結果
| 問題 | No.2365 Present of good number |
| ユーザー |
 iiljj
|
| 提出日時 | 2023-06-30 22:29:26 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 3 ms / 2,000 ms |
| コード長 | 19,487 bytes |
| コンパイル時間 | 2,726 ms |
| コンパイル使用メモリ | 161,044 KB |
| 実行使用メモリ | 4,380 KB |
| 最終ジャッジ日時 | 2023-09-21 16:37:53 |
| 合計ジャッジ時間 | 3,141 ms |
|
ジャッジサーバーID （参考情報） |
judge13 / judge15 |
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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 | 1 ms
4,380 KB |
| testcase_01 | AC | 1 ms
4,380 KB |
| testcase_02 | AC | 2 ms
4,376 KB |
| testcase_03 | AC | 2 ms
4,380 KB |
| testcase_04 | AC | 2 ms
4,376 KB |
| testcase_05 | AC | 2 ms
4,380 KB |
| testcase_06 | AC | 2 ms
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| testcase_07 | AC | 2 ms
4,376 KB |
| testcase_08 | AC | 2 ms
4,376 KB |
| testcase_09 | AC | 2 ms
4,380 KB |
| testcase_10 | AC | 3 ms
4,376 KB |
| testcase_11 | AC | 1 ms
4,380 KB |
| testcase_12 | AC | 2 ms
4,380 KB |
| testcase_13 | AC | 2 ms
4,380 KB |
| testcase_14 | AC | 2 ms
4,376 KB |
| testcase_15 | AC | 2 ms
4,376 KB |
| testcase_16 | AC | 1 ms
4,380 KB |
| testcase_17 | AC | 2 ms
4,376 KB |
| testcase_18 | AC | 1 ms
4,380 KB |
| testcase_19 | AC | 1 ms
4,380 KB |
| testcase_20 | AC | 1 ms
4,376 KB |
| testcase_21 | AC | 1 ms
4,380 KB |
| testcase_22 | AC | 1 ms
4,376 KB |
| testcase_23 | AC | 2 ms
4,380 KB |
| testcase_24 | AC | 2 ms
4,376 KB |
| testcase_25 | AC | 2 ms
4,380 KB |
| testcase_26 | AC | 2 ms
4,380 KB |
| testcase_27 | AC | 2 ms
4,380 KB |
| testcase_28 | AC | 1 ms
4,376 KB |
| testcase_29 | AC | 2 ms
4,376 KB |
| testcase_30 | AC | 1 ms
4,380 KB |
| testcase_31 | AC | 2 ms
4,376 KB |
| testcase_32 | AC | 1 ms
4,376 KB |
| testcase_33 | AC | 1 ms
4,380 KB |
| testcase_34 | AC | 2 ms
4,376 KB |
| testcase_35 | AC | 1 ms
4,376 KB |
| testcase_36 | AC | 2 ms
4,380 KB |
| testcase_37 | AC | 2 ms
4,376 KB |
| testcase_38 | AC | 2 ms
4,376 KB |
| testcase_39 | AC | 2 ms
4,376 KB |
| testcase_40 | AC | 2 ms
4,380 KB |
ソースコード
/* #region Head */
// #include <bits/stdc++.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert> // assert.h
#include <cmath> // math.h
#include <cstring>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <memory>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <vector>
using namespace std;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pll = pair<ll, ll>;
template <class T> using vc = vector<T>;
template <class T> using vvc = vc<vc<T>>;
using vll = vc<ll>;
using vvll = vvc<ll>;
using vld = vc<ld>;
using vvld = vvc<ld>;
using vs = vc<string>;
using vvs = vvc<string>;
template <class T, class U> using um = unordered_map<T, U>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqa = priority_queue<T, vc<T>, greater<T>>;
template <class T> using us = unordered_set<T>;
#define TREP(T, i, m, n) for (T i = (m), i##_len = (T)(n); i < i##_len; ++(i))
#define TREPM(T, i, m, n) for (T i = (m), i##_max = (T)(n); i <= i##_max; ++(i))
#define TREPR(T, i, m, n) for (T i = (m), i##_min = (T)(n); i >= i##_min; --(i))
#define TREPD(T, i, m, n, d) for (T i = (m), i##_len = (T)(n); i < i##_len; i += (d))
#define TREPMD(T, i, m, n, d) for (T i = (m), i##_max = (T)(n); i <= i##_max; i += (d))
#define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i))
#define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i))
#define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i))
#define REPD(i, m, n, d) for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d))
#define REPMD(i, m, n, d) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d))
#define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++)
#define REPIR(itr, ds) for (auto itr = ds.rbegin(); itr != ds.rend(); itr++)
#define ALL(x) begin(x), end(x)
#define SIZE(x) ((ll)(x).size())
#define ISIZE(x) ((int)(x).size())
#define PERM(c) \
sort(ALL(c)); \
for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c)))
#define UNIQ(v) v.erase(unique(ALL(v)), v.end());
#define CEIL(a, b) (((a) + (b)-1) / (b))
#define endl '\n'
constexpr ll INF = 1'010'000'000'000'000'017LL;
