結果

問題 No.2365 Present of good number
ユーザー poyon
提出日時 2023-07-08 15:38:14
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 13,938 bytes
コンパイル時間 2,547 ms
コンパイル使用メモリ 221,448 KB
最終ジャッジ日時 2025-02-15 09:04:22
ジャッジサーバーID
(参考情報)
judge4 / judge2
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 1 WA * 1
other AC * 15 WA * 24
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ソースコード

diff #
プレゼンテーションモードにする

// clang-format off
#ifdef _LOCAL
#include <pch.hpp>
#else
#include <bits/stdc++.h>
#define cerr if (false) cerr
#define debug_bar
#define debug(...)
#define debug2(vv)
#define debug3(vvv)
#endif
using namespace std;
using ll = long long;
using ld = long double;
using str = string;
using P = pair<ll,ll>;
using VP = vector<P>;
using VVP = vector<VP>;
using VC = vector<char>;
using VS = vector<string>;
using VVS = vector<VS>;
using VI = vector<int>;
using VVI = vector<VI>;
using VVVI = vector<VVI>;
using VLL = vector<ll>;
using VVLL = vector<VLL>;
using VVVLL = vector<VVLL>;
using VB = vector<bool>;
using VVB = vector<VB>;
using VVVB = vector<VVB>;
using VD = vector<double>;
using VVD = vector<VD>;
using VVVD = vector<VVD>;
#define FOR(i,l,r) for (ll i = (l); i < (r); ++i)
#define RFOR(i,l,r) for (ll i = (r)-1; (l) <= i; --i)
#define REP(i,n) FOR(i,0,n)
#define RREP(i,n) RFOR(i,0,n)
#define FORE(e,c) for (auto&& e : c)
#define ALL(c) (c).begin(), (c).end()
#define SORT(c) sort(ALL(c))
#define RSORT(c) sort((c).rbegin(), (c).rend())
#define MIN(c) *min_element(ALL(c))
#define MAX(c) *max_element(ALL(c))
#define COUNT(c,v) count(ALL(c),(v))
#define len(c) ((ll)(c).size())
#define BIT(b,i) (((b)>>(i)) & 1)
#define PCNT(b) ((ll)__builtin_popcountll(b))
#define LB(c,v) distance((c).begin(), lower_bound(ALL(c), (v)))
#define UB(c,v) distance((c).begin(), upper_bound(ALL(c), (v)))
#define UQ(c) do { SORT(c); (c).erase(unique(ALL(c)), (c).end()); (c).shrink_to_fit(); } while (0)
#define END(...) do { print(__VA_ARGS__); exit(0); } while (0)
constexpr ld EPS = 1e-10;
constexpr ld PI = acosl(-1.0);
constexpr int inf = (1 << 30) - (1 << 15); // 1,073,709,056
constexpr ll INF = (1LL << 62) - (1LL << 31); // 4,611,686,016,279,904,256
template<class... T> void input(T&... a) { (cin >> ... >> a); }
void print() { cout << '\n'; }
template<class T> void print(const T& a) { cout << a << '\n'; }
template<class P1, class P2> void print(const pair<P1, P2>& a) { cout << a.first << " " << a.second << '\n'; }
template<class T, class... Ts> void print(const T& a, const Ts&... b) { cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; }
template<class T> void cout_line(const vector<T>& ans, int l, int r) { for (int i = l; i < r; i++) { if (i != l) { cout << ' '; } cout << ans[i]; }
    cout << '\n'; }
template<class T> void print(const vector<T>& a) { cout_line(a, 0, a.size()); }
template<class S, class T> bool chmin(S& a, const T b) { if (b < a) { a = b; return 1; } return 0; }
template<class S, class T> bool chmax(S& a, const T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> T SUM(const vector<T>& A) { return accumulate(ALL(A), T(0)); }
