#include <bits/stdc++.h>
#pragma GCC optimize("Ofast", "unroll-loops")
using namespace std;
const long long inf = numeric_limits<long long>::max() / 2;
const long double eps = 1e-9;
const long double pi = acos(-1);
inline void solve(), read();
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  read();
  solve();
  return 0;
}
const long long MAXN = 1e3 + 10;
long long n, k;
long long dp[MAXN][2 * MAXN][2][2];
const long long R = 998244353;
inline void solve() {
  dp[1][1][0][0] = dp[1][1][1][1] = 1;
  dp[1][2][0][1] = dp[1][2][1][0] = 1;
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= k; j++) {
      for (long long p = 0; p < 2; p++) {
        for (long long q = 0; q < 2; q++) {
          for (long long x = 0; x < 2; x++) {
            for (long long y = 0; y < 2; y++) {
              if (x == p && y == q) {
                dp[i + 1][j][x][y] += dp[i][j][p][q];
                dp[i + 1][j][x][y] %= R;
              }
              if (x != p && y == q) {
                if (x != y) {
                  dp[i + 1][j + 1][x][y] += dp[i][j][p][q];
                  dp[i + 1][j + 1][x][y] %= R;
                } else {
                  dp[i + 1][j][x][y] += dp[i][j][p][q];
                  dp[i + 1][j][x][y] %= R;
                }
              }
              if (x == p && y != q) {
                if (x != y) {
                  dp[i + 1][j + 1][x][y] += dp[i][j][p][q];
                  dp[i + 1][j + 1][x][y] %= R;
                } else {
                  dp[i + 1][j][x][y] += dp[i][j][p][q];
                  dp[i + 1][j][x][y] %= R;
                }
              }
              if (x != p && y != q) {
                if (x != y) {
                  dp[i + 1][j + 2][x][y] += dp[i][j][p][q];
                  dp[i + 1][j + 2][x][y] %= R;
                } else {
                  dp[i + 1][j + 1][x][y] += dp[i][j][p][q];
                  dp[i + 1][j + 1][x][y] %= R;
                }
              }
            }
          }
        }
      }
    }
  }
  long long ans = 0;
  for (long long p = 0; p < 2; p++) {
    for (long long q = 0; q < 2; q++) {
      ans += dp[n][k][p][q];
      ans %= R;
    }
  }
  cout << ans << "\n";
}
inline void read() { cin >> n >> k; }

### 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>
#pragma GCC optimize("Ofast", "unroll-loops")
using namespace std;
const long long inf = numeric_limits<long long>::max() / 2;
const long double eps = 1e-9;
const long double pi = acos(-1);
inline void solve(), read();
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  read();
  solve();
  return 0;
}
const long long MAXN = 1e3 + 10;
long long n, k;
long long dp[MAXN][2 * MAXN][2][2];
const long long R = 998244353;
inline void solve() {
  dp[1][1][0][0] = dp[1][1][1][1] = 1;
  dp[1][2][0][1] = dp[1][2][1][0] = 1;
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= k; j++) {
      for (long long p = 0; p < 2; p++) {
        for (long long q = 0; q < 2; q++) {
          for (long long x = 0; x < 2; x++) {
            for (long long y = 0; y < 2; y++) {
              if (x == p && y == q) {
                dp[i + 1][j][x][y] += dp[i][j][p][q];
                dp[i + 1][j][x][y] %= R;
              }
              if (x != p && y == q) {
                if (x != y) {
                  dp[i + 1][j + 1][x][y] += dp[i][j][p][q];
                  dp[i + 1][j + 1][x][y] %= R;
                } else {
                  dp[i + 1][j][x][y] += dp[i][j][p][q];
                  dp[i + 1][j][x][y] %= R;
                }
              }
              if (x == p && y != q) {
                if (x != y) {
                  dp[i + 1][j + 1][x][y] += dp[i][j][p][q];
                  dp[i + 1][j + 1][x][y] %= R;
                } else {
                  dp[i + 1][j][x][y] += dp[i][j][p][q];
                  dp[i + 1][j][x][y] %= R;
                }
              }
              if (x != p && y != q) {
                if (x != y) {
                  dp[i + 1][j + 2][x][y] += dp[i][j][p][q];
                  dp[i + 1][j + 2][x][y] %= R;
                } else {
                  dp[i + 1][j + 1][x][y] += dp[i][j][p][q];
                  dp[i + 1][j + 1][x][y] %= R;
                }
              }
            }
          }
        }
      }
    }
  }
  long long ans = 0;
  for (long long p = 0; p < 2; p++) {
    for (long long q = 0; q < 2; q++) {
      ans += dp[n][k][p][q];
      ans %= R;
    }
  }
  cout << ans << "\n";
}
inline void read() { cin >> n >> k; }

```