-
Notifications
You must be signed in to change notification settings - Fork 3
/
Copy pathFPS.cpp
186 lines (186 loc) · 6.93 KB
/
FPS.cpp
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
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
#include <atcoder/convolution>
using Modint = atcoder::modint998244353;
struct Poly{
vector<Modint> a;
Poly(){}
Poly(ll n): a(n){}
Poly(const vector<Modint>& a): a(a){}
Poly(vector<Modint>&& a): a(a){}
Modint& operator[](ll x){ return a[x]; }
Modint operator[](ll x) const { return a[x]; }
auto begin(){ return a.begin(); }
auto end(){ return a.end(); }
auto begin() const { return a.cbegin(); }
auto end() const { return a.cend(); }
ll size() const { return a.size(); }
Poly& resize(ll n){ a.resize(n); return *this; }
Poly& resize(const Poly& f){ if(size() < f.size()) resize(f.size()); return *this; }
Poly& operator+=(const Poly& f){
resize(f);
for(ll i = 0; i < f.size(); i++) a[i] += f[i];
return *this;
}
Poly operator+(const Poly& f) const {
if(size() < f.size()) return Poly(f) += *this;
return Poly(*this) += f;
}
Poly& operator-=(const Poly& f){
resize(f);
for(ll i = 0; i < f.size(); i++) a[i] -= f[i];
return *this;
}
Poly operator-(const Poly& f) const { return Poly(*this) -= f; }
Poly operator-(int) const {
Poly ans(size());
for(ll i = 0; i < size(); i++) ans[i] = -a[i];
return ans;
}
Poly operator*(const Poly& f) const { return atcoder::convolution(a, f.a); }
Poly& operator*=(const Poly& f){ a = atcoder::convolution(move(a), vector(f.a)); return *this; }
Poly inv(ll n = -1) const {
if(n == -1) n = size();
if(n == 0) return {};
assert(size() && a[0] != 0);
vector<Modint> ans = {a[0].inv()};
for(ll m = 1; m < n; m *= 2) {
const Modint M = Modint(m * m * 4).inv();
vector<Modint> x(a.begin(), a.begin() + min(size(), m * 2)), y = ans;
x.resize(m * 2); atcoder::internal::butterfly(x);
y.resize(m * 2); atcoder::internal::butterfly(y);
for(ll i = 0; i < m * 2; ++i) x[i] *= y[i];
atcoder::internal::butterfly_inv(x);
for(ll i = 0; i < m; i++) x[i] = 0;
for(ll i = m; i < m * 2; i++) x[i] *= M;
atcoder::internal::butterfly(x);
for(ll i = 0; i < m * 2; ++i) x[i] *= -y[i];
atcoder::internal::butterfly_inv(x);
ans.insert(ans.end(), x.begin() + m, x.end());
}
ans.resize(n);
return ans;
}
Poly operator/=(const Poly& f){
const ll n = size();
*this *= f.inv(n);
return resize(n);
}
Poly operator/(const Poly& f) const { return Poly(*this) /= f; }
Poly div(const Poly& f) const {
assert(f.size() && f.a.back() != 0);
Poly x = *this, y = f;
while(x.size() && !x.a.back().val()) x.a.pop_back();
while(y.size() && !y.a.back().val()) y.a.pop_back();
if(x.size() < f.size()) return {};
const ll n = x.size() - y.size() + 1;
reverse(x.begin(), x.end()); x.resize(n);
reverse(y.begin(), y.end()); y.resize(n);
x /= y;
reverse(x.begin(), x.end());
return x;
}
Poly operator%(const Poly& f) const {
assert(f.size() && f.a.back() != 0);
return (*this - f * div(f)).resize(f.size() - 1);
