結果
| 問題 | No.2062 Sum of Subset mod 999630629 |
| ユーザー |
 leaf_1415
|
| 提出日時 | 2022-09-06 06:15:09 |
| 言語 | C++11 (gcc 11.4.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 12,055 bytes |
| コンパイル時間 | 1,421 ms |
| コンパイル使用メモリ | 113,092 KB |
| 実行使用メモリ | 221,492 KB |
| 最終ジャッジ日時 | 2024-11-21 07:34:10 |
| 合計ジャッジ時間 | 201,519 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge2 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | TLE | - |
| testcase_01 | TLE | - |
| testcase_02 | TLE | - |
| testcase_03 | TLE | - |
| testcase_04 | TLE | - |
| testcase_05 | TLE | - |
| testcase_06 | TLE | - |
| testcase_07 | TLE | - |
| testcase_08 | TLE | - |
| testcase_09 | TLE | - |
| testcase_10 | TLE | - |
| testcase_11 | TLE | - |
| testcase_12 | TLE | - |
| testcase_13 | TLE | - |
| testcase_14 | TLE | - |
| testcase_15 | TLE | - |
| testcase_16 | TLE | - |
| testcase_17 | TLE | - |
| testcase_18 | TLE | - |
| testcase_19 | TLE | - |
| testcase_20 | TLE | - |
| testcase_21 | TLE | - |
| testcase_22 | TLE | - |
| testcase_23 | TLE | - |
| testcase_24 | TLE | - |
| testcase_25 | TLE | - |
| testcase_26 | TLE | - |
| testcase_27 | TLE | - |
| testcase_28 | TLE | - |
| testcase_29 | TLE | - |
| testcase_30 | TLE | - |
| testcase_31 | TLE | - |
ソースコード
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <ctime>
#include <cstdlib>
#include <cassert>
#include <vector>
#include <list>
#include <stack>
#include <queue>
#include <deque>
#include <map>
#include <set>
#include <bitset>
#include <string>
#include <algorithm>
#include <utility>
#include <complex>
#include <array>
#include <unordered_set>
#include <unordered_map>
#define rep(x, s, t) for(ll x = (s); (x) <= (t); (x)++)
#define per(x, s, t) for(ll x = (s); (x) >= (t); (x)--)
#define reps(x, s) for(ll x = 0; (x) < (ll)(s).size(); (x)++)
#define chmin(x, y) (x) = min((x), (y))
#define chmax(x, y) (x) = max((x), (y))
#define sz(x) ((ll)(x).size())
#define all(x) (x).begin(),(x).end()
#define rall(x) (x).rbegin(),(x).rend()
#define outl(...) dump_func(__VA_ARGS__)
#define outf(x) cout << fixed << setprecision(16) << (x) << endl
#define pb push_back
#define fi first
#define se second
#define inf 2e18
#define eps 1e-9
const double PI = 3.1415926535897932384626433;
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<ll, ll> P;
struct edge{
ll to, cost;
edge(){}
edge(ll a, ll b){ to = a, cost = b;}
};
const int dx[] = {1, 0, -1, 0}, dy[] = {0, -1, 0, 1};
//const int mod = 1000000007;
const int mod = 998244353;
struct mint{
int x;
mint(ll y = 0){if(y < 0 || y >= mod) y = (y%mod+mod)%mod; x = y;}
mint(const mint &ope) {x = ope.x;}
mint operator-(){return mint(-x);}
mint operator+(const mint &ope){return mint(x) += ope;}
mint operator-(const mint &ope){return mint(x) -= ope;}
mint operator*(const mint &ope){return mint(x) *= ope;}
mint operator/(const mint &ope){return mint(x) /= ope;}
mint& operator+=(const mint &ope){x += ope.x; if(x >= mod) x -= mod; return *this;}
mint& operator-=(const mint &ope){x += mod - ope.x; if(x >= mod) x -= mod; return *this;}
mint& operator*=(const mint &ope){ll tmp = x; tmp *= ope.x, tmp %= mod; x = tmp; return *this;}
mint& operator/=(const mint &ope){
ll n = mod-2; mint mul = ope;
