COGS 2189 帕秋莉的超级多项式

放模板啦！

以后打比赛的时候直接复制过来。

说句实话vector的效率真的不怎么样，但是似乎也还行，最主要是……写得比较爽。

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>
#include <cmath>
using namespace std;
typedef long long ll;
typedef vector <ll> poly;

namespace Poly {
    const int L = 1 << 20;
    const ll P = 998244353LL;

    int lim, pos[L];

    inline ll fpow(ll x, ll y) {
        ll res = 1;
        for (; y > 0; y >>= 1) {
            if (y & 1) res = res * x % P;
            x = x * x % P;
        }
        return res;
    }
    
    const ll inv2 = fpow(2, P - 2);

    template <typename T>
    inline void inc(T &x, T y) {
        x += y;
        if (x >= P) x -= P;
    }

    template <typename T>
    inline void sub(T &x, T y) {
        x -= y;
        if (x < 0) x += P;
    }

    inline void prework(int len) {
        int l = 0;
        for (lim = 1; lim < len; lim <<= 1, ++l);
        for (int i = 0; i < lim; i++)
            pos[i] = (pos[i >> 1] >> 1) | ((i & 1) << (l - 1));
    }

    inline void ntt(poly &c, int opt) {
        c.resize(lim, 0);
        for (int i = 0; i < lim; i++)
            if (i < pos[i]) swap(c[i], c[pos[i]]);
        for (int i = 1; i < lim; i <<= 1) {
            ll wn = fpow(3, (P - 1) / (i << 1));
            if (opt == -1) wn = fpow(wn, P - 2);
            for (int len = i << 1, j = 0; j < lim; j += len) {
                ll w = 1;
                for (int k = 0; k < i; k++, w = w * wn % P) {
                    ll x = c[j + k], y = w * c[j + k + i] % P;
                    c[j + k] = (x + y) % P, c[j + k + i] = (x - y + P) % P;
                }
            }
        }

        if (opt == -1) {
            ll inv = fpow(lim, P - 2);
            for (int i = 0; i < lim; i++) c[i] = c[i] * inv % P;
        }
    }

    inline poly operator * (const poly &x, const poly &y) {
        poly res, u = x, v = y;
        prework(u.size() + v.size() - 1);
        ntt(u, 1), ntt(v, 1);
        for (int i = 0; i < lim; i++) res.push_back(v[i] * u[i] % P);
        ntt(res, -1);
        res.resize(u.size() + v.size() - 1);
        return res;
    }

    poly getInv(poly x, int len) {
        x.resize(len);
        if (len == 1) {
            poly res;
            res.push_back(fpow(x[0], P - 2));
            return res;
        }
        poly y = getInv(x, (len + 1) >> 1);
        prework(len << 1);

        poly u = x, v = y, res;
        ntt(u, 1), ntt(v, 1);
        for (int i = 0; i < lim; i++) res.push_back(v[i] * (2LL - u[i] * v[i] % P + P) % P);
        ntt(res, -1);

        res.resize(len);
        return res;
    }

    inline void direv(poly &c) {
        for (int i = 0; i < (int)c.size() - 1; i++)
            c[i] = c[i + 1] * (i + 1) % P;
        c[c.size() - 1] = 0;
    }

    inline void integ(poly &c) {
        for (int i = (int)c.size() - 1; i > 0; i--)
            c[i] = c[i - 1] * fpow(i, P - 2) % P;
        c[0] = 0;
    }

    inline poly getLn(poly c) {
        poly a = getInv(c, (int)c.size());
        poly b = c;
        direv(b);

        poly res = b * a;
        res.resize(c.size());
        integ(res);
        return res;
    }
    
    poly getSqrt(poly x, int len) {
        x.resize(len);
        if (len == 1) {
            poly res;
            res.push_back(sqrt(x[0]));
            return res;
        }
        poly y = getSqrt(x, (len + 1) >> 1);
        poly u = x, v = y, w, res;
        w = getInv(y, len);
        
        prework(len << 1);
        ntt(u, 1), ntt(v, 1), ntt(w, 1);
        for (int i = 0; i < lim; i++) 
            res.push_back((v[i] * v[i] % P + u[i]) % P * w[i] % P * inv2 % P);
        ntt(res, -1);
        res.resize(len);
        
        return res;
    }
        
    poly getExp(poly x, int len) {
        x.resize(len, 0);
        if (len == 1) {
            poly res;
            res.push_back(1);
            return res;
        }
        
        poly y = getExp(x, (len + 1) >> 1);
        poly u = x, v = y, w = y, res;
        w.resize(len, 0);
        w = getLn(w);
        
        prework(len << 1);
        u[0] = (u[0] + 1 - w[0] + P) % P;
        for (int i = 1; i < (int)u.size(); i++) u[i] = (u[i] - w[i] + P) % P;
        
        ntt(u, 1), ntt(v, 1);
        for (int i = 0; i < lim; i++) res.push_back(u[i] * v[i] % P);
        ntt(res, -1);
        
        res.resize(len);
        return res;
    }
    
    inline poly fpow(poly x, ll y, int n) {
        x = getLn(x);
        for (int i = 0; i < n; i++) x[i] = x[i] * y % P;
        x = getExp(x, n);
        return x;
    }

}

template <typename T>
inline void read(T &X) {
    X = 0; char ch = 0; T op = 1;
    for (; ch > '9'|| ch < '0'; ch = getchar())
        if (ch == '-') op = -1;
    for (; ch >= '0' && ch <= '9'; ch = getchar())
        X = (X << 3) + (X << 1) + ch - 48;
    X *= op;
}

int main() {
//    freopen("Sample.txt", "r", stdin);    
    freopen("polynomial.in", "r", stdin);
    freopen("polynomial.out", "w", stdout);
    
    int n, k;
    read(n), read(k);
    poly a; a.resize(n);
    for (int i = 0; i < n; i++) read(a[i]);
    
    a = Poly :: getSqrt(a, n);
    
/*    for (int i = 0; i < n; i++)
        printf("%I64d%c", a[i], " 
"[i == n - 1]);    */
    
    a = Poly :: getInv(a, n);
    
/*    for (int i = 0; i < n; i++)
        printf("%I64d%c", a[i], " 
"[i == n - 1]);   */

    Poly :: integ(a);
    
/*    for (int i = 0; i < n; i++)
        printf("%I64d%c", a[i], " 
"[i == n - 1]);   */

    a = Poly :: getExp(a, n);
    
/*    for (int i = 0; i < n; i++)
        printf("%I64d%c", a[i], " 
"[i == n - 1]);   */

    a = Poly :: getInv(a, n);
    Poly :: inc(a[0], 1LL);
    
/*    for (int i = 0; i < n; i++)
        printf("%I64d%c", a[i], " 
"[i == n - 1]);    */

    a = Poly :: getLn(a);
    Poly :: inc(a[0], 1LL);
    
/*    for (int i = 0; i < n; i++)
        printf("%I64d%c", a[i], " 
"[i == n - 1]);    */

    a = Poly :: fpow(a, k, n);
    
/*    for (int i = 0; i < n; i++)
        printf("%I64d%c", a[i], " 
"[i == n - 1]);    */

    Poly :: direv(a);
    
    for (int i = 0; i < n; i++)
        printf("%lld%c", a[i], " 
"[i == n - 1]);
    return 0;
}