lld",
         (dp[s][n][0][0] + dp[s][n][0][1] + dp[s][n][1][0] + dp[s][n][1][1]) %
             mod);
  return 0;
}

```