#include <bits/stdc++.h>
using namespace std;
long long int mod = 998244353;
long long int n, k, dp[1001][2001][4];
long long int Mod(long long int a, long long int b) {
  long long int ans = ((a % mod) + (b % mod)) % mod;
  return ans;
}
long long int func(long long int i, long long int tot, long long int prev) {
  if (i == n + 1) {
    return (tot == k);
  }
  if (dp[i][tot][prev] != -1) {
    return dp[i][tot][prev];
  }
  long long int ans = 0;
  if (prev == 0) {
    ans = Mod(ans, func(i + 1, tot, 0));
    ans = Mod(ans, func(i + 1, tot + 1, 1));
    ans = Mod(ans, func(i + 1, tot + 1, 2));
    ans = Mod(ans, func(i + 1, tot + 1, 3));
  } else if (prev == 1) {
    ans = Mod(ans, func(i + 1, tot + 1, 0));
    ans = Mod(ans, func(i + 1, tot, 1));
    ans = Mod(ans, func(i + 1, tot + 1, 2));
    ans = Mod(ans, func(i + 1, tot + 1, 3));
  } else if (prev == 2) {
    ans = Mod(ans, func(i + 1, tot, 0));
    ans = Mod(ans, func(i + 1, tot, 1));
    ans = Mod(ans, func(i + 1, tot, 2));
    ans = Mod(ans, func(i + 1, tot + 2, 3));
  } else {
    ans = Mod(ans, func(i + 1, tot, 0));
    ans = Mod(ans, func(i + 1, tot, 1));
    ans = Mod(ans, func(i + 1, tot + 2, 2));
    ans = Mod(ans, func(i + 1, tot, 3));
  }
  return dp[i][tot][prev] = ans;
}
int main() {
  long long int i, j, ans = 0;
  cin >> n >> k;
  memset(dp, -1, sizeof dp);
  ans = Mod(ans, func(2, 1, 0));
  ans = Mod(ans, func(2, 1, 1));
  ans = Mod(ans, func(2, 2, 2));
  ans = Mod(ans, func(2, 2, 3));
  cout << ans << endl;
  return 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;
long long int mod = 998244353;
long long int n, k, dp[1001][2001][4];
long long int Mod(long long int a, long long int b) {
  long long int ans = ((a % mod) + (b % mod)) % mod;
  return ans;
}
long long int func(long long int i, long long int tot, long long int prev) {
  if (i == n + 1) {
    return (tot == k);
  }
  if (dp[i][tot][prev] != -1) {
    return dp[i][tot][prev];
  }
  long long int ans = 0;
  if (prev == 0) {
    ans = Mod(ans, func(i + 1, tot, 0));
    ans = Mod(ans, func(i + 1, tot + 1, 1));
    ans = Mod(ans, func(i + 1, tot + 1, 2));
    ans = Mod(ans, func(i + 1, tot + 1, 3));
  } else if (prev == 1) {
    ans = Mod(ans, func(i + 1, tot + 1, 0));
    ans = Mod(ans, func(i + 1, tot, 1));
    ans = Mod(ans, func(i + 1, tot + 1, 2));
    ans = Mod(ans, func(i + 1, tot + 1, 3));
  } else if (prev == 2) {
    ans = Mod(ans, func(i + 1, tot, 0));
    ans = Mod(ans, func(i + 1, tot, 1));
    ans = Mod(ans, func(i + 1, tot, 2));
    ans = Mod(ans, func(i + 1, tot + 2, 3));
  } else {
    ans = Mod(ans, func(i + 1, tot, 0));
    ans = Mod(ans, func(i + 1, tot, 1));
    ans = Mod(ans, func(i + 1, tot + 2, 2));
    ans = Mod(ans, func(i + 1, tot, 3));
  }
  return dp[i][tot][prev] = ans;
}
int main() {
  long long int i, j, ans = 0;
  cin >> n >> k;
  memset(dp, -1, sizeof dp);
  ans = Mod(ans, func(2, 1, 0));
  ans = Mod(ans, func(2, 1, 1));
  ans = Mod(ans, func(2, 2, 2));
  ans = Mod(ans, func(2, 2, 3));
  cout << ans << endl;
  return 0;
}

```