#include <bits/stdc++.h>
using namespace std;
const long long MOD = 998244353;
long long f[1010][2010][4];
int n, t;
inline long long sigama(long long a, long long b, long long c, long long d) {
  return (((a + b) % MOD + c) % MOD + d) % MOD;
}
int main() {
  register int i, j, k;
  scanf("%d%d", &n, &t);
  f[1][1][0] = 1;
  f[1][2][1] = 1;
  f[1][2][2] = 1;
  f[1][1][3] = 1;
  for (i = 2; i <= n; ++i) {
    for (j = 1; j <= t; ++j) {
      f[i][j][0] = sigama(f[i - 1][j][1], f[i - 1][j][2], f[i - 1][j - 1][3],
                          f[i - 1][j][0]);
      f[i][j][1] = sigama(f[i - 1][j][1], f[i - 1][j - 1][0],
                          f[i - 1][j - 2][2], f[i - 1][j - 1][3]);
      f[i][j][2] = sigama(f[i - 1][j - 1][0], f[i - 1][j - 2][1],
                          f[i - 1][j][2], f[i - 1][j - 1][3]);
      f[i][j][3] = sigama(f[i - 1][j - 1][0], f[i - 1][j][1], f[i - 1][j][2],
                          f[i - 1][j][3]);
    }
  }
  printf("%lld", sigama(f[n][t][0], f[n][t][1], f[n][t][2], f[n][t][3]) % MOD);
}

### Prompt

Your challenge is to write 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 MOD = 998244353;
long long f[1010][2010][4];
int n, t;
inline long long sigama(long long a, long long b, long long c, long long d) {
  return (((a + b) % MOD + c) % MOD + d) % MOD;
}
int main() {
  register int i, j, k;
  scanf("%d%d", &n, &t);
  f[1][1][0] = 1;
  f[1][2][1] = 1;
  f[1][2][2] = 1;
  f[1][1][3] = 1;
  for (i = 2; i <= n; ++i) {
    for (j = 1; j <= t; ++j) {
      f[i][j][0] = sigama(f[i - 1][j][1], f[i - 1][j][2], f[i - 1][j - 1][3],
                          f[i - 1][j][0]);
      f[i][j][1] = sigama(f[i - 1][j][1], f[i - 1][j - 1][0],
                          f[i - 1][j - 2][2], f[i - 1][j - 1][3]);
      f[i][j][2] = sigama(f[i - 1][j - 1][0], f[i - 1][j - 2][1],
                          f[i - 1][j][2], f[i - 1][j - 1][3]);
      f[i][j][3] = sigama(f[i - 1][j - 1][0], f[i - 1][j][1], f[i - 1][j][2],
                          f[i - 1][j][3]);
    }
  }
  printf("%lld", sigama(f[n][t][0], f[n][t][1], f[n][t][2], f[n][t][3]) % MOD);
}

```