#include <bits/stdc++.h>
using namespace std;
bool isPrime(long long int n) {
  if (n <= 1) return false;
  if (n <= 3) return true;
  if (n % 2 == 0 || n % 3 == 0) return false;
  for (long long int i = 5; i * i <= n; i = i + 6)
    if (n % i == 0 || n % (i + 2) == 0) return false;
  return true;
}
long long int dp[1005][2005][(1 << 2) + 1];
int n, k;
long long int add(long long int a, long long int b) {
  return (a % 998244353 + b % 998244353) % 998244353;
}
long long int solve(int pos, int com, int mask) {
  if (dp[pos][com][mask] != -1) return dp[pos][com][mask];
  if (pos == n) return (com == k) ? 1 : 0;
  long long int ans = 0;
  for (long long int i = 0; i < 4; i++) {
    int ncom = 0;
    if (pos == 0)
      ncom = (i == 0 || i == 3) ? 1 : 2;
    else {
      if ((i ^ mask) == 3)
        ncom = (i == 0 || i == 3) ? 1 : 2;
      else if ((i ^ mask) == 1 || (i ^ mask) == 2)
        ncom = (i == 0 || i == 3) ? 0 : 1;
    }
    ans = add(ans, solve(pos + 1, com + ncom, i));
  }
  return dp[pos][com][mask] = ans;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> k;
  memset(dp, -1, sizeof(dp));
  cout << solve(0, 0, 0);
}

### Prompt

Please create a solution in cpp 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;
bool isPrime(long long int n) {
  if (n <= 1) return false;
  if (n <= 3) return true;
  if (n % 2 == 0 || n % 3 == 0) return false;
  for (long long int i = 5; i * i <= n; i = i + 6)
    if (n % i == 0 || n % (i + 2) == 0) return false;
  return true;
}
long long int dp[1005][2005][(1 << 2) + 1];
int n, k;
long long int add(long long int a, long long int b) {
  return (a % 998244353 + b % 998244353) % 998244353;
}
long long int solve(int pos, int com, int mask) {
  if (dp[pos][com][mask] != -1) return dp[pos][com][mask];
  if (pos == n) return (com == k) ? 1 : 0;
  long long int ans = 0;
  for (long long int i = 0; i < 4; i++) {
    int ncom = 0;
    if (pos == 0)
      ncom = (i == 0 || i == 3) ? 1 : 2;
    else {
      if ((i ^ mask) == 3)
        ncom = (i == 0 || i == 3) ? 1 : 2;
      else if ((i ^ mask) == 1 || (i ^ mask) == 2)
        ncom = (i == 0 || i == 3) ? 0 : 1;
    }
    ans = add(ans, solve(pos + 1, com + ncom, i));
  }
  return dp[pos][com][mask] = ans;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> k;
  memset(dp, -1, sizeof(dp));
  cout << solve(0, 0, 0);
}

```