ARC116D

// Problem: D - I Wanna Win The Game
// Contest: AtCoder - AtCoder Regular Contest 116
// URL: https://atcoder.jp/contests/arc116/tasks/arc116_d
// Memory Limit: 1024 MB
// Time Limit: 2000 ms
//
// Powered by CP Editor (https://cpeditor.org)

#include <assert.h>
#include <bits/stdc++.h>
#include <atcoder/modint>

using namespace std;
#define dbg(...) logger(#__VA_ARGS__, __VA_ARGS__)
template <typename... Args> void logger(string vars, Args &&... values)
{
    cerr << vars << " = ";
    string delim = "";
    (..., (cerr << delim << values, delim = ", "));
    cerr << endl;
}

template <class T> inline auto vv(int m) { return vector<vector<T>>(m, vector<T>(m)); }
template <class T> inline auto vv(int m, int n) { return vector<vector<T>>(m, vector<T>(n)); }
template <class T, T init> inline auto vv(int m) { return vector<vector<T>>(m, vector<T>(m, init)); }
template <class T, T init> inline auto vv(int m, int n) { return vector<vector<T>>(m, vector<T>(n, init)); }

template <class T> using mpq = priority_queue<T, vector<T>, greater<T>>;
using vi = vector<int>;
using ll = long long;
using pii = pair<int, int>;
using mint = atcoder::modint998244353;

const int mod = 998244353;
int n, m;
vi f;

mint comb(int n, int r)
{
    /*
    static auto dp = vv<int>(5001);
    if (dp[n][r] != 0)
        return dp[n][r];
    assert(n >= r);
    int step = min(r, n - r);
    mint ans = 1, ub = n, lb = r;
    for (int i = 0; i < step; ++i) {
        ans *= ub / lb;
        --ub, --lb;
    }
    dp[n][r] = ans.val();
    return ans;
    */

    static vi dp(5001);
    if (dp[0] == 0) {
        dp[0] = 1;
        for (int i = 1; i <= n; ++i) {
            for (int j = i; j > 0; --j)
                dp[j] = (dp[j] + dp[j - 1]) % mod;
        }
    }
    return dp[r];
}

int getf(int x)
{
    if (f[x] != -1)
        return f[x];
    if (x % 2)
        return f[x] = 0;
    mint ans = 0;

    /*
    WA
    for (int i = min(x, n); i >= 0; i -= 2) {
        ans += getf((x - i) / 2) * comb(n, i);
    }
    */

    // AC
    for (int i = 0; i <= min(x, n); i += 2) {
        ans += mint(getf((x - i) / 2)) * comb(n, i);
    }

    return f[x] = ans.val();
}

int main(int argc, char **argv)
{
    cin >> n >> m;
    f = vi(m + 1, -1);
    f[0] = 1;
    if (m % 2) {
        cout << 0 << endl;
        return 0;
    }
    int ans;
    for (int i = 2; i <= m; ++i)
        ans = getf(i);
    cout << ans << endl;
    return 0;
};