#include <bits/stdc++.h>
using namespace std;
const long long N = 1005;
const long long MOD = 998244353;
long long dp[N][2 * N][4];
long long n, k;
long long solve(long long i, long long j, long long p) {
  if (i == n) {
    if (j == k)
      return 1;
    else
      return 0;
  }
  long long &temp = dp[i][j][p];
  if (temp != -1) return temp;
  temp = 0;
  if (p == 0) {
    temp += solve(i + 1, j, 0) % MOD;
    temp += solve(i + 1, j + 1, 1) % MOD;
    temp += solve(i + 1, j + 1, 2) % MOD;
    temp += solve(i + 1, j + 1, 3) % MOD;
  }
  if (p == 3) {
    temp += solve(i + 1, j + 1, 0) % MOD;
    temp += solve(i + 1, j + 1, 1) % MOD;
    temp += solve(i + 1, j + 1, 2) % MOD;
    temp += solve(i + 1, j, 3) % MOD;
  }
  if (p == 1) {
    temp += solve(i + 1, j, 0) % MOD;
    temp += solve(i + 1, j, 1) % MOD;
    temp += solve(i + 1, j + 2, 2) % MOD;
    temp += solve(i + 1, j, 3) % MOD;
  }
  if (p == 2) {
    temp += solve(i + 1, j, 0) % MOD;
    temp += solve(i + 1, j + 2, 1) % MOD;
    temp += solve(i + 1, j, 2) % MOD;
    temp += solve(i + 1, j, 3) % MOD;
  }
  return temp;
}
int32_t main() {
  ios::sync_with_stdio(false), cin.tie(0);
  ;
  memset(dp, -1, sizeof(dp));
  cin >> n >> k;
  long long ans =
      (solve(1, 1, 0) + solve(1, 2, 1) + solve(1, 2, 2) + solve(1, 1, 3)) % MOD;
  cout << ans;
}

### 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;
const long long N = 1005;
const long long MOD = 998244353;
long long dp[N][2 * N][4];
long long n, k;
long long solve(long long i, long long j, long long p) {
  if (i == n) {
    if (j == k)
      return 1;
    else
      return 0;
  }
  long long &temp = dp[i][j][p];
  if (temp != -1) return temp;
  temp = 0;
  if (p == 0) {
    temp += solve(i + 1, j, 0) % MOD;
    temp += solve(i + 1, j + 1, 1) % MOD;
    temp += solve(i + 1, j + 1, 2) % MOD;
    temp += solve(i + 1, j + 1, 3) % MOD;
  }
  if (p == 3) {
    temp += solve(i + 1, j + 1, 0) % MOD;
    temp += solve(i + 1, j + 1, 1) % MOD;
    temp += solve(i + 1, j + 1, 2) % MOD;
    temp += solve(i + 1, j, 3) % MOD;
  }
  if (p == 1) {
    temp += solve(i + 1, j, 0) % MOD;
    temp += solve(i + 1, j, 1) % MOD;
    temp += solve(i + 1, j + 2, 2) % MOD;
    temp += solve(i + 1, j, 3) % MOD;
  }
  if (p == 2) {
    temp += solve(i + 1, j, 0) % MOD;
    temp += solve(i + 1, j + 2, 1) % MOD;
    temp += solve(i + 1, j, 2) % MOD;
    temp += solve(i + 1, j, 3) % MOD;
  }
  return temp;
}
int32_t main() {
  ios::sync_with_stdio(false), cin.tie(0);
  ;
  memset(dp, -1, sizeof(dp));
  cin >> n >> k;
  long long ans =
      (solve(1, 1, 0) + solve(1, 2, 1) + solve(1, 2, 2) + solve(1, 1, 3)) % MOD;
  cout << ans;
}

```