結果
| 問題 | No.2589 Prepare Integers |
| ユーザー |
 hitonanode
|
| 提出日時 | 2023-12-17 02:21:45 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
RE
|
| 実行時間 | - |
| コード長 | 19,759 bytes |
| コンパイル時間 | 2,268 ms |
| コンパイル使用メモリ | 198,544 KB |
| 実行使用メモリ | 6,944 KB |
| 最終ジャッジ日時 | 2024-09-27 07:54:35 |
| 合計ジャッジ時間 | 8,368 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 | AC | 2 ms
6,816 KB |
| testcase_01 | AC | 2 ms
6,940 KB |
| testcase_02 | AC | 2 ms
6,944 KB |
| testcase_03 | AC | 2 ms
6,940 KB |
| testcase_04 | RE | - |
| testcase_05 | RE | - |
| testcase_06 | WA | - |
| testcase_07 | RE | - |
| testcase_08 | WA | - |
| testcase_09 | WA | - |
| testcase_10 | WA | - |
| testcase_11 | WA | - |
| testcase_12 | RE | - |
| testcase_13 | RE | - |
| testcase_14 | WA | - |
| testcase_15 | RE | - |
| testcase_16 | WA | - |
| testcase_17 | WA | - |
| testcase_18 | WA | - |
| testcase_19 | WA | - |
| testcase_20 | WA | - |
| testcase_21 | WA | - |
| testcase_22 | WA | - |
| testcase_23 | WA | - |
| testcase_24 | WA | - |
| testcase_25 | AC | 103 ms
6,944 KB |
| testcase_26 | WA | - |
| testcase_27 | AC | 39 ms
6,940 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 <memory>
#include <numeric>
#include <optional>
#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> 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; }
const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }
template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }
template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }
template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <class 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 <class 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 <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::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) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl
#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr)
#else
#define dbg(x) ((void)0)
#define dbgif(cond, x) ((void)0)
#endif
#include <iostream>
#include <set>
#include <vector>
struct ModIntRuntime {
private:
static int md;
public:
using lint = long long;
static int mod() { return md; }
int val_;
static std::vector<ModIntRuntime> &facs() {
static std::vector<ModIntRuntime> facs_;
return facs_;
}
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 (ModIntRuntime(g).power((md - 1) / i) == 1) {
ok = false;
break;
}
if (ok) return g;
}
return -1;
}();
}
return primitive_root_;
}
static void set_mod(const int &m) {
if (md != m) facs().clear();
md = m;
get_primitive_root() = 0;
}
ModIntRuntime &_setval(lint v) {
val_ = (v >= md ? v - md : v);
return *this;
}
int val() const noexcept { return val_; }
ModIntRuntime() : val_(0) {}
ModIntRuntime(lint v) { _setval(v % md + md); }
explicit operator bool() const { return val_ != 0; }
ModIntRuntime operator+(const ModIntRuntime &x) const {
return ModIntRuntime()._setval((lint)val_ + x.val_);
}
ModIntRuntime operator-(const ModIntRuntime &x) const {
return ModIntRuntime()._setval((lint)val_ - x.val_ + md);
}
ModIntRuntime operator*(const ModIntRuntime &x) const {
return ModIntRuntime()._setval((lint)val_ * x.val_ % md);
}
// ModIntRuntime operator/(const ModIntRuntime &x) const {
// return ModIntRuntime()._setval((lint)val_ * x.inv().val() % md);
// }
ModIntRuntime operator-() const { return ModIntRuntime()._setval(md - val_); }
ModIntRuntime &operator+=(const ModIntRuntime &x) { return *this = *this + x; }
ModIntRuntime &operator-=(const ModIntRuntime &x) { return *this = *this - x; }
ModIntRuntime &operator*=(const ModIntRuntime &x) { return *this = *this * x; }
// ModIntRuntime &operator/=(const ModIntRuntime &x) { return *this = *this / x; }
friend ModIntRuntime operator+(lint a, const ModIntRuntime &x) {
return ModIntRuntime()._setval(a % md + x.val_);
