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;
typedef long long ll;
typedef pair<ll, ll> l_l;
typedef pair<int, int> i_i;
template<class T>
inline bool chmax(T &a, T b) {
    if(a < b) {
        a = b;
        return true;
    }
    return false;
}

template<class T>
inline bool chmin(T &a, T b) {
    if(a > b) {
        a = b;
        return true;
    }
    return false;
}

#define EPS (1e-7)
#define INF (1e9)
#define PI (acos(-1))
const ll mod = 998244353;
ll inv[10000100];
ll FactorialInv[10000100];
ll Factorial[10000100];
ll beki(ll a, ll b){
    a %= mod;
    if(b == 0){
        return 1;
    }
    ll ans = beki(a, b / 2);
    ans = ans * ans % mod;
    if(b % 2 == 1){
        ans = ans * a % mod;
    }
    return ans;
}
void init_combination(){
    const int MAX = 10000002;
    Factorial[0] = 1;
    inv[0] = 1;
    for(int i = 1; i <= MAX; i++){
        Factorial[i] = Factorial[i - 1] * i % mod;
    }
    FactorialInv[MAX] = beki(Factorial[MAX], mod - 2);
    for(ll i = MAX - 1; i >= 0; i--) {
        FactorialInv[i] = FactorialInv[i+1] * (i+1) % mod;
    }
    for(int i = 1; i <= MAX; i++) {
        inv[i] = FactorialInv[i] * Factorial[i-1] % mod;
    }
}
ll combination(ll a, ll b){
    if((a == b) || (b == 0)){
        return 1;
    }
    if(a < b) return 0;
    ll ans = Factorial[a] * FactorialInv[b] % mod;
    ans = ans * FactorialInv[a - b] % mod;
    return ans;
}
ll N, X;
ll ans;

int main() {
    //cout.precision(10);
    cin >> N >> X;
    init_combination();
    for(ll sum = 0; sum <= 2 * N; sum++) {
        if(sum >= X and sum % 2 == X % 2) continue;
        if(sum < X) {
            for(ll num = 0; num <= sum; num++) {
                ll two = sum - num;
                ll one = num - two;
                ll zero = N - two - one;
                if(two < 0 or one < 0 or zero < 0) continue;
                ll tmp = combination(N, one) * combination(N - one, two) % mod;
                ans += tmp;
                ans %= mod;
            }
        }
        if(sum >= X) {
            ll sidetwo = (sum - X + 1);
            for(ll mid = 0; mid <= sum; mid++) {
                ll two = (sum - 2 * sidetwo) - mid;
                ll one = mid - two;
                ll zero = N - sidetwo - two - one;
                //cerr << sum << " " << sidetwo << " " << two << " " << one << " " << zero << endl;
                if(sidetwo < 0 or two < 0 or one < 0 or zero < 0) continue;
                ll tmp = combination(N, zero) * combination(one + two, one) % mod;
                ans += tmp;
                ans %= mod;
            }
            if(sidetwo * 2 > sum and X % 2 == 1) {
                ll tmp = combination(N, sum / 2);
                //cerr << sum << " " << sidetwo << endl;
                ans += tmp;
                ans %= mod;
            }
        }
    }
    cout << ans << endl;
    return 0;
}
