結果
| 問題 |
No.1287 えぬけー
|
| コンテスト | |
| ユーザー |
 iiljj
|
| 提出日時 | 2020-11-15 18:14:17 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 276 ms / 2,000 ms |
| コード長 | 18,597 bytes |
| コンパイル時間 | 3,607 ms |
| コンパイル使用メモリ | 234,848 KB |
| 最終ジャッジ日時 | 2025-01-16 00:59:58 |
|
ジャッジサーバーID （参考情報） |
judge1 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 5 |
ソースコード
/* #region Head */
#include <bits/stdc++.h>
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 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 ALL(x) begin(x), end(x)
#define SIZE(x) ((ll)(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))
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, 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, 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, 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, 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, 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, map<T, U> &map_var) { return out_iter(os, map_var); }
template <typename T, typename U> ostream &operator<<(ostream &os, 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, set<T> &set_var) { return out_iter(os, set_var); }
template <typename T> ostream &operator<<(ostream &os, us<T> &set_var) { return out_iter(os, set_var); }
template <typename T> ostream &operator<<(ostream &os, 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 << "}";
}
void pprint() { cout << endl; }
template <class Head, class... Tail> void pprint(Head &&head, Tail &&... tail) {
cout << head;
if (sizeof...(Tail) > 0) 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
#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__; \
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), cin.tie(nullptr), cout.tie(nullptr);
cout << fixed << setprecision(IOS_PREC);
if (AUTOFLUSH) cout << unitbuf;
}
} ATCODER_INITIALIZE;
void Yn(bool p) { cout << (p ? "Yes" : "No") << endl; }
void YN(bool p) { cout << (p ? "YES" : "NO") << endl; }
/* #endregion */
// #include <atcoder/all>
// using namespace atcoder;
/* #region kth_root */
// 以下から拝借
// Submitted https://judge.yosupo.jp/submission/23481
namespace inner {
using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;
template <typename T> T gcd(T a, T b) {
while (b) swap(a %= b, b);
return a;
}
template <typename T> T inv(T a, T p) {
T b = p, x = 1, y = 0;
while (a) {
T q = b / a;
swap(a, b %= a);
swap(x, y -= q * x);
}
assert(b == 1);
return y < 0 ? y + p : y;
}
template <typename T, typename U> T modpow(T a, U n, T p) {
T ret = 1 % p;
for (; n; n >>= 1, a = U(a) * a % p)
if (n & 1) ret = U(ret) * a % p;
return ret;
}
} // namespace inner
using namespace std;
struct ArbitraryLazyMontgomeryModInt {
using mint = ArbitraryLazyMontgomeryModInt;
using i32 = int32_t;
using u32 = uint32_t;
using u64 = uint64_t;
static u32 mod;
static u32 r;
static u32 n2;
static u32 get_r() {
u32 ret = mod;
for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
return ret;
}
static void set_mod(u32 m) {
assert(m < (1 << 30));
assert((m & 1) == 1);
mod = m;
n2 = -u64(m) % m;
r = get_r();
assert(r * mod == 1);
}
u32 a;
ArbitraryLazyMontgomeryModInt() : a(0) {}
ArbitraryLazyMontgomeryModInt(const int64_t &b) : a(reduce(u64(b % mod + mod) * n2)){};
static u32 reduce(const u64 &b) { return (b + u64(u32(b) * u32(-r)) * mod) >> 32; }
mint &operator+=(const mint &b) {
if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
return *this;
}
mint &operator-=(const mint &b) {
if (i32(a -= b.a) < 0) a += 2 * mod;
return *this;
}
mint &operator*=(const mint &b) {
a = reduce(u64(a) * b.a);
return *this;
}
mint &operator/=(const mint &b) {
*this *= b.inverse();
return *this;
}
mint operator+(const mint &b) const { return mint(*this) += b; }
mint operator-(const mint &b) const { return mint(*this) -= b; }
mint operator*(const mint &b) const { return mint(*this) *= b; }
mint operator/(const mint &b) const { return mint(*this) /= b; }
bool operator==(const mint &b) const { return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a); }