template<class T> vector<T> cumsum(const vector<T>& A, bool offset = false) { int N = A.size(); vector<T> S(N+1, 0); for (int i = 0; i < N; i++) {
    S[i+1] = S[i] + A[i]; } if (not offset) { S.erase(S.begin()); } return S; }
template<class T> string to_binary(T x, int B = 0) { string s; while (x) { s += ('0' + (x & 1)); x >>= 1; } while ((int)s.size() < B) { s += '0'; }
    reverse(s.begin(), s.end()); return s; }
template<class F> ll binary_search(const F& is_ok, ll ok, ll ng) { while (abs(ok - ng) > 1) { ll m = (ok + ng) / 2; (is_ok(m) ? ok : ng) = m; }
    return ok; }
template<class F> double binary_search_real(const F& is_ok, double ok, double ng, int iter = 90) { for (int i = 0; i < iter; i++) { double m = (ok +
    ng) / 2; (is_ok(m) ? ok : ng) = m; } return ok; }
template<class T> using PQ_max = priority_queue<T>;
template<class T> using PQ_min = priority_queue<T, vector<T>, greater<T>>;
template<class T> T pick(stack<T>& s) { assert(not s.empty()); T x = s.top(); s.pop(); return x; }
template<class T> T pick(queue<T>& q) { assert(not q.empty()); T x = q.front(); q.pop(); return x; }
template<class T> T pick_front(deque<T>& dq) { assert(not dq.empty()); T x = dq.front(); dq.pop_front(); return x; }
template<class T> T pick_back(deque<T>& dq) { assert(not dq.empty()); T x = dq.back(); dq.pop_back(); return x; }
template<class T> T pick(PQ_min<T>& pq) { assert(not pq.empty()); T x = pq.top(); pq.pop(); return x; }
template<class T> T pick(PQ_max<T>& pq) { assert(not pq.empty()); T x = pq.top(); pq.pop(); return x; }
template<class T> T pick(vector<T>& v) { assert(not v.empty()); T x = v.back(); v.pop_back(); return x; }
int to_int(const char c) { if (islower(c)) { return (c - 'a'); } if (isupper(c)) { return (c - 'A'); } if (isdigit(c)) { return (c - '0'); } assert
    (false); }
char to_a(const int i) { assert(0 <= i && i < 26); return ('a' + i); }
char to_A(const int i) { assert(0 <= i && i < 26); return ('A' + i); }
char to_d(const int i) { assert(0 <= i && i <= 9); return ('0' + i); }
ll min(int a, ll b) { return min((ll)a, b); }
ll min(ll a, int b) { return min(a, (ll)b); }
ll max(int a, ll b) { return max((ll)a, b); }
ll max(ll a, int b) { return max(a, (ll)b); }
ll mod(ll x, ll m) { assert(m > 0); return (x % m + m) % m; }
ll ceil(ll a, ll b) { if (b < 0) { return ceil(-a, -b); } assert(b > 0); return (a < 0 ? a / b : (a + b - 1) / b); }
ll floor(ll a, ll b) { if (b < 0) { return floor(-a, -b); } assert(b > 0); return (a > 0 ? a / b : (a - b + 1) / b); }
ll powint(ll x, ll n) { assert(n >= 0); if (n == 0) { return 1; }; ll res = powint(x, n>>1); res *= res; if (n & 1) { res *= x; } return res; }
pair<ll,ll> divmod(ll a, ll b) { assert(b != 0); ll q = floor(a, b); return make_pair(q, a - q * b); }
ll bitlen(ll b) { if (b <= 0) { return 0; } return (64LL - __builtin_clzll(b)); }
ll digitlen(ll n) { assert(n >= 0); if (n == 0) { return 1; } ll sum = 0; while (n > 0) { sum++; n /= 10; } return sum; }
ll msb(ll b) { return (b <= 0 ? -1 : (63 - __builtin_clzll(b))); }
ll lsb(ll b) { return (b <= 0 ? -1 : __builtin_ctzll(b)); }