while(n){if(n & 1) *this *= mul; mul *= mul; n >>= 1;}
return *this;
}
mint inverse(){return mint(1) / *this;}
bool operator ==(const mint &ope){return x == ope.x;}
bool operator !=(const mint &ope){return x != ope.x;}
bool operator <(const mint &ope)const{return x < ope.x;}
};
mint modpow(mint a, ll n){
if(n == 0) return mint(1);
if(n % 2) return a * modpow(a, n-1);
else return modpow(a*a, n/2);
}
istream& operator >>(istream &is, mint &ope){ll t; is >> t, ope.x = t; return is;}
ostream& operator <<(ostream &os, mint &ope){return os << ope.x;}
ostream& operator <<(ostream &os, const mint &ope){return os << ope.x;}
ll modpow(ll a, ll n, ll mod){
if(n == 0) return 1;
if(n % 2) return ((a%mod) * (modpow(a, n-1, mod)%mod)) % mod;
else return modpow((a*a)%mod, n/2, mod) % mod;
}
vector<mint> fact, fact_inv;
void make_fact(int n){
fact.resize(n+1), fact_inv.resize(n+1);
fact[0] = mint(1); rep(i, 1, n) fact[i] = fact[i-1] * mint(i);
fact_inv[n] = fact[n].inverse(); per(i, n-1, 0) fact_inv[i] = fact_inv[i+1] * mint(i+1);
}
mint comb(int n, int k){ if(n < 0 || k < 0 || n < k) return mint(0); return fact[n] * fact_inv[k] * fact_inv[n-k];}
mint perm(int n, int k){ return comb(n, k) * fact[k]; }
template<typename T> T comb2(ll n, ll k){ T ret = 1; rep(i, 1, k) ret *= n-k+i, ret /= i; return ret;}
vector<int> prime, pvec, qrime;
void make_prime(int n){
prime.resize(n+1);
rep(i, 2, n){
if(prime[i] == 0) pvec.push_back(i), prime[i] = i;
for(auto p : pvec){ if(i*p > n || p > prime[i]) break; prime[i*p] = p;}
}
}
void make_qrime(int n){
qrime.resize(n+1);
rep(i, 2, n){int ni = i / prime[i]; if(prime[i] == prime[ni]) qrime[i] = qrime[ni] * prime[i]; else qrime[i] = prime[i];}
}
bool exceed(ll x, ll y, ll m){return y > 0 && x >= m / y + 1;}
void mark(){ cout << "*" << endl; }
void yes(){ cout << "YES" << endl; }
void no(){ cout << "NO" << endl; }
ll floor(ll a, ll b){ if(b < 0) a *= -1, b *= -1; if(a >= 0) return a/b; else return -((-a+b-1)/b); }
ll ceil(ll a, ll b){ if(b < 0) a *= -1, b *= -1; if(a >= 0) return (a+b-1)/b; else return -((-a)/b); }
ll modulo(ll a, ll b){ b = abs(b); return a - floor(a, b) * b;}
ll sgn(ll x){ if(x > 0) return 1; if(x < 0) return -1; return 0;}
ll gcd(ll a, ll b){if(b == 0) return a; return gcd(b, a%b);}
ll lcm(ll a, ll b){return a/gcd(a, b)*b;}
ll arith(ll x){return x*(x+1)/2;}
ll arith(ll l, ll r){return arith(r) - arith(l-1);}
ll digitnum(ll x, ll b = 10){ll ret = 0; for(; x; x /= b) ret++; return ret;}
ll digitsum(ll x, ll b = 10){ll ret = 0; for(; x; x /= b) ret += x % b; return ret;}
string lltos(ll x, ll b = 10){string ret; for(;x;x/=b) ret += x % b + '0'; reverse(all(ret)); return ret;}
ll stoll(string &s, ll b = 10){ll ret = 0; for(auto c : s) ret *= b, ret += c - '0'; return ret;}
template<typename T> void uniq(T &vec){sort(all(vec)); vec.erase(unique(all(vec)), vec.end());}
int popcount(ull x){
x -= ((x>>1)&0x5555555555555555ULL), x = (x & 0x3333333333333333ULL) + ((x>>2) & 0x3333333333333333ULL);
return (((x + (x>>4)) & 0x0F0F0F0F0F0F0F0FULL) * 0x0101010101010101ULL) >> 56;
}
template<class S, class T> pair<S, T>& operator+=(pair<S, T> &s, const pair<S, T> &t){s.first += t.first, s.second += t.second; return s;}