bool operator!=(const mint &b) const { return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a); }
mint operator-() const { return mint() - mint(*this); }
mint pow(u64 n) const {
mint ret(1), mul(*this);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
friend ostream &operator<<(ostream &os, const mint &b) { return os << b.get(); }
friend istream &operator>>(istream &is, mint &b) {
int64_t t;
is >> t;
b = ArbitraryLazyMontgomeryModInt(t);
return (is);
}
mint inverse() const { return pow(mod - 2); }
u32 get() const {
u32 ret = reduce(a);
return ret >= mod ? ret - mod : ret;
}
static u32 get_mod() { return mod; }
};
typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::mod;
typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::r;
typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::n2;
struct montgomery64 {
using mint = montgomery64;
using i64 = int64_t;
using u64 = uint64_t;
using u128 = __uint128_t;
static u64 mod;
static u64 r;
static u64 n2;
static u64 get_r() {
u64 ret = mod;
for (i64 i = 0; i < 5; ++i) ret *= 2 - mod * ret;
return ret;
}
static void set_mod(u64 m) {
assert(m < (1LL << 62));
assert((m & 1) == 1);
mod = m;
n2 = -u128(m) % m;
r = get_r();
assert(r * mod == 1);
}
u64 a;
montgomery64() : a(0) {}
montgomery64(const int64_t &b) : a(reduce((u128(b) + mod) * n2)){};
static u64 reduce(const u128 &b) { return (b + u128(u64(b) * u64(-r)) * mod) >> 64; }
mint &operator+=(const mint &b) {
if (i64(a += b.a - 2 * mod) < 0) a += 2 * mod;
return *this;
}
mint &operator-=(const mint &b) {
if (i64(a -= b.a) < 0) a += 2 * mod;
return *this;
}
mint &operator*=(const mint &b) {
a = reduce(u128(a) * b.a);
return *this;
}
mint &operator/=(const mint &b) {
*this *= b.inverse();
return *this;
}
mint operator+(const mint &b) const { return mint(*this) += b; }
mint operator-(const mint &b) const { return mint(*this) -= b; }
mint operator*(const mint &b) const { return mint(*this) *= b; }
mint operator/(const mint &b) const { return mint(*this) /= b; }
bool operator==(const mint &b) const { return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a); }
bool operator!=(const mint &b) const { return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a); }
mint operator-() const { return mint() - mint(*this); }
mint pow(u128 n) const {
mint ret(1), mul(*this);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
friend ostream &operator<<(ostream &os, const mint &b) { return os << b.get(); }
friend istream &operator>>(istream &is, mint &b) {
int64_t t;
is >> t;
b = montgomery64(t);
return (is);
}
mint inverse() const { return pow(mod - 2); }
u64 get() const {
u64 ret = reduce(a);
return ret >= mod ? ret - mod : ret;
}
static u64 get_mod() { return mod; }
};
typename montgomery64::u64 montgomery64::mod, montgomery64::r, montgomery64::n2;
unsigned long long rng() {
static unsigned long long x_ = 88172645463325252ULL;
x_ = x_ ^ (x_ << 7);
return x_ = x_ ^ (x_ >> 9);
}
namespace fast_factorize {
using u64 = uint64_t;
template <typename mint> bool miller_rabin(u64 n, vector<u64> as) {
if (mint::get_mod() != n) mint::set_mod(n);
u64 d = n - 1;
while (~d & 1) d >>= 1;
mint e{1}, rev{int64_t(n - 1)};
for (u64 a : as) {
if (n <= a) break;
u64 t = d;
mint y = mint(a).pow(t);
while (t != n - 1 && y != e && y != rev) {
y *= y;
t *= 2;
}
if (y != rev && t % 2 == 0) return false;
}
return true;
}
bool is_prime(u64 n) {
if (~n & 1) return n == 2;
if (n <= 1) return false;
if (n < (1LL << 30))
return miller_rabin<ArbitraryLazyMontgomeryModInt>(n, {2, 7, 61});
else
return miller_rabin<montgomery64>(n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022});
}
template <typename mint, typename T> T pollard_rho(T n) {
if (~n & 1) return 2;
if (is_prime(n)) return n;
if (mint::get_mod() != n) mint::set_mod(n);
mint R, one = 1;
auto f = [&](mint x) { return x * x + R; };
auto rnd = [&]() { return rng() % (n - 2) + 2; };
while (1) {
mint x, y, ys, q = one;
R = rnd(), y = rnd();
T g = 1;
constexpr int m = 128;
for (int r = 1; g == 1; r <<= 1) {
