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| #include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#define MAXN 400010
#define MOD 998244353
#define G 3
#define I 86583718
void read(int &x) {
int f = 1;
x = 0;
char c = getchar();
while (c < '0' || c > '9') {if (c == '-') f = -1; c = getchar();}
while (c >= '0' && c <= '9') {x = x * 10 + c - '0'; c = getchar();}
x *= f;
}
void write(int x) {
if (x < 0) {
putchar('-');
x = -x;
}
if (x > 9) write(x / 10);
putchar(x % 10 + '0');
}
int qpow(int a, int b) {
int res = 1;
while (b) {
if (b & 1) res = (1LL * res * a) % MOD;
b >>= 1;
a = (1LL * a * a) % MOD;
}
return res % MOD;
}
int n, m;
int a[MAXN], b[MAXN], f[MAXN], rev[MAXN];
void ntt(int *a, int n, int f) {
for (int i = 0; i < n; i++) {
if (1LL * i < rev[i]) {
std::swap(a[i], a[rev[i]]);
}
}
for (int i = 1; i < n; i <<= 1) {
int wn = qpow(G, (MOD - 1) / ((long long)i << 1));
for (int j = 0; j < n; j += ((long long)i << 1)) {
int w = 1LL;
for (int k = 0; k < i; ++k, w = 1LL * w * wn % MOD) {
int x = a[j + k], y = 1LL * w * a[j + k + i] % MOD;
a[j + k] = (x + y) % MOD, a[j + k + i] = (x - y + MOD) % MOD;
}
}
}
if (f == 1) return;
int tmp = qpow(n, MOD - 2);
std::reverse(a + 1, a + n);
for (int i = 0; i < n; i++) {
a[i] = 1LL * a[i] * tmp % MOD;
}
}
int c[MAXN];
void inv(int d, int *a, int *b) {
if (d == 1) {
b[0] = qpow(a[0], MOD - 2);
return;
}
inv((d + 1) >> 1, a, b);
int l = 0, _n = 1;
while (_n < (d << 1)) _n <<= 1, l++;
for (int i = 1; i < _n; i++) {
rev[i] = (rev[i >> 1] >> 1) | (((long long)i & 1) << (l - 1));
}
for (int i = 0; i < d; i++) c[i] = a[i];
for (int i = d; i < _n; i++) c[i] = 0;
ntt(c, _n, 1);
ntt(b, _n, 1);
for (int i = 0; i < _n; i++) {
b[i] = (2 - 1LL * b[i] * c[i] % MOD + MOD) % MOD * b[i] % MOD;
}
ntt(b, _n, -1);
for (int i = d; i < _n; i++) {
b[i] = 0;
}
return;
}
int d[MAXN], e[MAXN];
void Deriv(int *a, int *b, int l) {
for (int i = 1; i < l; i++) {
b[i - 1] = 1LL * a[i] * i % MOD;
}
b[l - 1] = 0;
}
void Integ(int *a, int *b, int l) {
for (int i = 1; i < l; i++) {
b[i] = 1LL * a[i - 1] * qpow(i, MOD - 2) % MOD;
}
b[0] = 0;
}
void Ln(int *a, int *b, int k) {
for (int i = 0; i < 2 * k; i++) d[i] = 0;
inv(k, a, d);
Deriv(a, e, k);
int l = 0, _n = 1;
while (_n < (k << 1)) _n <<= 1, l++;
for (int i = 1; i < _n; i++) {
rev[i] = (rev[i >> 1] >> 1) | (((long long)i & 1) << (l - 1));
}
ntt(e, _n, 1);
ntt(d, _n, 1);
for (int i = 0; i < _n; i++) {
e[i] = 1LL * e[i] * d[i] % MOD;
}
ntt(e, _n, -1);
Integ(e, b, k);
}
int g[MAXN], h[MAXN];
void Exp(int *a, int *b, int k) {
if (k == 1) {
b[0] = 1;
return;
}
Exp(a, b, (k + 1) >> 1);
int l = 0, _n = 1;
while (_n < (k << 1)) _n <<= 1, l++;
