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 <algorithm>
#include <iostream>
#include <cstdio>
#define N 3003
using namespace std;
const int Mod = 998244353;

int n, fac[N], inv[N], ifac[N];

void prework() {
    fac[0] = inv[1] = ifac[0] = 1;
    for (int i = 1; i <= n; ++i)
        fac[i] = 1ll * fac[i - 1] * i % Mod;
    for (int i = 2; i <= n; ++i)
        inv[i] = 1ll * inv[Mod % i] * (Mod - Mod / i) % Mod;
    for (int i = 1; i <= n; ++i)
        ifac[i] = 1ll * ifac[i - 1] * inv[i] % Mod;
}

inline int C(int x, int y) {
    return x < y ? 0 : 1ll * fac[x] * ifac[y] % Mod * ifac[x - y] % Mod;
}

int x, f[N][N << 1];

int main() {
#ifdef whyqx
    freopen("work.in", "r", stdin);
    freopen("work.out", "w", stdout);
#endif
    cin >> n >> x;
    prework();
    f[0][0] = 1;
    for (int i = 0; i < n; ++i)
        for (int j = 0; j < (n << 1); ++j)
            (f[i + 1][j + 1] += f[i][j]) %= Mod,
            (f[i + 1][j + 2] += f[i][j]) %= Mod;
    int ans = 0;
    for (int i = 1; i <= n; ++i) {
        int tmp = 0;
        for (int j = 0; j < x; ++j)
            (tmp += f[i][j]) %= Mod;
        for (int j = x + 1; j <= (i << 1); j += 2) {
            if (j < i) continue;
            int a = i - (j - (x - 1)), b = j - 2 * (j - (x - 1));
            if (2 * (x - 1) > j) (tmp += (a >= 0 && b >= 0 ? f[a][b] : 0)) %= Mod;
            else (tmp += ((j == (i << 1)) && (x & 1))) %= Mod;
        }
        (ans += 1ll * tmp * C(n, i) % Mod) %= Mod;
    }
    cout << ans + 1 << endl;
    return 0;
}