template<class S, class T> pair<S, T>& operator-=(pair<S, T> &s, const pair<S, T> &t){s.first -= t.first, s.second -= t.second; return s;}
template<class S, class T> pair<S, T> operator+(const pair<S, T> &s, const pair<S, T> &t){return pair<S,T>(s.first+t.first, s.second+t.second);}
template<class S, class T> pair<S, T> operator-(const pair<S, T> &s, const pair<S, T> &t){return pair<S,T>(s.first-t.first, s.second-t.second);}
template<class T> T dot(const pair<T, T> &s, const pair<T, T> &t){return s.first*t.first + s.second*t.second;}
template<class T> T cross(const pair<T, T> &s, const pair<T, T> &t){return s.first*t.second - s.second*t.first;}
template<class T> T mdist(pair<T, T> s, pair<T, T> t){return abs(s.first-t.first) + abs(s.second-t.second);}
template<class T> T cdist(pair<T, T> s, pair<T, T> t){return max(abs(s.first-t.first), abs(s.second-t.second));}
template<class T> T edist2(pair<T, T> s, pair<T, T> t){return (s.first-t.first)*(s.first-t.first) + (s.second-t.second)*(s.second-t.second);}
template<typename T> ostream& operator << (ostream& os, vector<T>& vec){reps(i, vec) os << vec[i] << " "; return os;}
template<typename T> ostream& operator << (ostream& os, const vector<T>& vec){reps(i, vec) os << vec[i] << " "; return os;}
template<typename T> ostream& operator << (ostream& os, list<T>& ls){for(auto x : ls) os << x << " "; return os;}
template<typename T> ostream& operator << (ostream& os, const list<T>& ls){for(auto x : ls) os << x << " "; return os;}
template<typename T> ostream& operator << (ostream& os, deque<T>& deq){reps(i, deq) os << deq[i] << " "; return os;}
template<typename T, typename U> ostream& operator << (ostream& os, pair<T, U>& ope){ os << "(" << ope.first << ", " << ope.second << ")"; return os;}
template<typename T, typename U> ostream& operator << (ostream& os, const pair<T, U>& ope){ os << "(" << ope.first << ", " << ope.second << ")"; return os;}
template<typename T, typename U> ostream& operator << (ostream& os, map<T, U>& ope){ for(auto p : ope) os << "(" << p.first << ", " << p.second << "),";return os;}
template<typename T> ostream& operator << (ostream& os, set<T>& ope){for(auto x : ope) os << x << " "; return os;}
template<typename T> ostream& operator << (ostream& os, multiset<T>& ope){for(auto x : ope) os << x << " "; return os;}
template<typename T> void outa(T a[], ll s, ll t){rep(i, s, t){ cout << a[i]; if(i < t) cout << " ";} cout << endl;}
template<typename T, size_t N> ostream& operator << (ostream& os, array<T, N>& arr){reps(i, arr) os << arr[i] << " "; return os;}
template<typename T, size_t N> ostream& operator << (ostream& os, const array<T, N>& arr){reps(i, arr) os << arr[i] << " "; return os;}
void dump_func(){cout << endl;}
template <class Head, class... Tail>
void dump_func(Head &&head, Tail &&... tail){cout << head; if(sizeof...(Tail) > 0) cout << " "; dump_func(std::move(tail)...);}
struct NTT_Convolution{
NTT_Convolution(){};
static int rev(int x, int n){
int ret = 0;
for(int i = 0; i < n; i++) ret <<= 1, ret |= (x>>i) & 1;
return ret;
}
static void DFT(vector<mint> &f, vector<mint> &F, int n, mint root, bool inv = false)
{
int N = 1<<n;
F.resize(N);
for(int i = 0; i < N; i++) F[rev(i, n)] = f[i];
if(inv) root = root.inverse();
mint a, b, x, z;