for (int i = 1; i < _n; i++) {
rev[i] = (rev[i >> 1] >> 1) | (((long long)i & 1) << (l - 1));
}
for (int i = 0; i < (k << 1); i++) g[i] = h[i] = 0;
Ln(b, g, k);
for (int i = 0; i < k; i++) h[i] = a[i];
ntt(b, _n, 1);
ntt(h, _n, 1);
ntt(g, _n, 1);
for (int i = 0; i < _n; i++) {
b[i] = 1LL * (1LL - g[i] + h[i] + MOD) * b[i] % MOD;
}
ntt(b, _n, -1);
for (int i = k; i < _n; i++) {
b[i] = 0;
}
return;
}
void mult(int *a, int *b, int *c, int n) {
int _n = 1, l = 0;
while (_n < (n << 1)) _n <<= 1, l++;
for (int i = 1; i < _n; i++) {
rev[i] = (rev[i >> 1] >> 1) | (((1LL * i) & 1) << (l - 1));
}
ntt(a, _n, 1);
ntt(b, _n, 1);
for (int i = 0; i < _n; i++) {
c[i] = 1LL * a[i] * b[i] % MOD;
}
ntt(c, _n, -1);
}
int fl, tt[MAXN], rr[MAXN], gg[MAXN], pp[MAXN], kk[MAXN], ss[MAXN], yy[MAXN], hh[MAXN], ww[MAXN];
void clear() {
for (int i = 1; i < (n << 2); i++) {
b[i] = c[i] = h[i] = g[i] = d[i] = e[i] = 0;
tt[i] = rr[i] = kk[i] = ss[i] = yy[i] = hh[i] = 0;
}
}
void _clr() {
for (int i = 1; i < (n << 2); i++) {
ww[i] = pp[i] = gg[i] = tt[i] = rr[i] = kk[i] = ss[i] = yy[i] = hh[i] = 0;
}
}
void sqrt(int *a, int *b, int d) {
clear();
Ln(a, kk, d);
int inv2 = qpow(2, MOD - 2);
for (int i = 0; i < d; i++) {
kk[i] = (1LL * kk[i] * inv2) % MOD;
}
clear();
Exp(kk, b, d);
}
void pow(int *a, int *b, int k, int d) {
clear();
_clr();
Ln(a, kk, n);
clear();
for (int i = 0; i < d; i++) {
kk[i] = 1LL * kk[i] * k % MOD;
}
Exp(kk, b, d);
return;
}
void sin(int *a, int *b, int d) {
clear();
_clr();
for (int i = 0; i < d; i++) {
tt[i] = 1LL * a[i] * I % MOD;
}
Exp(tt, rr, d);
clear();
inv(d, rr, gg);
for (int i = 0; i < d; i++) {
b[i] = 1LL * (rr[i] - gg[i] + MOD) * qpow(I * 2, MOD - 2) % MOD;
}
}
void cos(int *a, int *b, int d) {
clear();
_clr();
for (int i = 0; i < d; i++) {
tt[i] = 1LL * a[i] * I % MOD;
}
Exp(tt, rr, d);
clear();
inv(d, rr, gg);
for (int i = 0; i < d; i++) {
b[i] = 1LL * (rr[i] + gg[i]) * qpow(2, MOD - 2) % MOD;
}
}
void arcsin(int *a, int *b, int d) {
clear();
_clr();
for (int i = 0; i < d; i++) {
ww[i] = gg[i] = a[i];
}
Deriv(a, tt, d);
mult(gg, ww, pp, d);
for (int i = 0; i < d; i++) {
pp[i] = (MOD - pp[i]) % MOD;
}
pp[0] = (pp[0] + 1) % MOD;
sqrt(pp, ss, d);
clear();
inv(d, ss, yy);
clear();
mult(tt, yy, hh, d);
clear();
Integ(hh, b, d);
}
void arctan(int *a, int *b, int d) {
clear();
_clr();
for (int i = 0; i < d; i++) {
ww[i] = gg[i] = a[i];
}
Deriv(a, tt, d);
mult(gg, ww, pp, d);
pp[0] = (1 + pp[0]) % MOD;
clear();
inv(d, pp, yy);
clear();
mult(tt, yy, hh, d);
clear();
Integ(hh, b, d);
}
int main() {
read(n), read(fl);
for (int i = 0; i < n; i++) {
read(a[i]);
}
for (int i = 0; i < n; i++) {
write(f[i]), putchar(' ');
}
return 0;
}
|