constexpr int IINF = 1'000'000'007LL;
constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7
// constexpr ll MOD = 998244353;
constexpr ld EPS = 1e-12;
constexpr ld PI = 3.14159265358979323846;
template <typename T> istream &operator>>(istream &is, vc<T> &vec) { // vector 入力
for (T &x : vec) is >> x;
return is;
}
template <typename T> ostream &operator<<(ostream &os, const vc<T> &vec) { // vector 出力 (for dump)
os << "{";
REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", ");
os << "}";
return os;
}
template <typename T> ostream &operator>>(ostream &os, const vc<T> &vec) { // vector 出力 (inline)
REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\n" : " ");
return os;
}
template <typename T, size_t _Nm> istream &operator>>(istream &is, array<T, _Nm> &arr) { // array 入力
REP(i, 0, SIZE(arr)) is >> arr[i];
return is;
}
template <typename T, size_t _Nm> ostream &operator<<(ostream &os, const array<T, _Nm> &arr) { // array 出力 (for dump)
os << "{";
REP(i, 0, SIZE(arr)) os << arr[i] << (i == i_len - 1 ? "" : ", ");
os << "}";
return os;
}
template <typename T, typename U> istream &operator>>(istream &is, pair<T, U> &pair_var) { // pair 入力
is >> pair_var.first >> pair_var.second;
return is;
}
template <typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &pair_var) { // pair 出力
os << "(" << pair_var.first << ", " << pair_var.second << ")";
return os;
}
// map, um, set, us 出力
template <class T> ostream &out_iter(ostream &os, const T &map_var) {
os << "{";
REPI(itr, map_var) {
os << *itr;
auto itrcp = itr;
if (++itrcp != map_var.end()) os << ", ";
}
return os << "}";
}
template <typename T, typename U> ostream &operator<<(ostream &os, const map<T, U> &map_var) {
return out_iter(os, map_var);
}
template <typename T, typename U> ostream &operator<<(ostream &os, const um<T, U> &map_var) {
os << "{";
REPI(itr, map_var) {
auto [key, value] = *itr;
os << "(" << key << ", " << value << ")";
auto itrcp = itr;
if (++itrcp != map_var.end()) os << ", ";
}
os << "}";
return os;
}
template <typename T> ostream &operator<<(ostream &os, const set<T> &set_var) { return out_iter(os, set_var); }
template <typename T> ostream &operator<<(ostream &os, const us<T> &set_var) { return out_iter(os, set_var); }
template <typename T> ostream &operator<<(ostream &os, const pq<T> &pq_var) {
pq<T> pq_cp(pq_var);
os << "{";
if (!pq_cp.empty()) {
os << pq_cp.top(), pq_cp.pop();
while (!pq_cp.empty()) os << ", " << pq_cp.top(), pq_cp.pop();
}
return os << "}";
}
// tuple 出力
template <size_t N = 0, bool end_line = false, typename... Args> ostream &operator<<(ostream &os, tuple<Args...> &a) {
if constexpr (N < std::tuple_size_v<tuple<Args...>>) {
os << get<N>(a);
if constexpr (N + 1 < std::tuple_size_v<tuple<Args...>>) {
os << ' ';
} else if constexpr (end_line) {
os << '\n';
}
return operator<< <N + 1, end_line>(os, a);
}
return os;
}
template <typename... Args> void print_tuple(tuple<Args...> &a) { operator<< <0, true>(std::cout, a); }
void pprint() { std::cout << endl; }
template <class Head, class... Tail> void pprint(Head &&head, Tail &&...tail) {
std::cout << head;
if (sizeof...(Tail) > 0) std::cout << ' ';
pprint(move(tail)...);
}
// dump
#define DUMPOUT cerr
void dump_func() { DUMPOUT << endl; }
template <class Head, class... Tail> void dump_func(Head &&head, Tail &&...tail) {
DUMPOUT << head;
if (sizeof...(Tail) > 0) DUMPOUT << ", ";
dump_func(move(tail)...);
}
// chmax (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>> bool chmax(T &xmax, const U &x, Comp comp = {}) {
if (comp(xmax, x)) {
xmax = x;
return true;
}
return false;
}
// chmin (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>> bool chmin(T &xmin, const U &x, Comp comp = {}) {
if (comp(x, xmin)) {
xmin = x;
return true;
}
return false;
}
// ローカル用
#ifndef ONLINE_JUDGE
#define DEBUG_
#endif
#ifndef MYLOCAL
#undef DEBUG_
#endif
#ifdef DEBUG_
#define DEB
#define dump(...) \
DUMPOUT << " " << string(#__VA_ARGS__) << ": " \
<< "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl \
<< " ", \
dump_func(__VA_ARGS__)
#else
#define DEB if (false)
#define dump(...)