x = y;
for (int i = 0; i < r; ++i) y = f(y);
for (int k = 0; g == 1 && k < r; k += m) {
ys = y;
for (int i = 0; i < m && i < r - k; ++i) q *= x - (y = f(y));
g = inner::gcd<T>(q.get(), n);
}
}
if (g == n) do
g = inner::gcd<T>((x - (ys = f(ys))).get(), n);
while (g == 1);
if (g != n) return g;
}
exit(1);
}
vector<u64> inner_factorize(u64 n) {
if (n <= 1) return {};
u64 p;
if (n <= (1LL << 30))
p = pollard_rho<ArbitraryLazyMontgomeryModInt, uint32_t>(n);
else
p = pollard_rho<montgomery64, uint64_t>(n);
if (p == n) return {p};
auto l = inner_factorize(p);
auto r = inner_factorize(n / p);
copy(begin(r), end(r), back_inserter(l));
return l;
}
vector<u64> factorize(u64 n) {
auto ret = inner_factorize(n);
sort(begin(ret), end(ret));
return ret;
}
} // namespace fast_factorize
using fast_factorize::factorize;
using fast_factorize::is_prime;
/**
* @brief 高速素因数分解(Miller Rabin/Pollard's Rho)
* @docs docs/prime/fast-factorize.md
*/
namespace kth_root_mod {
// fast BS-GS
template <typename T> struct Memo {
Memo(const T &g, int s, int period)
: size(1 << __lg(min(s, period))), mask(size - 1), period(period), vs(size), os(size + 1) {
T x(1);
for (int i = 0; i < size; ++i, x *= g) os[x.get() & mask]++;
for (int i = 1; i < size; ++i) os[i] += os[i - 1];
x = 1;
for (int i = 0; i < size; ++i, x *= g) vs[--os[x.get() & mask]] = {x, i};
gpow = x;
os[size] = size;
}
int find(T x) const {
for (int t = 0; t < period; t += size, x *= gpow) {
for (int m = (x.get() & mask), i = os[m]; i < os[m + 1]; ++i) {
if (x == vs[i].first) {
int ret = vs[i].second - t;
return ret < 0 ? ret + period : ret;
}
}
}
assert(0);
}
T gpow;
int size, mask, period;
vector<pair<T, int>> vs;
vector<int> os;
};
using inner::gcd;
using inner::inv;
using inner::modpow;
template <typename INT, typename LINT, typename mint> mint pe_root(INT c, INT pi, INT ei, INT p) {
if (mint::get_mod() != decltype(mint::a)(p)) mint::set_mod(p);
INT s = p - 1, t = 0;
while (s % pi == 0) s /= pi, ++t;
INT pe = 1;
for (INT _ = 0; _ < ei; ++_) pe *= pi;
INT u = inv(pe - s % pe, pe);
mint mc = c, one = 1;
mint z = mc.pow((s * u + 1) / pe);
mint zpe = mc.pow(s * u);
if (zpe == one) return z;
assert(t > ei);
mint vs;
{
INT ptm1 = 1;
for (INT _ = 0; _ < t - 1; ++_) ptm1 *= pi;
for (mint v = 2;; v += one) {
vs = v.pow(s);
if (vs.pow(ptm1) != one) break;
}
}
mint vspe = vs.pow(pe);
INT vs_e = ei;
mint base = vspe;
for (INT _ = 0; _ < t - ei - 1; _++) base = base.pow(pi);
Memo<mint> memo(base, (INT)(sqrt(t - ei) * sqrt(pi)) + 1, pi);
while (zpe != one) {
mint tmp = zpe;
INT td = 0;
while (tmp != 1) ++td, tmp = tmp.pow(pi);
INT e = t - td;
while (vs_e != e) {
vs = vs.pow(pi);
vspe = vspe.pow(pi);
++vs_e;
}
// BS-GS ... find (zpe * ( vspe ^ n ) ) ^( p_i ^ (td - 1) ) = 1
mint base_zpe = zpe.inverse();
for (INT _ = 0; _ < td - 1; _++) base_zpe = base_zpe.pow(pi);
INT bsgs = memo.find(base_zpe);
z *= vs.pow(bsgs);
zpe *= vspe.pow(bsgs);
}
return z;
}
template <typename INT, typename LINT, typename mint> INT inner_kth_root(INT a, INT k, INT p) {
a %= p;
if (k == 0) return a == 1 ? a : -1;
if (a <= 1 || k <= 1) return a;
assert(p > 2);
if (mint::get_mod() != decltype(mint::a)(p)) mint::set_mod(p);
INT g = gcd(p - 1, k);
if (modpow<INT, LINT>(a, (p - 1) / g, p) != 1) return -1;
a = mint(a).pow(inv(k / g, (p - 1) / g)).get();
unordered_map<INT, int> fac;
for (auto &f : factorize(g)) fac[f]++;
if (mint::get_mod() != decltype(mint::a)(p)) mint::set_mod(p);
for (auto pp : fac) a = pe_root<INT, LINT, mint>(a, pp.first, pp.second, p).get();
return a;
}
int64_t kth_root(int64_t a, int64_t k, int64_t p) {
if (max({a, k, p}) < (1LL << 30))
return inner_kth_root<int32_t, int64_t, ArbitraryLazyMontgomeryModInt>(a, k, p);
else
return inner_kth_root<int64_t, __int128_t, montgomery64>(a, k, p);
}
} // namespace kth_root_mod
using kth_root_mod::kth_root;
/* #endregion */
// Problem
void solve() {
VAR(int, t);
REP(i, 0, t) {
VAR(ll, x, k);
pprint(kth_root(x, k, MOD));
}
}
// entry point
int main() {
solve();
return 0;
}