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
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
| #include <assert.h>
#include <cstdio>
#include <iostream>
using namespace std;
using ll = long long;
const int NR = 1 << 21;
const int G = 3, Gi = 332748118;
const int mod = 998244353;
template <int MOD, int RT>
struct mint
{
static const int mod = MOD;
static constexpr mint rt() { return RT; }
int v;
explicit operator int() const { return v; }
mint() : v(0) {}
mint(ll _v)
{
v = int((-MOD < _v && _v < MOD) ? _v : _v % MOD);
if (v < 0)
v += MOD;
}
bool operator==(const mint &o) const
{
return v == o.v;
}
friend bool operator!=(const mint &a, const mint &b)
{
return !(a == b);
}
friend bool operator<(const mint &a, const mint &b)
{
return a.v < b.v;
}
mint &operator+=(const mint &o)
{
if ((v += o.v) >= MOD)
v -= MOD;
return *this;
}
mint &operator-=(const mint &o)
{
if ((v -= o.v) < 0)
v += MOD;
return *this;
}
mint &operator*=(const mint &o)
{
v = int((ll)v * o.v % MOD);
return *this;
}
mint &operator/=(const mint &o) { return (*this) *= inv(o); }
friend mint pow(mint a, ll p)
{
mint ans = 1;
assert(p >= 0);
for (; p; p /= 2, a *= a)
if (p & 1)
ans *= a;
return ans;
}
friend mint inv(const mint &a)
{
assert(a.v != 0);
return pow(a, MOD - 2);
}
mint operator-() const { return mint(-v); }
mint &operator++() { return *this += 1; }
mint &operator--() { return *this -= 1; }
friend mint operator+(mint a, const mint &b) { return a += b; }
friend mint operator-(mint a, const mint &b) { return a -= b; }
friend mint operator*(mint a, const mint &b) { return a *= b; }
friend mint operator/(mint a, const mint &b) { return a /= b; }
};
using mi = mint<mod, 3>;
int rev[NR];
void NTT(mi *a, int n, int type)
{
for (int i = 0; i < n; ++i)
if (i < rev[i])
swap(a[i], a[rev[i]]);
for (int k = 1; k < n; k <<= 1)
{
mi wn = pow((type == 1 ? mi(G) : mi(Gi)), (mod - 1) / (k << 1));
for (int i = 0; i < n; i += (k << 1))
{
mi w = mi(1);
for (int j = 0; j < k; ++j, w = w * wn)
{
mi x = a[i + j], y = w * a[i + j + k];
a[i + j] = x + y;
a[i + j + k] = x - y;
}
}
}
if (type == 1)
return;
mi invn = inv(mi(n));
for (int i = 0; i < n; ++i)
a[i] = a[i] * invn;
}
int n;
mi A[NR], B[NR], C[NR],D[NR];
void cdq(int l, int r)
{
if(l==r)return ;
int mid = (l + r) >> 1;
cdq(l, mid);
int bit = 0, num = 1;
while(num<((r-l+1)<<1))
num <<= 1, bit += 1;
for (int i = 0; i < num; ++i)
rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << (bit - 1));
for (int i = 0; i < num;++i)
C[i] = D[i] = 0;
for (int i = l; i <= r;++i)
C[i - l] = A[i - l];
for (int i = l; i <= mid;++i)
D[i - l] = B[i];
NTT(C, num, 1), NTT(D, num, 1);
for (int i = 0; i < num;++i)
C[i] = C[i] * D[i];
NTT(C, num, 0);
for (int i = mid + 1; i <= r;++i)
B[i] += C[i - l];
cdq(mid + 1, r);
}
int main()
{
scanf("%d", &n);
for (int i = 1,x; i <= n-1;++i){
scanf("%d", &x);
A[i] = mi(x);
}
B[0] = mi(1);
cdq(0, n-1);
for (int i = 0; i <= n - 1;++i)
printf("%d ", B[i].v);
}
|