///////////////////////////////////////////////////////////////////////////////

#include <bits/stdc++.h>
#include <unistd.h>
#include <time.h>
#include <sys/time.h>

using namespace std;

///////////////////////////////////////////////////////////////////////////////

#define DEBUG 0

#define pb push_back
#define V vector
#define M unordered_map
#define S static
#define PI  (3.1415926535)

#define rep(i,n) for(ll i=0LL; i<n; ++i)
#define srep(i,s,n) for(ll i=s; i<n; ++i)
#define rrep(i,n) for(ll i=n-1LL; i>=0LL; --i)
#define ALL(a) (a).begin(),(a).end()
#define RALL(a) (a).rbegin(),(a).rend()
#define CIN(x) do { \
        assert(!cin.eof()); \
        cin >> x; \
        assert(!cin.fail()); \
} while(0);
#if DEBUG
#define debug_print(...) _debug_print(__VA_ARGS__)
#define debug_printf(...) printf(__VA_ARGS__)
#define debug_print_time _debug_print_time
#else // DEBUG
#define debug_print(...)
#define debug_printf(...)
#define debug_print_time
#endif // DEBUG

typedef long long ll;
typedef unsigned long long ull;
typedef tuple<ll, ll> t2;
typedef tuple<ll, ll, ll> t3;
typedef tuple<ll, ll, ll, ll> t4;
typedef tuple<ll, ll, ll, ll, ll> t5;
template <typename T>
using priority_queue_incr = priority_queue<T, V<T>, greater<T> >;

///////////////////////////////////////////////////////////////////////////////

template <typename TT, typename T>
T get_m(M<TT, T> &m, TT k, T default_value)
{
    if (m.find(k) == m.end()) return m[k] = default_value;
    return m[k];
}

template <typename TT, typename T>
void incr_m(M<TT, T> &m, TT k)
{
    if (m.find(k) == m.end()) m[k] = 0;
    m[k]++;
}

void llin(ll &a)
{
    CIN(a);
}

void llinl1(auto &v, ll count)
{
    for (ll i = 0LL; i < count; ++i) {
        ll a;
        CIN(a);
        v.push_back(a);
    }
}

void llinl2(auto &v, ll count)
{
    for (ll i = 0LL; i < count; ++i) {
        ll a, b;
        CIN(a >> b);
        v.push_back(t2(a, b));
    }
}

void llinl3(auto &v, ll count)
{
    for (ll i = 0LL; i < count; ++i) {
        ll a, b, c;
        CIN(a >> b >> c);
        v.push_back(t3(a, b, c));
    }
}

void llinl4(auto &v, ll count)
{
    for (ll i = 0LL; i < count; ++i) {
        ll a, b, c, d;
        CIN(a >> b >> c >> d);
        v.push_back(t4(a, b, c, d));
    }
}

void llina(auto &v, ll count)
{
    llinl1(v, count);
}

template <typename T>
void sort(V<T> &v)
{
    sort(v.begin(), v.end());
}

template <typename T>
void sort_reverse(V<T> &v)
{
    sort(v.begin(), v.end(), greater<T>());
}

void _debug_print(auto x)
{
    cout << x << endl;
}

void _debug_print(const t2 &x)
{
    ll x1 = get<0>(x);
    ll x2 = get<1>(x);
    cout << "-- " << x1 << " -- " << x2 << endl;
}

void _debug_print(const t3 &x)
{
    ll x1 = get<0>(x);
    ll x2 = get<1>(x);
    ll x3 = get<2>(x);
    cout << "-- " << x1 << " -- " << x2 << " -- " << x3 << endl;
}

void _debug_print(const t4 &x)
{
    ll x1 = get<0>(x);
    ll x2 = get<1>(x);
    ll x3 = get<2>(x);
    ll x4 = get<3>(x);
    cout << "-- " << x1 << " -- " << x2
         << " -- " << x3 << " -- " << x4 << endl;
}

template <typename T>
void _debug_print(T xarray[], ll n)
{
    rep (i, n) _debug_print(xarray[i]);
}

template <typename T>
void _debug_print(const V<T> &xlist)
{
    for (auto x : xlist) {
        cout << "-- ";
        _debug_print(x);
    }
}

template <typename T>
void _debug_print(const set<T> &xset)
{
    for (auto x : xset) {
        cout << "-- ";
        _debug_print(x);
    }
}

template <typename TT, typename T>
void _debug_print(const M<TT, T> &xlist)
{
    for (auto x : xlist) {
        TT k = x.first;
        T v = x.second;
        cout << "====" << endl;
        cout << "K=";
        _debug_print(k);
        cout << "V=";
        _debug_print(v);
    }
}

void _debug_print_time(const char *prefix)
{
    struct timeval tv;
    gettimeofday(&tv, NULL);
    struct tm *tm = localtime(&tv.tv_sec);
    printf("-- %s %02d:%02d:%02d.%06ld\n",
           prefix, tm->tm_hour, tm->tm_min, tm->tm_sec, tv.tv_usec);
}








