結果
| 問題 | No.1697 Deque House |
| ユーザー |
 hitonanode
|
| 提出日時 | 2021-10-01 23:21:23 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 77 ms / 3,500 ms |
| コード長 | 13,822 bytes |
| コンパイル時間 | 2,096 ms |
| コンパイル使用メモリ | 181,664 KB |
| 実行使用メモリ | 35,828 KB |
| 最終ジャッジ日時 | 2024-07-19 16:10:24 |
| 合計ジャッジ時間 | 3,830 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge3 |
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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 | AC | 2 ms
5,248 KB |
| testcase_01 | AC | 1 ms
5,376 KB |
| testcase_02 | AC | 3 ms
5,376 KB |
| testcase_03 | AC | 2 ms
5,376 KB |
| testcase_04 | AC | 1 ms
5,376 KB |
| testcase_05 | AC | 2 ms
5,376 KB |
| testcase_06 | AC | 2 ms
5,376 KB |
| testcase_07 | AC | 5 ms
5,376 KB |
| testcase_08 | AC | 16 ms
10,496 KB |
| testcase_09 | AC | 57 ms
13,824 KB |
| testcase_10 | AC | 26 ms
9,088 KB |
| testcase_11 | AC | 26 ms
8,960 KB |
| testcase_12 | AC | 20 ms
8,064 KB |
| testcase_13 | AC | 13 ms
5,632 KB |
| testcase_14 | AC | 18 ms
6,656 KB |
| testcase_15 | AC | 35 ms
11,108 KB |
| testcase_16 | AC | 31 ms
8,704 KB |
| testcase_17 | AC | 18 ms
6,272 KB |
| testcase_18 | AC | 18 ms
6,912 KB |
| testcase_19 | AC | 77 ms
35,828 KB |
| testcase_20 | AC | 55 ms
13,696 KB |
| testcase_21 | AC | 57 ms
13,824 KB |
| testcase_22 | AC | 56 ms
13,696 KB |
ソースコード
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template <typename T> vector<T> sort_unique(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <typename T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <typename T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T, size_t sz> ostream &operator<<(ostream &os, const array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
#if __cplusplus >= 201703L
template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
#endif
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <typename TK, typename TV, typename TH> ostream &operator<<(ostream &os, const unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl
#define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr)
#else
#define dbg(x) (x)
#define dbgif(cond, x) 0
#endif
template <int md> struct ModInt {
#if __cplusplus >= 201402L
#define MDCONST constexpr
#else
#define MDCONST
#endif
using lint = long long;
MDCONST static int mod() { return md; }
static int get_primitive_root() {
static int primitive_root = 0;
if (!primitive_root) {
primitive_root = [&]() {
std::set<int> fac;
int v = md - 1;
for (lint i = 2; i * i <= v; i++)
while (v % i == 0) fac.insert(i), v /= i;
if (v > 1) fac.insert(v);
for (int g = 1; g < md; g++) {
bool ok = true;
for (auto i : fac)
if (ModInt(g).pow((md - 1) / i) == 1) {
ok = false;
break;
}
if (ok) return g;
}
return -1;
}();
}
return primitive_root;
}
int val;
MDCONST ModInt() : val(0) {}
MDCONST ModInt &_setval(lint v) { return val = (v >= md ? v - md : v), *this; }
MDCONST ModInt(lint v) { _setval(v % md + md); }
MDCONST explicit operator bool() const { return val != 0; }
MDCONST ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); }
MDCONST ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + md); }
MDCONST ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % md); }
MDCONST ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % md); }
MDCONST ModInt operator-() const { return ModInt()._setval(md - val); }
MDCONST ModInt &operator+=(const ModInt &x) { return *this = *this + x; }
MDCONST ModInt &operator-=(const ModInt &x) { return *this = *this - x; }
MDCONST ModInt &operator*=(const ModInt &x) { return *this = *this * x; }
MDCONST ModInt &operator/=(const ModInt &x) { return *this = *this / x; }
friend MDCONST ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % md + x.val); }
friend MDCONST ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % md - x.val + md); }
friend MDCONST ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % md * x.val % md); }
friend MDCONST ModInt operator/(lint a, const ModInt &x) {
return ModInt()._setval(a % md * x.inv() % md);
}
MDCONST bool operator==(const ModInt &x) const { return val == x.val; }
MDCONST bool operator!=(const ModInt &x) const { return val != x.val; }
MDCONST bool operator<(const ModInt &x) const { return val < x.val; } // To use std::map<ModInt, T>
friend std::istream &operator>>(std::istream &is, ModInt &x) {
lint t;
return is >> t, x = ModInt(t), is;
