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using namespace std; const int mod = 998244353, G = 3, Ginv = (998244353 + 1) / 3; const int maxn = 400010; int rev[maxn]; inline int (int x) {return x >= mod ? x - mod : x;} inline void get_rev(int l) { for(int i = 1; i < (1 << l); i++) rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << (l - 1)); } inline int power(int a, int b) { long long res = a, ans = 1; for(; b; b >>= 1, res = res * res % mod) if(b & 1) ans = ans * res % mod; return ans; } int gg[maxn], ggi[maxn]; inline void ntt(int *a, int l, int type) { for(int i = 0; i < (1 << l); i++) if(rev[i] < i) a[i] ^= a[rev[i]] ^= a[i] ^= a[rev[i]]; for(register int p = 1; p < (1 << l); p <<= 1) { int wn = (type == 1 ? gg[p] : ggi[p]); for(register int s = 0; s < (1 << l); s += p << 1) { int w = 1; for(register int i = 0; i < p; i++) { int h1 = a[s + i], h2 = 1ll * w * a[s + p + i] % mod; a[s + i] = fast(h1 + h2); a[s + p + i] = fast(h1 - h2 + mod); w = 1ll * w * wn % mod; } } } if(type == -1) { int inv = power(1 << l, mod - 2); for(register int i = 0; i < (1 << l); i++) a[i] = 1ll * a[i] * inv % mod; } } inline void add(int *a, int sizea, int *b, int sizeb, int *c) { for(register int i = 0; i < max(sizea, sizeb); i++) c[i] = fast((i < sizea ? a[i] : 0) + (i < sizeb ? b[i] : 0)); } inline void del(int *a, int sizea, int *b, int sizeb, int *c) { for(register int i = 0; i < max(sizea, sizeb); i++) c[i] = fast((i < sizea ? a[i] : 0) - (i < sizeb ? b[i] : 0) + mod); } int f[maxn], g[maxn], h[maxn]; inline void mult(int *a, int sizea, int *b, int sizeb, int *c) { register int l = 0; for(; (1 << l) < sizea + sizeb - 1; l++); get_rev(l); for(register int i = 0; i < (1 << l); i++) { f[i] = (i < sizea ? a[i] : 0); g[i] = (i < sizeb ? b[i] : 0); } ntt(f, l, 1); ntt(g, l, 1); for(int i = 0; i < (1 << l); i++) f[i] = 1ll * f[i] * g[i] % mod; ntt(f, l, -1); for(register int i = 0; i < sizea + sizeb - 1; i++) c[i] = f[i]; } inline void T(int *a, int sizea, int *b) { for(int i = 0; i < sizea; i++) b[i] = a[sizea - i - 1]; } inline void inv(int *a, int sizea, int *b, int sizeb) { b[0] = power(a[0], mod - 2); for(int now = 1; now < sizeb; now <<= 1) { mult(b, now, b, now, h); mult(h, now * 2 - 1, a, min(sizea, now << 1), h); for(int i = 0; i < now << 1; i++) { if(i < now) b[i] = fast(fast(b[i] + b[i]) - h[i] + mod); else b[i] = fast(mod - h[i]); } } } inline void der(int *a, int sizea, int *b) { for(int i = 0; i < sizea - 1; i++) b[i] = 1ll * a[i + 1] * (i + 1) % mod; } int ta[maxn], tb[maxn], invtb[maxn]; inline void div(int *a, int sizea, int *b, int sizeb, int *c) { T(a, sizea, ta); T(b, sizeb, tb); inv(tb, sizeb, invtb, sizea - sizeb + 1); mult(ta, sizea - sizeb + 1, invtb, sizea - sizeb + 1, ta); T(ta, sizea - sizeb + 1, c); } inline void modu(int *a, int sizea, int *b, int sizeb, int *c) { div(a, sizea, b, sizeb, h); mult(b, sizeb, h, sizea - sizeb + 1, h); for(int i = 0; i < sizeb - 1; i++) { c[i] = fast(a[i] - h[i] + mod); } } struct POOL { int buf[3000010], cnt; inline int* get(int size) { return buf + (cnt += size) - size; } } pool; int *p[maxn]; int y[100010]; void get_p(int now, int l, int r) { if(l == r) { p[now] = pool.get(2); p[now][0] = fast(mod - l); p[now][1] = 1; return; } int mid = (l + r) >> 1; get_p(now << 1, l, mid); get_p(now << 1 | 1, mid + 1, r); p[now] = pool.get(r - l + 2); mult(p[now << 1], mid - l + 2, p[now << 1 | 1], r - mid + 1, p[now]); } int *sta[30], cnt; void get_y(int now, int l, int r, int *a) { if(l == r) { y[l] = a[0]; return; } cnt++; if(sta[cnt] == 0) sta[cnt] = pool.get(r - l + 1); int mid = (l + r) >> 1; int *aa = sta[cnt]; modu(a, r - l + 1, p[now << 1], mid - l + 2, aa); get_y(now << 1, l, mid, aa); modu(a, r - l + 1, p[now << 1 | 1], r - mid + 1, aa); get_y(now << 1 | 1, mid + 1, r, aa); cnt--; } int n; int ar[maxn], ans[maxn]; int dinv[maxn], fac[maxn], finv[maxn]; int main() { for(int i = 1; i < maxn; i <<= 1) gg[i] = power(G, (mod - 1) / 2 / i); for(int i = 1; i < maxn; i <<= 1) ggi[i] = power(Ginv, (mod - 1) / 2 / i); scanf("%d", &n); for(int i = 0; i < n; i++) scanf("%d", ar + i); for(int i = fac[0] = 1; i < n; i++) fac[i] = 1ll * i * fac[i - 1] % mod; finv[n - 1] = power(fac[n - 1], mod - 2); for(int i = n - 1; i > 0; i--) finv[i - 1] = 1ll * i * finv[i] % mod; for(int i = 0; i < n; i++) dinv[i] = i & 1 ? mod - finv[i] : finv[i]; get_p(1, 0, n - 1); get_y(1, 0, n - 1, ar); for(int i = 0; i < n; i++) y[i] = 1ll * y[i] * finv[i] % mod; mult(y, n, dinv, n, ans); for(int i = 0; i < n; i++) printf("%d%c", ans[i], " n"[i == n - 1]); return 0; }
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