#include <bits/stdc++.h>
using namespace std;
const int N = 1002, MOD = 998244353;
int n, k;
long long dp[N][N << 1][2][2];
long long solve(int i, int k, bool u, bool l) {
  if (k < 0) return 0;
  if (i == n + 1) return !k;
  long long &ret = dp[i][k][u][l];
  if (~ret) return ret;
  ret = 0;
  for (int(x) = (0); (x) <= (int)(1); (x)++)
    for (int(y) = (0); (y) <= (int)(1); (y)++) {
      if (x == y) {
        if (x == u || y == l)
          ret += solve(i + 1, k, x, y);
        else
          ret += solve(i + 1, k - 1, x, y);
      } else {
        if (x == u && y == l)
          ret += solve(i + 1, k, x, y);
        else if (x == u || y == l)
          ret += solve(i + 1, k - 1, x, y);
        else
          ret += solve(i + 1, k - 2, x, y);
      }
    }
  return ret %= MOD;
}
int main() {
  scanf("%d%d", &n, &k);
  memset(dp, -1, sizeof dp);
  long long ans = 0;
  for (int(i) = (0); (i) <= (int)(1); (i)++)
    for (int(j) = (0); (j) <= (int)(1); (j)++)
      ans += solve(2, k - 1 - (i != j), i, j);
  printf("%lld\n", ans %= MOD);
  return 0;
}

### Prompt

Develop a solution in CPP to the problem described below:

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 int N = 1002, MOD = 998244353;
int n, k;
long long dp[N][N << 1][2][2];
long long solve(int i, int k, bool u, bool l) {
  if (k < 0) return 0;
  if (i == n + 1) return !k;
  long long &ret = dp[i][k][u][l];
  if (~ret) return ret;
  ret = 0;
  for (int(x) = (0); (x) <= (int)(1); (x)++)
    for (int(y) = (0); (y) <= (int)(1); (y)++) {
      if (x == y) {
        if (x == u || y == l)
          ret += solve(i + 1, k, x, y);
        else
          ret += solve(i + 1, k - 1, x, y);
      } else {
        if (x == u && y == l)
          ret += solve(i + 1, k, x, y);
        else if (x == u || y == l)
          ret += solve(i + 1, k - 1, x, y);
        else
          ret += solve(i + 1, k - 2, x, y);
      }
    }
  return ret %= MOD;
}
int main() {
  scanf("%d%d", &n, &k);
  memset(dp, -1, sizeof dp);
  long long ans = 0;
  for (int(i) = (0); (i) <= (int)(1); (i)++)
    for (int(j) = (0); (j) <= (int)(1); (j)++)
      ans += solve(2, k - 1 - (i != j), i, j);
  printf("%lld\n", ans %= MOD);
  return 0;
}

```