#endif
#define VAR(type, ...) \
type __VA_ARGS__; \
assert((std::cin >> __VA_ARGS__));
template <typename T> istream &operator,(istream &is, T &rhs) { return is >> rhs; }
template <typename T> ostream &operator,(ostream &os, const T &rhs) { return os << ' ' << rhs; }
struct AtCoderInitialize {
static constexpr int IOS_PREC = 15;
static constexpr bool AUTOFLUSH = false;
AtCoderInitialize() {
ios_base::sync_with_stdio(false), std::cin.tie(nullptr), std::cout.tie(nullptr);
std::cout << fixed << setprecision(IOS_PREC);
if (AUTOFLUSH) std::cout << unitbuf;
}
} ATCODER_INITIALIZE;
void Yn(bool p) { std::cout << (p ? "Yes" : "No") << endl; }
void YN(bool p) { std::cout << (p ? "YES" : "NO") << endl; }
template <typename T> constexpr void operator--(vc<T> &v, int) noexcept {
for (int i = 0; i < ISIZE(v); ++i) v[i]--;
}
template <typename T> constexpr void operator++(vc<T> &v, int) noexcept {
for (int i = 0; i < ISIZE(v); ++i) v[i]++;
}
/* #endregion */
// #include <atcoder/all>
// using namespace atcoder;
/* #region mint */
// 自動で MOD を取る整数
template <ll MOD> struct mint {
ll x;
constexpr mint(ll x = 0) : x((x % MOD + MOD) % MOD) {}
constexpr mint &operator+=(const mint &a) {
if ((x += a.x) >= MOD) x -= MOD;
return *this;
}
constexpr mint &operator-=(const mint &a) {
if ((x += MOD - a.x) >= MOD) x -= MOD;
return *this;
}
constexpr mint &operator*=(const mint &a) {
(x *= a.x) %= MOD;
return *this;
}
constexpr mint operator+(const mint &a) const {
mint res(*this);
return res += a;
}
constexpr mint operator-(const mint &a) const {
mint res(*this);
return res -= a;
}
constexpr mint operator*(const mint &a) const {
mint res(*this);
return res *= a;
}
// O(log(t))
constexpr mint pow_rec(ll t) const {
if (!t) return 1;
mint a = pow(t >> 1); // ⌊t/2⌋ 乗
a *= a; // ⌊t/2⌋*2 乗
if (t & 1) // ⌊t/2⌋*2 == t-1 のとき
a *= *this; // ⌊t/2⌋*2+1 乗 => t 乗
return a;
}
constexpr mint pow(ll t) const {
mint a(*this);
mint res = 1;
while (t) {
if (t & 1) res *= a;
t >>= 1, a *= a;
}
return res;
}
// for prime mod
constexpr mint inv_prime() const {
return pow(MOD - 2); // オイラーの定理から， x^(-1) ≡ x^(p-2)
}
constexpr mint inv() const {
ll a = this->x, b = MOD, u = 1, v = 0, t = 0;
mint res;
while (b) {
t = a / b;
a -= t * b;
swap(a, b);
u -= t * v;
swap(u, v);
}
if (u < 0) u += MOD;
res = u;
return res;
}
constexpr mint &operator/=(const mint &a) { return (*this) *= a.inv(); }
constexpr mint operator/(const mint &a) const {
mint res(*this);
return res /= a;
}
constexpr bool operator==(const mint &a) const { return this->x == a.x; }
constexpr bool operator==(const ll a) const { return this->x == a; }
constexpr bool operator!=(const mint &a) const { return this->x != a.x; }
