結果
| 問題 |
No.2952 Invision of Multiples
|
| コンテスト | |
| ユーザー |
 apricity
|
| 提出日時 | 2024-11-24 15:43:51 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 1,449 ms / 4,000 ms |
| コード長 | 8,727 bytes |
| コンパイル時間 | 2,189 ms |
| コンパイル使用メモリ | 136,744 KB |
| 最終ジャッジ日時 | 2025-02-25 06:05:50 |
|
ジャッジサーバーID （参考情報） |
judge5 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 41 |
ソースコード
#include<iostream>
#include<string>
#include<vector>
#include<algorithm>
#include<numeric>
#include<cmath>
#include<utility>
#include<tuple>
#include<cstdint>
#include<cstdio>
#include<iomanip>
#include<map>
#include<queue>
#include<set>
#include<stack>
#include<deque>
#include<unordered_map>
#include<unordered_set>
#include<bitset>
#include<cctype>
#include<chrono>
#include<random>
#include<cassert>
#include<cstddef>
#include<iterator>
#include<string_view>
#include<type_traits>
#ifdef LOCAL
# include "debug_print.hpp"
# define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
# define debug(...) (static_cast<void>(0))
#endif
using namespace std;
#define rep1(a) for(int i = 0; i < a; i++)
#define rep2(i, a) for(int i = 0; i < a; i++)
#define rep3(i, a, b) for(int i = a; i < b; i++)
#define rep4(i, a, b, c) for(int i = a; i < b; i += c)
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define rrep1(a) for(int i = (a)-1; i >= 0; i--)
#define rrep2(i, a) for(int i = (a)-1; i >= 0; i--)
#define rrep3(i, a, b) for(int i = (b)-1; i >= a; i--)
#define rrep4(i, a, b, c) for(int i = (b)-1; i >= a; i -= c)
#define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__)
#define ALL(v) v.begin(), v.end()
#define RALL(v) v.rbegin(), v.rend()
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() );
#define pb push_back
using ll = long long;
using D = double;
using LD = long double;
using P = pair<int, int>;
using vi = vector<int>;
using vl = vector<ll>;
template <class T> using vc = vector<T>;
template <class T> using vvc = vector<vc<T>>;
template <class T> using vvvc = vector<vvc<T>>;
template <class T> using vvvvc = vector<vvvc<T>>;
template <class T> using vvvvvc = vector<vvvvc<T>>;
#define vv(type, name, h, ...) \
vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) \
vector<vector<vector<type>>> name( \
h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) \
vector<vector<vector<vector<type>>>> name( \
a, vector<vector<vector<type>>>( \
b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
template<typename T> using PQ = priority_queue<T,vector<T>>;
template<typename T> using minPQ = priority_queue<T, vector<T>, greater<T>>;
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }
void yesno(bool flag) {cout << (flag?"Yes":"No") << "\n";}
template<typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
os << p.first << " " << p.second;
return os;
}
template<typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
is >> p.first >> p.second;
return is;
}
template<typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
int s = (int)v.size();
for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
return os;
}
template<typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (auto &x : v) is >> x;
return is;
}
void in() {}
template<typename T, class... U>
void in(T &t, U &...u) {
cin >> t;
in(u...);
}
void out() { cout << "\n"; }
template<typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
void outr() {}
template<typename T, class... U, char sep = ' '>
void outr(const T &t, const U &...u) {
cout << t;
outr(u...);
}
template <uint32_t mod>
struct LazyMontgomeryModInt {
using mint = LazyMontgomeryModInt;
using i32 = int32_t;
using u32 = uint32_t;
using u64 = uint64_t;
static constexpr u32 get_r() {
u32 ret = mod;
