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>
using namespace std;
const int MAXN = 3e3 + 5;
const int P = 998244353;
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
template <typename T> void chkmax(T &x, T y) {x = max(x, y); }
template <typename T> void chkmin(T &x, T y) {x = min(x, y); }
template <typename T> void read(T &x) {
	x = 0; int f = 1;
	char c = getchar();
	for (; !isdigit(c); c = getchar()) if (c == '-') f = -f;
	for (; isdigit(c); c = getchar()) x = x * 10 + c - '0';
	x *= f;
}
template <typename T> void write(T x) {
	if (x < 0) x = -x, putchar('-');
	if (x > 9) write(x / 10);
	putchar(x % 10 + '0');
}
template <typename T> void writeln(T x) {
	write(x);
	puts("");
}
int binom[MAXN][MAXN];
void update(int &x, int y) {
	x += y;
	if (x >= P) x -= P;
}
int getans(int n, int x) {
	int ans = 0;
	if (2 * n < x || x % 2 == 1) ans = 1;
	for (int i = n; i <= 2 * n - 1; i++) {
		if (i < x) update(ans, binom[n][i - n]);
		else {
			if ((i - x) % 2 == 0) continue;
			int cnt = (i - x + 1) / 2;
			if (2 * cnt >= n) continue;
			int rp = n - 2 * cnt, rs = i - 4 * cnt;
			if (rs >= rp && rs <= 2 * rp) update(ans, binom[rp][rs - rp]);
		}
	}
	return ans;
}
int main() {
	int n, x; read(n), read(x);
	for (int i = 0; i <= n; i++) {
		binom[i][0] = 1;
		for (int j = 1; j <= i; j++)
			binom[i][j] = (binom[i - 1][j - 1] + binom[i - 1][j]) % P;
	}
	int ans = 0;
	for (int i = 0; i <= n; i++)
		update(ans, 1ll * binom[n][i] * getans(n - i, x) % P);
	writeln(ans);
	return 0;
}