// #define MOD   (1000000007LL)
#define MOD   (998244353LL)

ll mod_mlt(ll x, ll y, ll mod)
{
    ll ret = 0LL;
    x %= mod;

    while (y) {
        if (y & 1LL) {
            ret += x;
            ret %= mod;
        }
        y >>= 1;
        x <<= 1;
        x %= mod;
    }

    return ret;
}

// O(log(exp))
ll mod_pow(ll base, ll exp, ll mod)
{
    ll ret = 1LL;

    for ( ; exp; ) {
        if (exp & 1LL) {
            ret *= base;
            ret %= mod;
        }
        base = (base * base) % mod;
        exp >>= 1;
    }

    return ret;
}

// O(log(mod))
ll mod_inv(ll x, ll mod)
{
    // available only when mod is prime
    return mod_pow(x, mod - 2LL, mod);
}

ull mod_combination(ll x, ll y, ll mod)
{
    if (y > x / 2LL) y = x - y;

    ll ret = 1;

    for (ll i = 0LL; i < y; ++i) {
        ret = (ret * x--) % mod;
        ret = (ret * mod_inv(i + 1LL, mod)) % mod;
    }

    return ret;
}

void make_perms(ll perms[], ll perm_invs[], ll size, ll mod)
{
    perms[0] = 1LL;
    srep (i, 1, size) {
        perms[i] = perms[i-1] * i;
        perms[i] %= mod;
    }

    rep (i, size) {
        perm_invs[i] = mod_inv(perms[i], mod);
    }
}



///////////////////////////////////////////////////////////////////////////////

void _main();
int main()
{
    cout << setprecision(12);
#if !DEBUG
    ios::sync_with_stdio(false);
    cin.tie(0);
#endif

    _main();
    return 0;
}

void solve(ll cnts[3005], const ll dp[3005][6005], ll n, ll x, ll total)
{
    if (total < x) {
        rep (len, n+1) {
            cnts[len] += dp[len][total];
            cnts[len] %= MOD;
        }
        return;
    }

    if ((x & 1LL) == (total & 1LL)) return;
    // if (!(total & 1LL) && (x & 1LL)) cnts[total/2LL]++;

    ll edge_sum = total - (x - 1LL);
    edge_sum *= 2LL;
    ll center_sum = total - edge_sum;
    ll edge_len = edge_sum / 2LL;

    if (center_sum < 0) return;

    rep (center_len, n+1) {
        ll len = edge_len + center_len;
        if (len > n) break;
        assert(center_sum >= 0LL);
        assert(center_sum <= 6000LL);
        assert(center_len >= 0LL);
        assert(center_len <= 3000LL);
        debug_printf("==== len=%lld center_len=%lld center_sum=%lld "
                     "dp[len][center_sum]=%lld\n",
                     len, center_len, center_sum, dp[center_len][center_sum]);
        cnts[len] += dp[center_len][center_sum];
        cnts[len] %= MOD;
        if (center_len && center_len * 2LL == center_sum) cnts[len]--;
        if (cnts[len] < 0) cnts[len] += MOD;
    }
}

void _main()
{
    ll n; llin(n);
    ll x; llin(x);

    S ll dp[3005][6005];
    memset(dp, 0, sizeof(dp));
    dp[0][0] = 1;
    srep (len, 1, n+1) {
        srep (sum, 1, n * 2LL + 1LL) {
            dp[len][sum] += dp[len-1][sum-1];
            dp[len][sum] %= MOD;
            if (sum >= 2LL) dp[len][sum] += dp[len-1][sum-2];
            dp[len][sum] %= MOD;
        }
    }
    dp[0][0] = 0;

    rep (i, 6) {
        debug_printf("---- dp[%lld]\n", i);
        debug_print(dp[i], 12);
    }

    S ll cnts[3005] = {};
    srep (total, 1, 6001) solve(cnts, dp, n, x, total);

    if (x & 1LL) {
        srep (len, x / 2LL + 1LL, n+1LL) {
            cnts[len]++;
            cnts[len] %= MOD;
        }
    }

    debug_printf("---- cnts\n");
    debug_print(cnts, 16);

    S ll perms[6020];
    S ll perm_invs[6020];
    make_perms(perms, perm_invs, 6020, MOD);

    ll ans = 1;
    rep (len, n+1) {
        ll cnt = cnts[len];
        cnt *= perms[n];
        cnt %= MOD;
        cnt *= perm_invs[len];
        cnt %= MOD;
        cnt *= perm_invs[n-len];
        cnt %= MOD;
        ans += cnt;
        ans %= MOD;
    }

    debug_printf("---- ans\n");
    cout << ans << endl;
}

///////////////////////////////////////////////////////////////////////////////


Measured memory_bytes: 141440