#include <bits/stdc++.h>
using namespace std;
int n, k;
long long dp[4][1002][2002];
const long long MOD = 998244353;
long long do_dp(int move, int inx, int faltantes) {
  if (dp[move][inx][faltantes] != -1) {
    return dp[move][inx][faltantes];
  }
  if (inx == n && faltantes == 0) {
    return dp[move][inx][faltantes] = 1;
  }
  if (inx > n || faltantes < 0) return 0;
  long long ans = 0;
  if (inx == 0) {
    ans += do_dp(0, inx + 1, k - 1);
    ans %= MOD;
    ans += do_dp(1, inx + 1, k - 2);
    ans %= MOD;
    ans += do_dp(2, inx + 1, k - 2);
    ans %= MOD;
    ans += do_dp(3, inx + 1, k - 1);
    ans %= MOD;
    return dp[move][inx][faltantes] = ans;
  }
  ans += do_dp(0, inx + 1, faltantes - ((move == 3) ? 1 : 0));
  ans %= MOD;
  ans +=
      do_dp(1, inx + 1, faltantes - ((move == 2) ? 2 : ((move == 1) ? 0 : 1)));
  ans %= MOD;
  ans +=
      do_dp(2, inx + 1, faltantes - ((move == 1) ? 2 : ((move == 2) ? 0 : 1)));
  ans %= MOD;
  ans += do_dp(3, inx + 1, faltantes - ((move == 0) ? 1 : 0));
  ans %= MOD;
  return dp[move][inx][faltantes] = ans;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  ;
  cin >> n >> k;
  for (int i = 0; i < 4; i++)
    for (int j = 0; j < 1001; j++)
      for (int k = 0; k < 2001; k++) dp[i][j][k] = -1;
  cout << do_dp(0, 0, 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>
using namespace std;
int n, k;
long long dp[4][1002][2002];
const long long MOD = 998244353;
long long do_dp(int move, int inx, int faltantes) {
  if (dp[move][inx][faltantes] != -1) {
    return dp[move][inx][faltantes];
  }
  if (inx == n && faltantes == 0) {
    return dp[move][inx][faltantes] = 1;
  }
  if (inx > n || faltantes < 0) return 0;
  long long ans = 0;
  if (inx == 0) {
    ans += do_dp(0, inx + 1, k - 1);
    ans %= MOD;
    ans += do_dp(1, inx + 1, k - 2);
    ans %= MOD;
    ans += do_dp(2, inx + 1, k - 2);
    ans %= MOD;
    ans += do_dp(3, inx + 1, k - 1);
    ans %= MOD;
    return dp[move][inx][faltantes] = ans;
  }
  ans += do_dp(0, inx + 1, faltantes - ((move == 3) ? 1 : 0));
  ans %= MOD;
  ans +=
      do_dp(1, inx + 1, faltantes - ((move == 2) ? 2 : ((move == 1) ? 0 : 1)));
  ans %= MOD;
  ans +=
      do_dp(2, inx + 1, faltantes - ((move == 1) ? 2 : ((move == 2) ? 0 : 1)));
  ans %= MOD;
  ans += do_dp(3, inx + 1, faltantes - ((move == 0) ? 1 : 0));
  ans %= MOD;
  return dp[move][inx][faltantes] = ans;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  ;
  cin >> n >> k;
  for (int i = 0; i < 4; i++)
    for (int j = 0; j < 1001; j++)
      for (int k = 0; k < 2001; k++) dp[i][j][k] = -1;
  cout << do_dp(0, 0, k);
}

```