constexpr bool operator!=(const ll a) const { return this->x != a; }
mint operator+() const { return *this; }
mint operator-() const { return *this * (-1); }
// mint 入力
friend istream &operator>>(istream &is, mint &x) {
is >> x.x;
return is;
}
// mint 出力
friend ostream &operator<<(ostream &os, const mint x) {
os << x.x;
return os;
}
};
/* #endregion */
/* #region Mat */
template <typename T> constexpr bool false_v = false;
// 行列，==, !=, [] あたりは vector と一緒
template <class Num> class Mat : public vc<vc<Num>> {
public:
// using vc<vc<Num>>::vector;
size_t h, w;
// コンストラクタ
Mat<Num>(const size_t h, size_t w) : vc<vc<Num>>(h, vc<Num>(w, 0)), h(h), w(w) {}
// Mat<Num>(const Mat<Num> &mt) : vc<vc<Num>>(mt), h(mt.h), w(mt.w) {}
Mat<Num>(std::initializer_list<vc<Num>> init) : vc<vc<Num>>() {
for (auto iter = init.begin(); iter != init.end(); ++iter) this->emplace_back(*iter);
h = this->size(), w = (*this)[0].size();
}
// 行列に別の行列を足す
Mat &operator+=(const Mat &another) {
assert(this->h == another.h && this->w == another.w);
REP(i, 0, this->h) REP(j, 0, this->w)(*this)[i][j] += another[i][j];
return *this;
}
// 行列から別の行列を引く
Mat &operator-=(const Mat &another) {
assert(this->h == another.h && this->w == another.w);
REP(i, 0, this->h) REP(j, 0, this->w)(*this)[i][j] -= another[i][j];
return *this;
}
// 行列に別の行列を右から掛ける
Mat &operator*=(const Mat &another) {
assert(w == another.h);
Mat<Num> ret(this->h, another.w);
REP(i, 0, this->h) REP(j, 0, another.w) REP(k, 0, this->w) ret[i][j] += (*this)[i][k] * another[k][j];
*this = ret;
return *this;
}
// 行列に別の行列を足す
Mat operator+(const Mat &another) const {
Mat<Num> ret(*this);
return ret += another;
}
// 行列から別の行列を引く
Mat operator-(const Mat &another) const {
Mat<Num> ret(*this);
return ret -= another;
}
// 行列に別の行列を右から掛ける
Mat operator*(const Mat &another) const {
Mat<Num> ret(*this);
return ret *= another;
}
// 行列の n 乗を計算する
Mat pow(ll n) const {
assert(this->h == this->w);
Mat<Num> ret(this->h, this->w);
Mat<Num> a(*this);
REP(i, 0, this->h) ret[i][i] = 1;
while (n) {
if (n & 1) ret = a * ret;
a = a * a, n >>= 1;
}
return ret;
}
template <class... T> Mat assign(T... nums) {
vc<Num> num_list = vc<Num>{nums...};
assert(num_list.size() == this->h * this->w);
REP(i, 0, this->h) REP(j, 0, this->w)(*this)[i][j] = num_list[this->w * i + j];
return *this;
}
void fill(Num num) { REP(i, 0, this->h) REP(j, 0, this->w)(*this)[i][j] = num; }
void print() { REP(i, 0, h) REP(j, 0, w) cout << (*this)[i][j] << (j == (ll)w - 1 ? '\n' : ' '); }
};
/* #endregion */
struct Sieve {
int n;
int sqrtn;
vc<int> sieve; // sieve[i] := i の最小の素因数
// コンストラクタ．前処理を行う．
Sieve(int n) : n(n), sqrtn((int)sqrtl(n)), sieve(n + 1) {
iota(ALL(sieve), 0); // 各要素をインデックスで初期化（0, 1, ..., n）．使用するのは 2, 3, ...