for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
return ret;
}
static constexpr u32 r = get_r();
static constexpr u32 n2 = -u64(mod) % mod;
static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
static_assert(r * mod == 1, "this code has bugs.");
u32 a;
constexpr LazyMontgomeryModInt() : a(0) {}
constexpr LazyMontgomeryModInt(const int64_t &b)
: a(reduce(u64(b % mod + mod) * n2)){};
static constexpr u32 reduce(const u64 &b) {
return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
}
constexpr mint &operator+=(const mint &b) {
if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
return *this;
}
constexpr mint &operator-=(const mint &b) {
if (i32(a -= b.a) < 0) a += 2 * mod;
return *this;
}
constexpr mint &operator*=(const mint &b) {
a = reduce(u64(a) * b.a);
return *this;
}
constexpr mint &operator/=(const mint &b) {
*this *= b.inverse();
return *this;
}
constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
constexpr bool operator==(const mint &b) const {
return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
}
constexpr bool operator!=(const mint &b) const {
return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
}
constexpr mint operator-() const { return mint() - mint(*this); }
constexpr mint operator+() const { return mint(*this); }
constexpr mint pow(u64 n) const {
mint ret(1), mul(*this);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
constexpr mint inverse() const {
int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0;
while (y > 0) {
t = x / y;
x -= t * y, u -= t * v;
tmp = x, x = y, y = tmp;
tmp = u, u = v, v = tmp;
}
return mint{u};
}
friend ostream &operator<<(ostream &os, const mint &b) {
return os << b.get();
}
friend istream &operator>>(istream &is, mint &b) {
int64_t t;
is >> t;
b = LazyMontgomeryModInt<mod>(t);
return (is);
}
constexpr u32 get() const {
u32 ret = reduce(a);
return ret >= mod ? ret - mod : ret;
}
static constexpr u32 get_mod() { return mod; }
};
const int mod = 998244353;
//const int mod = 1000000007;
using mint = LazyMontgomeryModInt<mod>;
/*
* dual segtree
* range apply / point get
* operator (com) must be commutative:
* f g = g f
* ex) range add, chmax/chmin, (apply)
* https://hackmd.io/@tatyam-prime/DualSegmentTree
*/
template< class T, T (*id)(), void(*com)(T&, const T&) >
struct DualSegmentTree {
int sz;
vector< T > dat;
DualSegmentTree(int n){
sz = 1;
while(sz < n) sz <<= 1;
dat.assign(2*sz, id());
}
void apply(int l, int r, const T &t){
l += sz; r += sz;
for(;l<r;l>>=1,r>>=1){
if(l&1) com(dat[l++], t);
if(r&1) com(dat[--r], t);
}
}
T get(int i) const{
T res = id();
i += sz;
for(;i;i>>=1){
com(res, dat[i]);
}
return res;
}
};
using T = mint;
T id() {return 0;}
void com(T &a, const T &b) {a += b;}
#include "atcoder/math.hpp"
constexpr int MX = 50005;
constexpr int B = 224;
int f1[B][MX]; // f1[x][y] = #(i<j) di=x, dj=y
int f2[MX][B];
DualSegmentTree<T,id, com> g(MX);
int main(){
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
int n,m; in(n,m);
vector<int> d(n); in(d);
vector<mint> im(m+1);
rep(i,1,m+1) im[i] = mint(m/i).inverse();
vector<int> cntd(m+1);
rep(i,n) {
rep(j,B) f1[j][d[i]] += cntd[j];
cntd[d[i]]++;
}
cntd.assign(m+1,0);
rrep(i,n){
rep(j,B) f2[d[i]][j] += cntd[j];
cntd[d[i]]++;
}
mint ans = 0;
rep(x,1,B) rep(y,1,m+1) {
ans += im[x] * im[y] * f1[x][y] * atcoder::floor_sum(m/x, y, x, x-1);
}
rep(x,B,m+1) rep(y,1,B) {
ans += im[x] * im[y] * f2[x][y] * atcoder::floor_sum(m/x, y, x, x-1);
}
rrep(i,n) if(d[i] >= B) {
mint tmp = 0;
rep(l,1,m/d[i]+1) tmp += g.get(l*d[i]-1);
ans += tmp * im[d[i]];
rep(t,1,m/d[i]+1) {
int l = t*d[i], r = min(m,(t+1)*d[i]-1) + 1;
g.apply(l,r,im[d[i]]*t);
}
}
rep(i,n) ans *= m/d[i];
out(ans);
}