}
MDCONST friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { return os << x.val; }
MDCONST ModInt pow(lint n) const {
ModInt ans = 1, tmp = *this;
while (n) {
if (n & 1) ans *= tmp;
tmp *= tmp, n >>= 1;
}
return ans;
}
static std::vector<ModInt> facs, facinvs, invs;
MDCONST static void _precalculation(int N) {
int l0 = facs.size();
if (N > md) N = md;
if (N <= l0) return;
facs.resize(N), facinvs.resize(N), invs.resize(N);
for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i;
facinvs[N - 1] = facs.back().pow(md - 2);
for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1);
for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1];
}
MDCONST lint inv() const {
if (this->val < std::min(md >> 1, 1 << 21)) {
while (this->val >= int(facs.size())) _precalculation(facs.size() * 2);
return invs[this->val].val;
} else {
return this->pow(md - 2).val;
}
}
MDCONST ModInt fac() const {
while (this->val >= int(facs.size())) _precalculation(facs.size() * 2);
return facs[this->val];
}
MDCONST ModInt facinv() const {
while (this->val >= int(facs.size())) _precalculation(facs.size() * 2);
return facinvs[this->val];
}
MDCONST ModInt doublefac() const {
lint k = (this->val + 1) / 2;
return (this->val & 1) ? ModInt(k * 2).fac() / (ModInt(2).pow(k) * ModInt(k).fac())
: ModInt(k).fac() * ModInt(2).pow(k);
}
MDCONST ModInt nCr(const ModInt &r) const {
return (this->val < r.val) ? 0 : this->fac() * (*this - r).facinv() * r.facinv();
}
MDCONST ModInt nPr(const ModInt &r) const {
return (this->val < r.val) ? 0 : this->fac() * (*this - r).facinv();
}
ModInt sqrt() const {
if (val == 0) return 0;
if (md == 2) return val;
if (pow((md - 1) / 2) != 1) return 0;
ModInt b = 1;
while (b.pow((md - 1) / 2) == 1) b += 1;
int e = 0, m = md - 1;
while (m % 2 == 0) m >>= 1, e++;
ModInt x = pow((m - 1) / 2), y = (*this) * x * x;
x *= (*this);
ModInt z = b.pow(m);
while (y != 1) {
int j = 0;
ModInt t = y;
while (t != 1) j++, t *= t;
z = z.pow(1LL << (e - j - 1));
x *= z, z *= z, y *= z;
e = j;
}
return ModInt(std::min(x.val, md - x.val));
}
};
template <int md> std::vector<ModInt<md>> ModInt<md>::facs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::facinvs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::invs = {0};
using mint = ModInt<998244353>;
int main() {
int N, K;
cin >> N >> K;
vector<mint> A(N);
cin >> A;
vector ap(N, vector<mint>(K + 1));
REP(i, N) {
ap[i][0] = 1;
FOR(d, 1, ap[i].size()) ap[i][d] = ap[i][d - 1] * A[i];
}
mint ret = 0;
// const mint pow2invk = mint(2).pow(K).inv();
vector<mint> pow2(K * 2 + 10, 1);
FOR(i, 1, pow2.size()) pow2[i] = pow2[i - 1] * 2;
vector dpn(3, vector<mint>(K + 1));
vector dpsum(3, vector<mint>(K + 1));
dpn[0][0] = pow2[K * 2].inv();
// dpn[0][0] = 1;
dbg(ap);
REP(i, N) {
REP(k, K) {
dpsum[0][k + 1] += dpsum[0][k];
dpn[0][k + 1] += dpn[0][k];
}
IREP(k, K) {
dpsum[2][k] += dpsum[2][k + 1];
dpn[2][k] += dpn[2][k + 1];
}
REP(d, 3) REP(k, K + 1) {
dpsum[d][k] = (dpsum[d][k] + dpn[d][k] * ap[i][k]) * pow2[k];
dpn[d][k] *= pow2[k];
}
IREP(d, 2) {
dpsum[d + 1][K] += dpsum[d][K];
dpn[d + 1][K] += dpn[d][K];
dpsum[d][K] = dpn[d][K] = 0;
}
dbg(dpn);
dbg(dpsum);
}
cout << accumulate(ALL(dpsum[2]), mint(0)) << '\n';
// auto rec = [&](auto &&self, int l, int r) -> void {
// if (l + 2 > r) return;
// int c = (l + r) / 2;
// mint nl, suml, nr, sumr;
// {
// vector<mint> dpnr(K + 1), dpsumr(K + 1);
// dpnr[K] = 1, dpsumr[K] = ap[c][K];
// FOR(i, c + 1, r) {
// IFOR(k, 1, K + 1) {
// dpnr[k - 1] += dpnr[k];
// dpsumr[k - 1] += dpsumr[k];
// }
// REP(k, K + 1) {
// dpsumr[k] = (dpsumr[k] + dpnr[k] * ap[i][k]) * pow2[k];
// dpnr[k] = dpnr[k] * pow2[k];
// }
// }
// nr = accumulate(ALL(dpnr), mint(0));
// sumr = accumulate(ALL(dpsumr), mint(0));
// }
// {
// vector<mint> dpnl(K + 1), dpsuml(K + 1);
// dpnl[K] = 1, dpsuml[K] = ap[c - 1][K];
// IFOR(i, l, c - 1) {
// IFOR(k, 1, K + 1) {
// dpnl[k - 1] += dpnl[k];
// dpsuml[k - 1] += dpsuml[k];
// }
// REP(k, K + 1) {
// dpsuml[k] = (dpsuml[k] + dpnl[k] * ap[i][k]) * pow2[k];
// dpnl[k] = dpnl[k] * pow2[k];
// }
// }
// nl = accumulate(ALL(dpnl), mint(0));
// suml = accumulate(ALL(dpsuml), mint(0));
// }
// dbg((vector<int>{l, c, r}));
// ret += nr * suml + nl * sumr + nl * nr * (N - (r - l));
// dbg(ret);
// self(self, l, c);
// self(self, c, r);
// };
// rec(rec, 0, N);
// cout << ret << '\n';
}