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
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
| #include <bits/stdc++.h>
using namespace std;
constexpr int MAX = 1e5 + 5;
constexpr int MOD = 998244353;
constexpr int INF = 0x3f3f3f3f;
using i64 = long long;
using u64 = unsigned long long;
using pii = pair <int, int>;
inline int read()
{
int s = 0; int f = 1;
char ch = getchar();
while ((ch < '0' || ch > '9') && ch != EOF)
{
if (ch == '-') f = -1;
ch = getchar();
}
while (ch >= '0' && ch <= '9')
{
s = s * 10 + ch - '0';
ch = getchar();
}
return s * f;
}
template <int MOD = 998244353>
class NTT
{
vector <int> rev; int n = 1;
const int P = MOD;
const int G = 3;
int qpow(int x, int y)
{
int res = 1;
while (y)
{
if (y & 1) res = 1ll * res * x % P;
x = 1ll * x * x % P;
y >>= 1;
}
return res;
}
void init_rev(int tot)
{
int L = 0; n = 1;
while (n < tot) n <<= 1, ++L;
rev.resize(n);
for (int i = 0; i < n; ++i) rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << (L - 1));
}
void ntt(vector <int> &a, int op)
{
for (int i = 0; i < n; ++i)
if (i < rev[i]) swap (a[i] ,a[rev[i]]);
for (int len = 1; len < n; len <<= 1)
{
int wn = qpow(G, (P - 1) / (len << 1));
if (op == -1) wn = qpow (wn, P - 2);
for (int i = 0; i < n; i += len << 1)
{
int w = 1;
for(int j = 0; j < len; ++j)
{
int u = a[i + j] % P, v = 1ll * a[i + j + len] * w % P;
a[i + j] = (0ll + u + v) % P;
a[i + j + len] = (0ll + u - v + P) % P;
w = 1ll * w * wn % P;
}
}
}
if (op == -1)
{
int inv_n = qpow(n, P - 2);
for (auto &x : a) x = 1ll * x * inv_n % P;
}
}
public:
vector <int> Conv(vector <int> a, vector <int> b)
{
int tot = (int)a.size() + (int)b.size() - 1;
init_rev(tot);
a.resize(n); b.resize(n);
ntt(a, 1); ntt(b, 1);
for (int i = 0; i < n; ++i) a[i] = 1ll * a[i] * b[i] % P;
ntt(a, -1); a.resize(tot);
return a;
}
vector <int> Inv(vector <int> a, int m)
{
int inv = qpow(a[0], P - 2);
vector <int> b {inv};
for (int len = 2; (len >> 1) < m; len <<= 1)
{
int sz = min((int)a.size(), len);
vector <int> f(a.begin(), a.begin() + sz);
init_rev(len << 1);
f.resize(n);
vector <int> h = b; h.resize(n);
ntt(f, 1); ntt (h, 1);
for (int i = 0; i < n; ++i)
h[i] = 1ll * h[i] * (2ll - 1ll * f[i] * h[i] % P + P) % P;
ntt(h, -1);
b.assign (h.begin(), h.begin() + min(len, m));
}
b.resize (m);
return b;
}
pair <vector <int>, vector <int>> Divmod(vector <int> a, vector <int> b)
{
int n_sz = a.size(), m_sz = b.size();
if (n_sz < m_sz) return {{0},a};
int dq = n_sz - m_sz + 1;
vector <int> ra = a, rb = b;
reverse(ra.begin(), ra.end()); reverse(rb.begin(), rb.end());
ra.resize(dq); rb.resize(dq);
vector <int> inv_rb = Inv(rb, dq);
vector <int> q = Conv(ra, inv_rb);
q.resize(dq);
reverse(q.begin(), q.end());
vector <int> qb = Conv(q, b);
vector <int> r(m_sz - 1);
for (int i = 0; i < m_sz - 1; ++i)
r[i] = (0ll + a[i] - (i < (int)qb.size() ? qb[i] : 0) + P) % P;
return {q,r};
}
vector <int> Sqrt (vector <int> a, int m)
{
vector <int> b {1};
int inv2 = qpow(2, P - 2);
for (int len = 2; (len >> 1) < m; len <<= 1)
{
int sz = min((int)a.size(), len);
vector <int> f(a.begin(), a.begin() + sz);
vector <int> inv_b = Inv(b, len);
init_rev(len << 1);
f.resize(n); inv_b.resize(n);
ntt(f, 1); ntt(inv_b, 1);
for (int i = 0; i < n; ++i)
f[i] = 1ll * f[i] * inv_b[i] % P;
ntt(f, -1);
b.resize(len);
for (int i = 0; i < len; ++i)
b[i] = 1ll * (b[i] + f[i]) % P * inv2 % P;
}
b.resize(m);
return b;
}
};
constexpr int V = 1e5;
NTT <MOD> calc;
void solve()
{
int n = read(), m = read();
vector <int> G(m + 1);
for (int i = 1; i <= n; ++i)
{
int x = read();
if (x <= m) G[x] = MOD - 4;
}
G[0] = 1;
auto A = calc.Sqrt(G, m + 1);
A[0] = (A[0] + 1) % MOD;
auto B = calc.Inv(A, m + 1);
for (int i = 1; i <= m; ++i) printf("%d\n", 2 * B[i] % MOD);
}
int main()
{
int t = 1;
while (t--) solve();
return 0;
}
|
