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
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
| #include <cstdio>
#include <algorithm>
using namespace std;
template <class Type>
void read (Type &x)
{
char c;
bool flag = false;
while ((c = getchar()) < '0' || c > '9')
flag |= c == '-';
x = c - '0';
while ((c = getchar()) >= '0' && c <= '9')
x = (x << 3) + (x << 1) + c - '0';
if (flag) x = ~x + 1;
}
template <class Type, class ...Rest>
void read (Type &x, Rest &...y) { read(x); read(y...); }
template <class Type>
void write (Type x)
{
if (x < 0) putchar('-'), x = ~x + 1;
if (x > 9) write(x / 10);
putchar('0' + x % 10);
}
typedef long long LL;
const int N = 1e6 + 10, mod = 998244353, inv2 = mod + 1 >> 1;
int rev[N];
int binpow (int b, int k = mod - 2)
{
int res = 1;
for (; k; k >>= 1, b = (LL)b * b % mod)
if (k & 1) res = (LL)res * b % mod;
return res;
}
void ntt (int *x, int bit, int op)
{
int tot = 1 << bit;
for (int i = 1; i < tot; ++i)
if ((rev[i] = rev[i >> 1] >> 1 | (i & 1) << bit - 1) > i)
swap(x[rev[i]], x[i]);
for (int mid = 1; mid < tot; mid <<= 1)
{
int w1 = binpow(3, (mod - 1) / (mid << 1));
if (!~op) w1 = binpow(w1);
for (int i = 0; i < tot; i += mid << 1)
for (int j = 0, k = 1; j < mid; ++j, k = (LL)k * w1 % mod)
{
int p = x[i | j], q = (LL)k * x[i | j | mid] % mod;
x[i | j] = (p + q) % mod, x[i | j | mid] = (p - q) % mod;
}
}
if (~op) return;
int itot = binpow(tot);
for (int i = 0; i < tot; ++i)
x[i] = (LL)x[i] * itot % mod;
}
void PolyMul (int n, int *f, int m, int *g, int nm, int *res)
{
int bit = 0;
while (1 << bit < n + m - 1) ++bit;
int tot = 1 << bit;
for (int i = n; i < tot; ++i) f[i] = 0;
for (int i = m; i < tot; ++i) g[i] = 0;
ntt(f, bit, 1), ntt(g, bit, 1);
for (int i = 0; i < tot; ++i)
res[i] = (LL)f[i] * g[i] % mod;
ntt(res, bit, -1);
for (int i = nm; i < tot; ++i) res[i] = 0;
}
void PolyInv(int n, int *x, int *g)
{
if (n == 1) return void(g[0] = binpow(x[0]));
int m = n + 1 >> 1;
int bit = 0;
while (1 << bit < n + m + m - 2) ++bit;
int tot = 1 << bit;
PolyInv(m, x, g);
for (int i = m; i < tot; ++i) g[i] = 0;
static int A[N];
for (int i = 0; i < n; ++i) A[i] = x[i];
for (int i = n; i < tot; ++i) A[i] = 0;
ntt(g, bit, 1), ntt(A, bit, 1);
for (int i = 0; i < tot; ++i)
g[i] = (2 - (LL)g[i] * A[i]) % mod * g[i] % mod;
ntt(g, bit, -1);
for (int i = n; i < tot; ++i) g[i] = 0;
}
void PolyCalc (int n, int *g)
{
if (n == 1) return void(g[0] = 1);
int m = n + 1 >> 1;
PolyCalc(m, g);
int bit = 0;
while (1 << bit < n + n - 1) ++bit;
int tot = 1 << bit;
static int A[N], B[N], C[N], D[N];
for (int i = 0; i < tot; ++i)
A[i] = i % 2 ? 0 : g[i / 2];
for (int i = 0; i < tot; ++i)
B[i] = i % 3 ? 0 : g[i / 3];
for (int i = 0; i < m; ++i) C[i] = g[i];
for (int i = m; i < tot; ++i) C[i] = 0;
ntt(C, bit, 1), ntt(A, bit, 1), ntt(B, bit, 1);
for (int i = 0; i < tot; ++i)
{
D[i] = ((LL)C[i] * C[i] % mod * C[i] % mod + 3ll * A[i] * C[i] % mod + 2 * B[i]) % mod;
A[i] = (3ll * C[i] * C[i] % mod + 3ll * A[i]) % mod;
}
ntt(D, bit, -1), ntt(A, bit, -1);
for (int i = n - 1; i; --i)
D[i] = (D[i - 1] - 6ll * g[i]) % mod, A[i] = A[i - 1];
D[0] = (6 - 6 * g[0]) % mod, A[0] = -6;
PolyInv(n, A, B);
PolyMul(n, D, n, B, n, A);
for (int i = 0; i < n; ++i) (g[i] -= A[i]) %= mod;
}
int main ()
{
static int n, A[N], B[N], C[N];
read(n); ++n;
PolyCalc(n, A);
for (int i = 0; i < n; ++i) B[i] = C[i] = A[i];
PolyMul(n, A, n, B, n, A);
for (int i = n - 2; ~i; --i)
A[i + 1] = (LL)inv2 * (A[i] + (i & 1 ? 0 : C[i >> 1])) % mod;
A[0] = 0;
for (int i = 0; i < n; ++i) B[i] = C[i] = A[i];
PolyMul(n, A, n, B, n, A);
for (int i = n - 1; i; --i)
A[i] = (LL)inv2 * (A[i] + (i & 1 ? 0 : C[i >> 1])) % mod;
A[0] = 0;
for (int i = 2; i < n; ++i)
write((A[i] + mod) % mod), puts("");
return 0;
}
|