#include <bits/stdc++.h>
using namespace std;
const long cm = 998244353;
long n, k, f[2005][2005][2][2];
void pre() {
  f[1][2][1][0] = f[1][2][0][1] = 1;
  f[1][1][1][1] = f[1][1][0][0] = 1;
}
void add(long &x, long y) { x = (x + y) % cm; }
void nhap() {
  cin >> n >> k;
  pre();
  for (int i = 2; i <= n; ++i)
    for (int j = 1; j <= k; ++j)
      for (int x = 0; x < 2; ++x) {
        f[i][j][x][x] = f[i - 1][j][x][x];
        add(f[i][j][x][x], f[i - 1][j - 1][1 - x][1 - x]);
        add(f[i][j][x][x], f[i - 1][j][1 - x][x]);
        add(f[i][j][x][x], f[i - 1][j][x][1 - x]);
        f[i][j][x][1 - x] = f[i - 1][j][x][1 - x];
        add(f[i][j][x][1 - x], f[i - 1][j - 1][x][x]);
        add(f[i][j][x][1 - x], f[i - 1][j - 1][1 - x][1 - x]);
        if (j >= 2) add(f[i][j][x][1 - x], f[i - 1][j - 2][1 - x][x]);
      }
  long kq = 0;
  for (int i = 0; i <= 1; ++i)
    for (int j = 0; j <= 1; ++j) add(kq, f[n][k][i][j]);
  cout << kq;
}
int main(int argc, const char *argv[]) {
  nhap();
  return 0;
}

### Prompt

Construct a cpp code solution to the problem outlined:

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 cm = 998244353;
long n, k, f[2005][2005][2][2];
void pre() {
  f[1][2][1][0] = f[1][2][0][1] = 1;
  f[1][1][1][1] = f[1][1][0][0] = 1;
}
void add(long &x, long y) { x = (x + y) % cm; }
void nhap() {
  cin >> n >> k;
  pre();
  for (int i = 2; i <= n; ++i)
    for (int j = 1; j <= k; ++j)
      for (int x = 0; x < 2; ++x) {
        f[i][j][x][x] = f[i - 1][j][x][x];
        add(f[i][j][x][x], f[i - 1][j - 1][1 - x][1 - x]);
        add(f[i][j][x][x], f[i - 1][j][1 - x][x]);
        add(f[i][j][x][x], f[i - 1][j][x][1 - x]);
        f[i][j][x][1 - x] = f[i - 1][j][x][1 - x];
        add(f[i][j][x][1 - x], f[i - 1][j - 1][x][x]);
        add(f[i][j][x][1 - x], f[i - 1][j - 1][1 - x][1 - x]);
        if (j >= 2) add(f[i][j][x][1 - x], f[i - 1][j - 2][1 - x][x]);
      }
  long kq = 0;
  for (int i = 0; i <= 1; ++i)
    for (int j = 0; j <= 1; ++j) add(kq, f[n][k][i][j]);
  cout << kq;
}
int main(int argc, const char *argv[]) {
  nhap();
  return 0;
}

```