}
pair<Poly, Poly> divmod(const Poly& f) const {
assert(f.size() && f.a.back() != 0);
const Poly D = div(f);
return {D, (*this - f * D).resize(f.size() - 1)};
}
Poly D(ll n = -1) const {
if(n == -1) n = size();
if(n == 0) return {};
Poly ans(size() - 1);
for(ll i = 1; i < size(); i++) ans[i - 1] = a[i] * Modint::raw(i);
return ans;
}
Poly integral() const {
const ll n = size();
Poly ans(n + 1);
ans[0] = 1;
for(ll i = 0; i < n; i++) ans[i + 1] = ans[i] * Modint::raw(i + 1);
ans[n] = ans[n].inv();
for(ll i = n; i--; ){
swap(ans[i], ans[i + 1]);
ans[i + 1] *= ans[i] * a[i];
ans[i] *= Modint::raw(i + 1);
}
ans[0] = 0;
return ans;
}
Poly log(ll n = -1) const {
if(n == -1) n = size();
if(n == 0) return {};
assert(size() && a[0] == 1);
return (D(n) * inv(n)).resize(n - 1).integral();
}
Poly exp(ll n = -1) const {
if(n == -1) n = size();
if(n == 0) return {};
assert(a[0] == 0);
if(size() == 1) return vector<Modint>{1};
vector<Modint> b = {1, a[1]}, c = {1}, z1, z2 = {1, 1};
for(ll m = 2; m < n; m *= 2) {
const Modint M = Modint(m).inv(), M2 = Modint(m * 2).inv();
auto y = b;
y.resize(m * 2); atcoder::internal::butterfly(y);
z1 = move(z2);
vector<Modint> z(m);
for(ll i = 0; i < m; i++) z[i] = y[i] * z1[i];
atcoder::internal::butterfly_inv(z);
for(ll i = 0; i < m / 2; i++) z[i] = 0;
for(ll i = m / 2; i < m; i++) z[i] *= M * M;
atcoder::internal::butterfly(z);
for(ll i = 0; i < m; i++) z[i] *= -z1[i];
atcoder::internal::butterfly_inv(z);
c.insert(c.end(), z.begin() + m / 2, z.end());
z2 = c; z2.resize(m * 2);
atcoder::internal::butterfly(z2);
Poly x = vector<Modint>(begin(), begin() + min(size(), m));
x = x.D(); x.a.push_back(0);
atcoder::internal::butterfly(x.a);
for(ll i = 0; i < m; i++) x[i] *= y[i] * M;
atcoder::internal::butterfly_inv(x.a);
x -= Poly(b).D();
x.resize(m * 2);
for(ll i = 0; i < m - 1; i++){
x[m + i] = x[i]; x[i] = 0;
}
atcoder::internal::butterfly(x.a);
for (ll i = 0; i < m * 2; i++) x[i] *= z2[i] * M2;
atcoder::internal::butterfly_inv(x.a);
x = x.integral(); x.a.pop_back();
for(ll i = m; i < min(size(), m * 2); i++) x[i] += a[i];
for(ll i = 0; i < m; i++) x[i] = 0;
for(ll i = m; i < m * 2; i++) x[i] *= M2;
atcoder::internal::butterfly(x.a);
for(ll i = 0; i < m * 2; ++i) x[i] *= y[i];
atcoder::internal::butterfly_inv(x.a);
b.insert(b.end(), x.begin() + m, x.end());
}
return Poly(move(b)).resize(n);
}
Poly pow(ll k, ll n = -1){
if(n == -1) n = size();
if(n == 0) return {};
assert(k >= 0);
if(k == 0){
Poly ans(n);
ans[0] = 1;
return ans;
}
Poly ans = *this;
ll cnt = 0;
while(cnt < size() && ans[cnt] == 0) cnt++;
if(cnt == size() || cnt * k >= n) return Poly(n);
ans.a.erase(ans.a.begin(), ans.a.begin() + cnt);
const Modint c = ans[0], C = c.pow(k), D = c.inv(), K = k;
for(Modint& i : ans) i *= D;
ans = ans.log(n - cnt * k);
for(Modint& i : ans) i *= K;
ans = ans.exp();
for(Modint& i : ans) i *= C;
ans.a.insert(ans.a.begin(), cnt * k, 0);
return ans;
}
};