#include <bits/stdc++.h>
using namespace std;
template <typename T>
inline void read(T &x) {
  char c;
  bool nega = 0;
  while ((!isdigit(c = getchar())) && (c != '-'))
    ;
  if (c == '-') {
    nega = 1;
    c = getchar();
  }
  x = c - 48;
  while (isdigit(c = getchar())) x = x * 10 + c - 48;
  if (nega) x = -x;
}
template <typename T>
inline void writep(T x) {
  if (x > 9) writep(x / 10);
  putchar(x % 10 + 48);
}
template <typename T>
inline void write(T x) {
  if (x < 0) {
    putchar('-');
    x = -x;
  }
  writep(x);
}
template <typename T>
inline void writeln(T x) {
  write(x);
  putchar('\n');
}
const long long base = 998244353;
long long f[1001][2003][2];
int n, k;
int main() {
  read(n);
  read(k);
  f[1][2][0] = 2;
  f[1][1][1] = 2;
  for (int i = (1); i < (n); i++)
    for (int j = (1); j <= (k); j++)
      for (int s = (0); s < (2); s++)
        if (f[i][j][s]) {
          f[i][j][s] %= base;
          if (s) {
            f[i + 1][j][1] += f[i][j][s];
            f[i + 1][j + 1][1] += f[i][j][s];
            f[i + 1][j + 1][0] += f[i][j][s] * 2;
          } else {
            f[i + 1][j][1] += f[i][j][s] * 2;
            f[i + 1][j][0] += f[i][j][s];
            f[i + 1][j + 2][0] += f[i][j][s];
          }
        }
  writeln((f[n][k][0] + f[n][k][1]) % base);
}

### Prompt

Please provide a CPP coded solution 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;
template <typename T>
inline void read(T &x) {
  char c;
  bool nega = 0;
  while ((!isdigit(c = getchar())) && (c != '-'))
    ;
  if (c == '-') {
    nega = 1;
    c = getchar();
  }
  x = c - 48;
  while (isdigit(c = getchar())) x = x * 10 + c - 48;
  if (nega) x = -x;
}
template <typename T>
inline void writep(T x) {
  if (x > 9) writep(x / 10);
  putchar(x % 10 + 48);
}
template <typename T>
inline void write(T x) {
  if (x < 0) {
    putchar('-');
    x = -x;
  }
  writep(x);
}
template <typename T>
inline void writeln(T x) {
  write(x);
  putchar('\n');
}
const long long base = 998244353;
long long f[1001][2003][2];
int n, k;
int main() {
  read(n);
  read(k);
  f[1][2][0] = 2;
  f[1][1][1] = 2;
  for (int i = (1); i < (n); i++)
    for (int j = (1); j <= (k); j++)
      for (int s = (0); s < (2); s++)
        if (f[i][j][s]) {
          f[i][j][s] %= base;
          if (s) {
            f[i + 1][j][1] += f[i][j][s];
            f[i + 1][j + 1][1] += f[i][j][s];
            f[i + 1][j + 1][0] += f[i][j][s] * 2;
          } else {
            f[i + 1][j][1] += f[i][j][s] * 2;
            f[i + 1][j][0] += f[i][j][s];
            f[i + 1][j + 2][0] += f[i][j][s];
          }
        }
  writeln((f[n][k][0] + f[n][k][1]) % base);
}

```