#include <bits/stdc++.h>
using namespace std;
const int MAXN = 1e5 + 5;
const long long MOD = 998244353ll;
int N, M, K, Q, T;
int dp[1005][2005][4];
int go(int pos, int k, int o) {
  if (k <= 0) return 0;
  if (pos == 1) {
    if (o == 0 || o == 3)
      return (k == 1 ? 1 : 0);
    else
      return (k == 2 ? 1 : 0);
  }
  int &ret = dp[pos][k][o];
  if (ret != -1) return ret;
  ret = 0;
  if (o == 0)
    ret = ((long long)go(pos - 1, k, 0) + (long long)go(pos - 1, k, 1) +
           (long long)go(pos - 1, k, 2) + (long long)go(pos - 1, k - 1, 3)) %
          MOD;
  else if (o == 1)
    ret =
        ((long long)go(pos - 1, k - 1, 0) + (long long)go(pos - 1, k, 1) +
         (long long)go(pos - 1, k - 2, 2) + (long long)go(pos - 1, k - 1, 3)) %
        MOD;
  else if (o == 2)
    ret = ((long long)go(pos - 1, k - 1, 0) + (long long)go(pos - 1, k - 2, 1) +
           (long long)go(pos - 1, k, 2) + (long long)go(pos - 1, k - 1, 3)) %
          MOD;
  else
    ret = ((long long)go(pos - 1, k - 1, 0) + (long long)go(pos - 1, k, 1) +
           (long long)go(pos - 1, k, 2) + (long long)go(pos - 1, k, 3)) %
          MOD;
  return ret;
}
int main() {
  int i, j;
  scanf("%d%d", &N, &K);
  for (i = 1; i <= N; ++i) {
    for (j = 1; j <= K; ++j) {
      for (int k = 0; k < 4; ++k) dp[i][j][k] = -1;
    }
  }
  int ans = 0;
  for (i = 0; i < 4; ++i) {
    ans = ((long long)ans + (long long)go(N, K, i)) % MOD;
  }
  printf("%d", ans);
  return 0;
}

### 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;
const int MAXN = 1e5 + 5;
const long long MOD = 998244353ll;
int N, M, K, Q, T;
int dp[1005][2005][4];
int go(int pos, int k, int o) {
  if (k <= 0) return 0;
  if (pos == 1) {
    if (o == 0 || o == 3)
      return (k == 1 ? 1 : 0);
    else
      return (k == 2 ? 1 : 0);
  }
  int &ret = dp[pos][k][o];
  if (ret != -1) return ret;
  ret = 0;
  if (o == 0)
    ret = ((long long)go(pos - 1, k, 0) + (long long)go(pos - 1, k, 1) +
           (long long)go(pos - 1, k, 2) + (long long)go(pos - 1, k - 1, 3)) %
          MOD;
  else if (o == 1)
    ret =
        ((long long)go(pos - 1, k - 1, 0) + (long long)go(pos - 1, k, 1) +
         (long long)go(pos - 1, k - 2, 2) + (long long)go(pos - 1, k - 1, 3)) %
        MOD;
  else if (o == 2)
    ret = ((long long)go(pos - 1, k - 1, 0) + (long long)go(pos - 1, k - 2, 1) +
           (long long)go(pos - 1, k, 2) + (long long)go(pos - 1, k - 1, 3)) %
          MOD;
  else
    ret = ((long long)go(pos - 1, k - 1, 0) + (long long)go(pos - 1, k, 1) +
           (long long)go(pos - 1, k, 2) + (long long)go(pos - 1, k, 3)) %
          MOD;
  return ret;
}
int main() {
  int i, j;
  scanf("%d%d", &N, &K);
  for (i = 1; i <= N; ++i) {
    for (j = 1; j <= K; ++j) {
      for (int k = 0; k < 4; ++k) dp[i][j][k] = -1;
    }
  }
  int ans = 0;
  for (i = 0; i < 4; ++i) {
    ans = ((long long)ans + (long long)go(N, K, i)) % MOD;
  }
  printf("%d", ans);
  return 0;
}

```