for(int i = 0; i < n; i++){
int l = 1<<i;
z = modpow(root, 1<<(n-(i+1)));
for(int j = 0; j < N; j+=l*2){
x = 1;
for(int k = j; k < j+l; k++){
a = F[k], b = F[k+l] * x;
F[k] = a + b, F[k+l] = a - b, x *= z;
}
}
}
if(inv){
mint Ninv = mint(N).inverse();
for(int i = 0; i < N; i++) F[i] *= Ninv;
}
}
static void conv(vector<mint> f, vector<mint> g, vector<mint> &dest)
{
ll logf = 0, logg = 0, len = f.size() + g.size();
for(int i = f.size(); i; i /= 2) logf++;
for(int i = g.size(); i; i /= 2) logg++;
ll n = max(logf, logg)+1, N = 1<<n;
f.resize(N), g.resize(N);
mint root = modpow(mint(3), 119 * (1<<23-n));
vector<mint> F, G;
DFT(f, F, n, root), DFT(g, G, n, root);
for(int i = 0; i < N; i++) F[i] *= G[i];
DFT(F, f, n, root, true);
f.resize(len-1);
dest = f;
}
};
struct FPS{
static void inverse(vector<mint> f, int n, vector<mint> &dest)
{
int logn = digitnum(n, 2);
while(f.size() < (1<<logn)) f.push_back(mint(0));
vector<mint> fvec, gvec, Fvec, Gvec;
fvec.push_back(f[0]), gvec.push_back(f[0].inverse());
for(int i = 1; i <= logn; i++){
int l = 1<<i; mint root = modpow(mint(3), 119 * (1<<23-(i+1)));
while(fvec.size() < l) fvec.push_back(f[fvec.size()]);
fvec.resize(l*2);
NTT_Convolution::DFT(fvec, Fvec, i+1, root);
gvec.resize(l*2);
NTT_Convolution::DFT(gvec, Gvec, i+1, root);
for(int j = 0; j < l*2; j++) Gvec[j] = Gvec[j]*(mint(2) - Fvec[j]*Gvec[j]);
NTT_Convolution::DFT(Gvec, gvec, i+1, root, true);
fvec.resize(l), gvec.resize(l);
}
dest = gvec;
}
static void derivative(vector<mint> f, vector<mint> &dest)
{
dest.resize(f.size()-1);
if(dest.size() == 0){
dest.push_back(mint(0));
return;
}
for(int i = 0; i < dest.size(); i++) dest[i] = f[i+1] * mint(i+1);
}
static void integral(vector<mint> f, vector<mint> &dest)
{
dest.resize(f.size()+1);
dest[0] = mint(0);
for(int i = 0; i < f.size(); i++) dest[i+1] = f[i] / mint(i+1);
}
static void log(vector<mint> f, int n, vector<mint> &dest) //required: f[0] == 1
{
vector<mint> df;
FPS::derivative(f, df), FPS::inverse(f, n, f);
NTT_Convolution::conv(df, f, f);
FPS::integral(f, dest);
dest.resize(n);
}
static void exp(vector<mint> f, int n, vector<mint> &dest) //required: f[0] == 0
{
int logn = digitnum(n, 2);
while(f.size() < (1<<logn)) f.push_back(mint(0));
vector<mint> fvec, gvec, ngvec;
fvec.push_back(f[0]), gvec.push_back(mint(1));
for(int i = 1; i <= logn; i++){
while(fvec.size() < (1<<i)) fvec.push_back(f[fvec.size()]);
log(gvec, (1<<i), ngvec), ngvec.resize(1<<i);
for(int j = 0; j < (1<<i); j++) ngvec[j] = fvec[j] - ngvec[j];
ngvec[0] += mint(1);
NTT_Convolution::conv(gvec, ngvec, ngvec);
ngvec.resize(1<<i);
swap(gvec, ngvec);
}
dest = gvec, dest.resize(n);
}
};
ll n, m = 999630629;
ll a[100005];
ll cnt[10005];
mint inv[500005];
int main(void)
{
ios::sync_with_stdio(0);
cin.tie(0);
cin >> n;
rep(i, 1, n) cin >> a[i];
rep(i, 1, 500000) inv[i] = mint(i).inverse();
mint ans = 0;
rep(i, 1, n) ans += a[i];
ans *= modpow(2, n-1);
ll h = 1000000000 - m;
rep(i, 1, n) a[i] = 10000 - a[i], cnt[a[i]]++;
vector<mint> vec(h+1);
rep(i, 1, 10000){
if(cnt[i] == 0) continue;
for(int j = 1; j*i <= h; j++){
if(j % 2) vec[j*i] += inv[j] * cnt[i];
else vec[j*i] -= inv[j] * cnt[i];
}
}
FPS::exp(vec, h+1, vec);
ans -= vec[h]*m;
outl(ans);
return 0;
}