}
friend ModIntRuntime operator-(lint a, const ModIntRuntime &x) {
return ModIntRuntime()._setval(a % md - x.val_ + md);
}
friend ModIntRuntime operator*(lint a, const ModIntRuntime &x) {
return ModIntRuntime()._setval(a % md * x.val_ % md);
}
// friend ModIntRuntime operator/(lint a, const ModIntRuntime &x) {
// return ModIntRuntime()._setval(a % md * x.inv().val() % md);
// }
bool operator==(const ModIntRuntime &x) const { return val_ == x.val_; }
bool operator!=(const ModIntRuntime &x) const { return val_ != x.val_; }
bool operator<(const ModIntRuntime &x) const {
return val_ < x.val_;
} // To use std::map<ModIntRuntime, T>
friend std::istream &operator>>(std::istream &is, ModIntRuntime &x) {
lint t;
return is >> t, x = ModIntRuntime(t), is;
}
friend std::ostream &operator<<(std::ostream &os, const ModIntRuntime &x) {
return os << x.val_;
}
lint power(lint n) const {
lint ans = 1, tmp = this->val_;
while (n) {
if (n & 1) ans = ans * tmp % md;
tmp = tmp * tmp % md;
n /= 2;
}
return ans;
}
ModIntRuntime pow(lint n) const { return power(n); }
// ModIntRuntime inv() const { return this->pow(md - 2); }
// ModIntRuntime fac() const {
// int l0 = facs().size();
// if (l0 > this->val_) return facs()[this->val_];
// facs().resize(this->val_ + 1);
// for (int i = l0; i <= this->val_; i++)
// facs()[i] = (i == 0 ? ModIntRuntime(1) : facs()[i - 1] * ModIntRuntime(i));
// return facs()[this->val_];
// }
// ModIntRuntime doublefac() const {
// lint k = (this->val_ + 1) / 2;
// return (this->val_ & 1)
// ? ModIntRuntime(k * 2).fac() / (ModIntRuntime(2).pow(k) * ModIntRuntime(k).fac())
// : ModIntRuntime(k).fac() * ModIntRuntime(2).pow(k);
// }
// ModIntRuntime nCr(int r) const {
// if (r < 0 or this->val_ < r) return ModIntRuntime(0);
// return this->fac() / ((*this - r).fac() * ModIntRuntime(r).fac());
// }
// ModIntRuntime sqrt() const {
// if (val_ == 0) return 0;
// if (md == 2) return val_;
// if (power((md - 1) / 2) != 1) return 0;
// ModIntRuntime b = 1;
// while (b.power((md - 1) / 2) == 1) b += 1;
// int e = 0, m = md - 1;
// while (m % 2 == 0) m >>= 1, e++;
// ModIntRuntime x = power((m - 1) / 2), y = (*this) * x * x;
// x *= (*this);
// ModIntRuntime z = b.power(m);
// while (y != 1) {
// int j = 0;
// ModIntRuntime t = y;
// while (t != 1) j++, t *= t;
// z = z.power(1LL << (e - j - 1));
// x *= z, z *= z, y *= z;
// e = j;
// }
// return ModIntRuntime(std::min(x.val_, md - x.val_));
// }
};
int ModIntRuntime::md = 1;
using mint = ModIntRuntime;
// Solve ax+by=gcd(a, b)
template <class Int> Int extgcd(Int a, Int b, Int &x, Int &y) {
Int d = a;
if (b != 0) {
d = extgcd(b, a % b, y, x), y -= (a / b) * x;
} else {
x = 1, y = 0;
}
return d;
}
// Calculate a^(-1) (MOD m) s if gcd(a, m) == 1
// Calculate x s.t. ax == gcd(a, m) MOD m
template <class Int> Int mod_inverse(Int a, Int m) {
Int x, y;
extgcd<Int>(a, m, x, y);
x %= m;
return x + (x < 0) * m;
}
// Require: 1 <= b
// return: (g, x) s.t. g = gcd(a, b), xa = g MOD b, 0 <= x < b/g
template <class Int> /* constexpr */ std::pair<Int, Int> inv_gcd(Int a, Int b) {
a %= b;
if (a < 0) a += b;
if (a == 0) return {b, 0};
Int s = b, t = a, m0 = 0, m1 = 1;
while (t) {
Int u = s / t;
s -= t * u, m0 -= m1 * u;
auto tmp = s;
s = t, t = tmp, tmp = m0, m0 = m1, m1 = tmp;
}
if (m0 < 0) m0 += b / s;
return {s, m0};
}
template <class Int>
/* constexpr */ std::pair<Int, Int> crt(const std::vector<Int> &r, const std::vector<Int> &m) {
assert(r.size() == m.size());
int n = int(r.size());
// Contracts: 0 <= r0 < m0
Int r0 = 0, m0 = 1;
for (int i = 0; i < n; i++) {
assert(1 <= m[i]);
Int r1 = r[i] % m[i], m1 = m[i];
if (r1 < 0) r1 += m1;
if (m0 < m1) {
std::swap(r0, r1);
std::swap(m0, m1);
}
if (m0 % m1 == 0) {
if (r0 % m1 != r1) return {0, 0};
continue;
}
Int g, im;
std::tie(g, im) = inv_gcd<Int>(m0, m1);