REPM(i, 2, sqrtn) {
if (sieve[i] < i) continue; // i は合成数
// assert(i は素数)
sieve[i] = i;
// n 以下の任意の i の倍数 j について，j が i 未満の素数で割れなかった場合
REPMD(j, i * i, n, i) if (sieve[j] == j) sieve[j] = i; // j の最小の素因数は i
}
}
// 素因数分解クエリ，O(log n)
vc<int> pfd(int m) const {
assert(m <= n);
vc<int> prime_factors;
while (m > 1) {
prime_factors.push_back(sieve[m]);
m /= sieve[m];
}
return prime_factors;
}
// 素因数分解クエリ，O(log n)
map<int, int> pfd_map(int m) const {
assert(m <= n);
map<int, int> prime_factors; //
while (m > 1) {
prime_factors[sieve[m]]++;
m /= sieve[m];
}
return prime_factors;
}
// m が素数かどうかを返す
bool is_prime(const int m) const {
return sieve[m] == m; //
}
// n 以下の素数一覧を返す
vc<int> primes() const {
vc<int> ret;
REPM(i, 2, n) if (is_prime(i)) ret.push_back(i);
return ret;
}
// a の約数を列挙する
vc<int> devisors(const int a) const {
assert(a <= n);
map<int, int> mp = pfd_map(a);
vc<pair<int, int>> V; // mp をベクトルに変換したもの
for (auto pa : mp) {
V.push_back(pa);
}
// 戻り値（入れ物）
vc<int> Y;
auto dfsd = [&Y, &V](auto &&dfsd, int cur_idx, int cur_val) -> void {
if (cur_idx == (int)V.size()) {
// 値が完成
Y.push_back(cur_val);
return;
}
const auto [v, c] = V[cur_idx];
// p乗を全通り試す (0, ..., p乗)
int mul = 1;
REP(p, 0, c + 1) {
dfsd(dfsd, cur_idx + 1, cur_val * mul);
mul *= v;
}
return;
};
dfsd(dfsd, 0, 1);
sort(ALL(Y));
return Y;
}
};
// Problem
void solve() {
VAR(ll, n, k); //
Sieve sieve(n + 2);
map<int, int> pfactors = sieve.pfd_map(n);
int max_prime_factor = pfactors.rbegin()->first;
if (max_prime_factor == 2) {
max_prime_factor = 3;
}
// 使うかもしれない素数を列挙する
vc<int> primes = sieve.primes();
while (primes.size() && primes.back() > max_prime_factor) {
primes.pop_back();
}
// dump(SIZE(primes));
// 到達し得ない素数は除外する
vc<int> visited(primes.size(), 0);
auto dfs = [&](auto &&dfs, const int idx) -> void {
if (visited[idx]) return;
visited[idx] = 1;
// next
map<int, int> cur_pfactors = sieve.pfd_map(primes[idx]);
// 素因数ごとに見る
// dump(idx, primes[idx], cur_pfactors);
for (auto [p, a] : cur_pfactors) {
// p は素数なので， p+1 は p>3 なら必ず合成数
map<int, int> nxt_pfactors = sieve.pfd_map(p + 1);
// dump(p, p + 1, nxt_pfactors);
for (auto [np, na] : nxt_pfactors) {
const int nxt_idx = lower_bound(ALL(primes), np) - primes.begin();
// dump(np, primes, nxt_idx);
dfs(dfs, nxt_idx);
}
}
};
for (auto [p, a] : pfactors) {
const int idx = lower_bound(ALL(primes), p) - primes.begin();
// dump(idx);
dfs(dfs, idx);
}
// dump(primes);
// dump(visited);
// dump(accumulate(ALL(visited), 0));
vc<int> primes_to_use;
REP(i, 0, SIZE(primes)) {
if (visited[i]) {
primes_to_use.push_back(primes[i]);
}
}
ll SZ = SIZE(primes_to_use);
// 推移行列を用意する
using mat = Mat<mint<MOD - 1>>;
mat A(SZ, SZ);
REP(i, 0, SZ) {
const int p = primes_to_use[i];
map<int, int> cur_pfactors = sieve.pfd_map(p + 1);
// dump(p, cur_pfactors);
for (auto [np, na] : cur_pfactors) {
const int next_idx = lower_bound(ALL(primes_to_use), np) - primes_to_use.begin();
A[next_idx][i] = na;
}
}
// dump(primes_to_use);
// A.print();
mat x(SZ, 1);
for (const auto [p, a] : pfactors) {
const int idx = lower_bound(ALL(primes_to_use), p) - primes_to_use.begin();
x[idx][0] = a;
}
// x.print();
mat y = A.pow(k) * x;
// y.print();
mint<MOD> ans = 1;
REP(i, 0, SZ) {
if (y[i][0] == 0) continue;
const int p = primes_to_use[i];
ans *= mint<MOD>(p).pow(y[i][0].x);
}
pprint(ans);
}
// entry point
int main() {
solve();
return 0;
}