// --------------------------------------------------------
//
struct eratosthenes {
public:
//
// - O(N log log N)
eratosthenes(int N) : N(N) {
D.resize(N+1);
iota(D.begin(), D.end(), 0);
for (int p : {2, 3, 5}) {
for (int i = p*p; i <= N; i += p) { if (D[i] == i) { D[i] = p; } }
}
vector<int> inc = {4, 2, 4, 2, 4, 6, 2, 6};
int p = 7, idx = 0;
int root = floor(sqrt(N) + 0.5);
while (p <= root) {
if (D[p] == p) {
for (int i = p*p; i <= N; i += p) { if (D[i] == i) { D[i] = p; } }
}
p += inc[idx++];
if (idx == 8) { idx = 0; }
}
}
//
// - O(1)
bool is_prime(int x) const {
assert(1 <= x && x <= N);
if (x == 1) { return false; }
return D[x] == x;
}
//
// - O(log x), O(Σi ei)
vector<pair<int,int>> factorize(int x) const {
assert(1 <= x && x <= N);
vector<pair<int,int>> F;
while (x != 1) {
int p = D[x];
int e = 0;
while (x % p == 0) { x /= p; e++; }
F.emplace_back(p, e);
}
return F;
}
//
// - O(Πi(1+ei))
// -
vector<int> calc_divisors(int x) const {
assert(1 <= x && x <= N);
int n = 1; //
vector<pair<int,int>> F;
while (x != 1) {
int p = D[x];
int e = 0;
while (x % p == 0) { x /= p; e++; }
F.emplace_back(p, e);
n *= (1 + e);
}
vector<int> divisors(n,1);
int sz = 1; //
for (const auto& [p, e] : F) {
for (int i = 0; i < sz * e; i++) {
divisors[sz + i] = divisors[i] * p;
}
sz *= (1 + e);
}
return divisors;
}
// (least prime factor)
// - O(1)
int lpf(int x) const { assert(1 <= x && x <= N); return D[x]; }
// φ
// 1 x x φ(x)
// - O(log x), O(Σi ei)
int euler_phi(int x) const {
assert(1 <= x && x <= N);
int res = x;
while (x != 1) {
int p = D[x];
res -= res / p;
while (x % p == 0) { x /= p; }
}
return res;
}
//
// - O(N)
vector<int> calc_moebius() const {
vector<int> moebius(N+1, 0);
moebius[1] = 1;
for (int x = 2; x <= N; x++) {
int y = x / D[x];
if (D[x] != D[y]) { moebius[x] = -moebius[y]; }
}
return moebius;
}
private:
int N;
vector<int> D; // (least prime factor)
};
#include <atcoder/modint>
using namespace atcoder;
// constexpr ll MOD = 1000003;
// using mint = modint;
// mint::set_mod(MOD); // write in main()
using mint = modint1000000007;
// using mint = modint998244353;
using VM = vector<mint>;
using VVM = vector<VM>;
using VVVM = vector<VVM>;
using VVVVM = vector<VVVM>;
template<int M> istream &operator>>(istream &is, static_modint<M> &m) { ll v; is >> v; m = v; return is; }
template<int M> istream &operator>>(istream &is, dynamic_modint<M> &m) { ll v; is >> v; m = v; return is; }
template<int M> ostream &operator<<(ostream &os, const static_modint<M> &m) { return os << m.val(); }
template<int M> ostream &operator<<(ostream &os, const dynamic_modint<M> &m) { return os << m.val(); }
// It is assumed that M (= mod) is prime number
struct combination {
public:
combination() : combination(1) {}
combination(int n) : N(1), _fact(2,1), _ifact(2,1) {
M = mint().mod();
assert(0 < n && n < M);
if (N < n) { build(n); }
}
mint P(int n, int k) {
if (N < n) { build(n); }
if (n < 0 || k < 0 || n < k) { return 0; }
return _fact[n] * _ifact[n-k];
}
mint C(int n, int k) {
if (N < n) { build(n); }
if (n < 0 || k < 0 || n < k) { return 0; }