Int u1 = m1 / g;
if ((r1 - r0) % g) return {0, 0};
Int x = (r1 - r0) / g % u1 * im % u1;
r0 += x * m0;
m0 *= u1;
if (r0 < 0) r0 += m0;
}
return {r0, m0};
}
// 蟻本 P.262
// 中国剰余定理を利用して，色々な素数で割った余りから元の値を復元
// 連立線形合同式 A * x = B mod M の解
// Requirement: M[i] > 0
// Output: x = first MOD second (if solution exists), (0, 0) (otherwise)
template <class Int>
std::pair<Int, Int>
linear_congruence(const std::vector<Int> &A, const std::vector<Int> &B, const std::vector<Int> &M) {
Int r = 0, m = 1;
assert(A.size() == M.size());
assert(B.size() == M.size());
for (int i = 0; i < (int)A.size(); i++) {
assert(M[i] > 0);
const Int ai = A[i] % M[i];
Int a = ai * m, b = B[i] - ai * r, d = std::__gcd(M[i], a);
if (b % d != 0) {
return std::make_pair(0, 0); // 解なし
}
Int t = b / d * mod_inverse<Int>(a / d, M[i] / d) % (M[i] / d);
r += m * t;
m *= M[i] / d;
}
return std::make_pair((r < 0 ? r + m : r), m);
}
int K;
int D = 1;
vector<mint> to_basek(lint x) {
vector<mint> res(D);
REP(d, D) {
res.at(D - 1 - d) = x % K;
x /= K;
if (!x) break;
}
return res;
}
int main() {
int Q;
{
cin >> K >> Q;
mint::set_mod(K);
D = 1;
__int128 ub = K;
while (ub <= 1LL << 60) {
ub *= K;
D++;
}
}
dbg(D);
assert(pow(K, D) > 1e18);
vector<vector<mint>> base(D);
auto count_less_or_eq = [&](lint x) -> lint {
assert(x >= 0);
if (x == 0) return 1;
const auto ub = to_basek(x);
lint nall = 1;
REP(d, D) {
if (base.at(d).empty()) continue;
nall *= K / base.at(d).at(d).val();
}
// dbg(nall);
vector<mint> current(D);
lint ret = 0;
bool break_used = false;
REP(d, D) {
// const int lo = (mint(K) - current.at(d)).val();
// const int hi = (ub.at(d) - current.at(d)).val();
if (base.at(d).empty()) {
if (ub.at(d) < current.at(d)) {
break_used = true;
break;
} else if (ub.at(d) == current.at(d)) {
} else {
ret += nall;
nall = 0;
break_used = true;
break;
}
} else {
const int m = base.at(d).at(d).val();
nall /= K / m;
auto calc_width = [&](int lo, int hi) -> int {
int now = current.at(d).val();
chmax(lo, now);
if (lo >= hi) return 0;
assert(now <= lo and lo < hi);
lo -= now;
hi -= now;
int ilo = (lo + m - 1) / m;
int ihi = min(K / m, (hi + m - 1) / m);
return ihi - ilo;
};
const int width = calc_width(0, ub.at(d).val()) + calc_width(K, K + ub.at(d).val());
ret += lint(width) * nall;
if ((ub.at(d) - current.at(d)).val() % m == 0) {
const mint c = (ub.at(d) - current.at(d)).val() / m;
REP(i, D) current.at(i) += (c * base.at(d).at(i)).val();
assert(current.at(d) == ub.at(d));
} else {
break_used = true;
nall = 0;
break;
}
}
}
assert(nall == 0 or nall == 1);
return nall + ret;
// if (!break_used) ++ret;
// return ret;
};
while (Q--) {
int t;
cin >> t;
if (t == 1) {
int x;
cin >> x;
auto v = to_basek(x);
REP(d, D) {
if (!v.at(d)) continue;
if (base.at(d).empty()) {
int g = std::gcd(K, v.at(d).val());
mint c = mod_inverse<lint>(v.at(d).val() / g, K / g);
for (auto &x : v) x *= c;
base.at(d) = v;
break;
}
{
lint p, q;
const lint g = extgcd<lint>(v.at(d).val(), base.at(d).at(d).val(), p, q);
dbg(make_tuple(d, p, q));
if (q == 0) {
swap(p, q);
swap(base.at(d), v);
}
vector<mint> new_b(v.size());
REP(i, v.size()) new_b.at(i) = (mint(v.at(i)) * p + mint(base.at(d).at(i)) * q).val();
assert(new_b.at(d) == g);
base.at(d) = new_b;
mint w = v.at(d).val() / g;
REP(i, v.size()) v.at(i) = (mint(v.at(i)) - w * base.at(d).at(i)).val();
assert(v.at(d) == 0);
}
}
dbg(make_tuple("Added", x, to_basek(x), v));
for (auto b : base) if (b.size()) dbg(b);
} else {
lint x;
cin >> x;
if (t == 3) {
cout << count_less_or_eq(x) << '\n';
} else if (t == 2) {
// lo 以下は x 個未満、 hi 以下は x 個以上
constexpr lint inf = 1LL << 60;
lint lo = x - 2, hi = inf;
while (hi - lo > 1) {
const lint c = (lo + hi) / 2;
if (count_less_or_eq(c) < x) lo = c;
else hi = c;
}
if (hi == inf) cout << -1 << '\n';
else cout << hi << '\n';
}
}
}
}