Find the number, modulo 998244353, of sequences of length N consisting of 0, 1 and 2 such that none of their contiguous subsequences totals to X.

Constraints

* 1 \leq N \leq 3000
* 1 \leq X \leq 2N
* N and X are integers.

Input

Input is given from Standard Input in the following format:


N X


Output

Print the number, modulo 998244353, of sequences that satisfy the condition.

Examples

Input

3 3


Output

14


Input

8 6


Output

1179


Input

10 1


Output

1024


Input

9 13


Output

18402


Input

314 159


Output

459765451
#include<bits/stdc++.h>
#define maxn 3010
#define ll long long
#define mod 998244353
using namespace std;
int f[maxn][maxn * 2], C[maxn][maxn];
int main()
{
	int n, x;
	scanf("%d%d", &n, &x);
	for (int i = 0; i <= n; i++)
	{
		C[i][0] = 1;
		for (int j = 1; j <= i; j++)
			C[i][j] = (C[i - 1][j - 1] + C[i - 1][j]) % mod;
	}
	f[0][0] = 1;
	for (int i = 0; i <= n - 1; i++)
		for (int j = 0; j <= x; j++)
		{
			f[i + 1][j + 1] = (f[i + 1][j + 1] + f[i][j]) % mod;
			f[i + 1][j + 2] = (f[i + 1][j + 2] + f[i][j]) % mod;
		}
	int res = 0;
	for (int i = 0; i <= n; i++)
	{
		int tmp = 0;
		for (int j = 0; j <= x - 1; j++)
			tmp = (tmp + f[i][j]) % mod;
		for (int j = x + 1; j <= 2 * i; j += 2)
		{
			int need = (j - x + 1) / 2;
			if (2 * need <= i && x - 1 - 2 * need >= 0) tmp = (tmp + f[i - 2 * need][x - 1 - 2 * need]) % mod;
			if (2 * need > i && (x - 1) % 2 == 0 && (x - 1) / 2 + need == i) tmp = (tmp + 1) % mod;
		}
		res = (res + (ll)tmp * C[n][i] % mod) % mod;
	}
	printf("%d\n", res);
}