return _fact[n] * _ifact[n-k] * _ifact[k];
}
mint H(int n, int k) {
if (n == 0 && k == 0) { return 1; }
if (n < 0 || k < 0) { return 0; }
return C(n + k - 1, k);
}
mint fact(int n) {
if (N < n) { build(n); }
if (n < 0) { return 0; }
return _fact[n];
}
mint ifact(int n) {
if (N < n) { build(n); }
if (n < 0) { return 0; }
return _ifact[n];
}
mint P_naive(ll n, int k) const noexcept {
if (n < 0 || k < 0 || n < k) { return 0; }
mint res = 1;
for (int i = 1; i <= k; i++) { res *= (n - i + 1); }
return res;
}
mint C_naive(ll n, int k) const noexcept {
if (n < 0 || k < 0 || n < k) { return 0; }
if (k > n - k) { k = n - k; }
mint nume = 1, deno = 1;
for (int i = 1; i <= k; i++) { nume *= (n - i + 1); deno *= i; }
return nume / deno;
}
mint H_naive(ll n, int k) const noexcept {
if (n == 0 && k == 0) { return 1; }
if (n < 0 || k < 0) { return 0; }
return C_naive(n + k - 1, k);
}
mint catalan(int n) {
if (N < 2 * n) { build(2 * n); }
return _fact[2 * n] * _ifact[n + 1] * _ifact[n];
}
template<class... Ts>
mint C_multinomial(int n, int k, Ts... ks) {
if (N < n) { build(n); }
if (n < 0 || k < 0 || n < k) { return 0; }
return C_multinomial(n, ks...) * _ifact[k];
}
mint C_multinomial(int n, int k) {
if (N < n) { build(n); }
if (n < 0 || k < 0 || n < k) { return 0; }
return _fact[n] * _ifact[k];
}
private:
int N;
int M; // mod
vector<mint> _fact, _ifact;
void build(int N_new) {
assert(N < N_new);
assert(N_new < M);
_fact.resize(N_new + 1);
_ifact.resize(N_new + 1);
for (int i = N + 1; i <= N_new; i++) { _fact[i] = _fact[i - 1] * i; }
_ifact[N_new] = _fact[N_new].inv();
for (int i = N_new - 1; N + 1 <= i; i--) { _ifact[i] = _ifact[i + 1] * (i + 1); }
N = N_new;
}
};
#include <atcoder/math>
using namespace atcoder;
// a^b^c mod p
ll a_b_c(ll a, ll b, ll c, ll mod) {
if (a % mod == 0) { return 0; }
return pow_mod(a, pow_mod(b, c, mod-1), mod);
}
// clang-format on
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
cout << fixed << setprecision(15);
ll N, K;
input(N, K);
eratosthenes era(1e6);
map<P, tuple<ll, ll, mint>> mp; // ({n, k}, {e2, e3, others})
auto dp = [&](auto&& self, ll n, ll k) -> tuple<ll, ll, mint> {
if (k == 0) {
ll e2 = 0, e3 = 0;
while (n % 2 == 0) {
n /= 2;
e2++;
}
while (n % 3 == 0) {
n /= 3;
e3++;
}
return make_tuple(e2, e3, n);
}
auto it = mp.find({n, k});
if (it != mp.end()) { return it->second; }
ll e2 = 0, e3 = 0;
mint others = 1;
auto F = era.factorize(n);
for (auto [p, e] : F) {
auto [f2, f3, rem] = self(self, p + 1, k - 1);
e2 += f2 * e;
e3 += f3 * e;
others *= rem.pow(e);
}
return mp[make_pair(n, k)] = make_tuple(e2, e3, others);
};
ll K1 = min(100, K);
ll K2 = max(0, K - K1);
auto [x, y, others] = dp(dp, N, K1);
debug(K1, K2);
debug(x, y, others);
mint ans = others.pow(K2);
auto MOD = mint().mod();
if (K2 & 1) {
ans *= a_b_c(2, y, pow_mod(2, K2 / 2 + 1, MOD - 1), MOD);
ans *= a_b_c(3, x, pow_mod(2, K2 / 2, MOD - 1), MOD);
} else {
ans *= a_b_c(2, x, pow_mod(2, K2 / 2, MOD - 1), MOD);
ans *= a_b_c(3, y, pow_mod(2, K2 / 2, MOD - 1), MOD);
}
print(ans.val());
return 0;
}
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