1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
| #include <bits/stdc++.h>
using LL = long long;
const int N = 1 << 18 | 100, P = 998244353, G = 3, L = 1e5 + 1;
using poly = std::vector<int>;
void adj(int &x){ x += (x >> 31) & P; }
int qpow(int x, int y = P - 2)
{
int res = 1;
for (; y; y >>= 1, x = LL(x) * x % P) if (y & 1) res = LL(res) * x % P;
return res;
}
namespace Poly
{
int r[N], iv[N];
void rdy(int &bit, int &tot, int len){ for (bit = 0, tot =1; tot < len + 1; tot <<= 1, ++bit); }
void get_r(int bit, int tot){ for (int i = 1; i < tot; ++i) r[i] = (r[i >> 1] >> 1) | ((i & 1) << (bit - 1)); }
void ntt(int *x, int tot, int op)
{
static int gn[N];
for (int i = 1; i < tot; ++i) if (i < r[i]) std::swap(x[i], x[r[i]]);
for (int mid = 1; mid < tot; mid <<= 1)
{
int g0 = qpow(G, (P - 1) / (mid << 1));
if (op == -1) g0 = qpow(g0);
gn[0] = 1;
for (int i = 1; i < mid; ++i) gn[i] = LL(gn[i - 1]) * g0 % P;
for (int i = 0; i < tot; i += (mid << 1))
for (int *x1 = x + i, *x2 = x + i + mid, *ed = x2, *g = gn; x1 != ed; ++x1, ++x2, ++g)
{
int p = *x1, q = LL(*x2) * *g % P;
adj(*x1 = p + q - P), adj(*x2 = p - q);
}
}
if (op == 1) return ;
int t = qpow(tot);
for (int i = 0; i < tot; ++i) x[i] = LL(x[i]) * t % P;
}
poly operator * (poly x, poly y)
{
if (x.empty() || y.empty()) return {};
int n = x.size(), m = y.size(), bit, tot;
rdy(bit, tot, n + m), get_r(bit, tot);
x.resize(tot), y.resize(tot);
if (x != y) ntt(x.data(), tot, 1), ntt(y.data(), tot, 1);
else ntt(x.data(), tot, 1), y = x;
for (int i = 0; i < tot; ++i) x[i] = LL(x[i]) * y[i] % P;
ntt(x.data(), tot, -1), x.resize(n + m - 1);
return x;
}
poly operator - (poly x, poly y)
{
if (x.size() < y.size()) x.resize(y.size());
for (int i = y.size() - 1; ~i; --i) adj(x[i] -= y[i]);
return x;
}
poly inv(poly x)
{
int n = x.size();
if (n == 1) return {qpow(x[0])};
int bit, tot;
rdy(bit, tot, n << 1);
poly y = inv(poly(x.begin(), x.begin() + ((n + 1) >> 1))), z = y * y * x, res(n);
y.resize(n), z.resize(n);
for (int i = 0; i < n; ++i) adj(res[i] = 2ll * y[i] - z[i]);
return res;
}
poly dif(poly x)
{
poly res(x.size() - 1);
for (int i = x.size() - 1; i; --i) res[i - 1] = LL(i) * x[i] % P;
return res;
}
poly inte(poly x)
{
poly res(x.size() + 1);
if (!iv[1])
{
iv[1] = 1;
for (int i = 2; i < N; ++i) iv[i] = LL(P - P / i) * iv[P % i] % P;
}
for (int i = x.size(); i; --i) res[i] = LL(x[i - 1]) * iv[i] % P;
return res;
}
poly ln(poly x)
{
poly res(dif(x) * inv(x));
res.resize(x.size()), res = inte(res);
return res.resize(x.size()), res;
}
poly exp(poly x)
{
if (x.size() == 1) return {1};
int n = x.size();
poly y = exp(poly(x.begin(), x.begin() + ((n + 1) >> 1)));
y.resize(n);
poly z = ln(y);
x = x - z, ++x[0];
return x = x * y, x.resize(n), x;
}
}
int fac[N], ifac[N];
int main()
{
fac[0] = ifac[0] = fac[1] = ifac[1] = 1;
for (int i = 2; i < L; ++i) fac[i] = LL(i) * fac[i - 1] % P;
ifac[L - 1] = qpow(fac[L - 1]);
for (int i = L - 2; i > 1; --i) ifac[i] = LL(i + 1) * ifac[i + 1] % P;
poly f(L);
for (int i = 1; i < L; ++i) f[i] = ifac[i];
poly g = Poly::exp(f);
for (int i = 2; i < L; ++i) g[i] = LL(g[i]) * fac[i] % P;
int T, n;
for (scanf("%d", &T); T--; )
{
scanf("%d", &n);
printf("%d\n", g[n]);
}
return 0;
}
|