結果

問題 No.1287 えぬけー
ユーザー NyaanNyaanNyaanNyaan
提出日時 2020-11-13 21:22:30
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 146 ms / 2,000 ms
コード長 20,093 bytes
コンパイル時間 4,838 ms
コンパイル使用メモリ 350,272 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-07-22 20:24:50
合計ジャッジ時間 5,922 ms
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
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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
6,812 KB
testcase_01 AC 2 ms
6,816 KB
testcase_02 AC 2 ms
6,944 KB
testcase_03 AC 2 ms
6,944 KB
testcase_04 AC 2 ms
6,944 KB
testcase_05 AC 142 ms
6,940 KB
testcase_06 AC 141 ms
6,944 KB
testcase_07 AC 146 ms
6,940 KB
testcase_08 AC 134 ms
6,940 KB
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

/**
* date : 2020-11-13 21:22:26
*/
#pragma region kyopro_template
#define Nyaan_template
#include <immintrin.h>
#include <bits/stdc++.h>
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
#define each(x, v) for (auto &x : v)
#define all(v) (v).begin(), (v).end()
#define sz(v) ((int)(v).size())
#define mem(a, val) memset(a, val, sizeof(a))
#define ini(...) \
int __VA_ARGS__; \
in(__VA_ARGS__)
#define inl(...) \
long long __VA_ARGS__; \
in(__VA_ARGS__)
#define ins(...) \
string __VA_ARGS__; \
in(__VA_ARGS__)
#define inc(...) \
char __VA_ARGS__; \
in(__VA_ARGS__)
#define in2(s, t) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i]); \
}
#define in3(s, t, u) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i]); \
}
#define in4(s, t, u, v) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i], v[i]); \
}
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define die(...) \
do { \
out(__VA_ARGS__); \
return; \
} while (0)
using namespace std;
using ll = long long;
template <class T>
using V = vector<T>;
using vi = vector<int>;
using vl = vector<long long>;
using vvi = vector<vector<int>>;
using vd = V<double>;
using vs = V<string>;
using vvl = vector<vector<long long>>;
using P = pair<long long, long long>;
using vp = vector<P>;
using pii = pair<int, int>;
using vpi = vector<pair<int, int>>;
constexpr int inf = 1001001001;
constexpr long long infLL = (1LL << 61) - 1;
template <typename T, typename U>
inline bool amin(T &x, U y) {
return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
return (x < y) ? (x = y, true) : false;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
os << p.first << " " << p.second;
return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
int s = (int)v.size();
for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (auto &x : v) is >> x;
return is;
}
void in() {}
template <typename T, class... U>
void in(T &t, U &... u) {
cin >> t;
in(u...);
}
void out() { cout << "\n"; }
template <typename T, class... U>
void out(const T &t, const U &... u) {
cout << t;
if (sizeof...(u)) cout << " ";
out(u...);
}
#ifdef NyaanDebug
#define trc(...) \
do { \
cerr << #__VA_ARGS__ << " = "; \
dbg_out(__VA_ARGS__); \
} while (0)
#define trca(v, N) \
do { \
cerr << #v << " = "; \
array_out(v, N); \
} while (0)
#define trcc(v) \
do { \
cerr << #v << " = {"; \
each(x, v) { cerr << " " << x << ","; } \
cerr << "}" << endl; \
} while (0)
template <typename T>
void _cout(const T &c) {
cerr << c;
}
void _cout(const int &c) {
if (c == 1001001001)
cerr << "inf";
else if (c == -1001001001)
cerr << "-inf";
else
cerr << c;
}
void _cout(const unsigned int &c) {
if (c == 1001001001)
cerr << "inf";
else
cerr << c;
}
void _cout(const long long &c) {
if (c == 1001001001 || c == (1LL << 61) - 1)
cerr << "inf";
else if (c == -1001001001 || c == -((1LL << 61) - 1))
cerr << "-inf";
else
cerr << c;
}
void _cout(const unsigned long long &c) {
if (c == 1001001001 || c == (1LL << 61) - 1)
cerr << "inf";
else
cerr << c;
}
template <typename T, typename U>
void _cout(const pair<T, U> &p) {
cerr << "{ ";
_cout(p.fi);
cerr << ", ";
_cout(p.se);
cerr << " } ";
}
template <typename T>
void _cout(const vector<T> &v) {
int s = v.size();
cerr << "{ ";
for (int i = 0; i < s; i++) {
cerr << (i ? ", " : "");
_cout(v[i]);
}
cerr << " } ";
}
template <typename T>
void _cout(const vector<vector<T>> &v) {
cerr << "[ ";
for (const auto &x : v) {
cerr << endl;
_cout(x);
cerr << ", ";
}
cerr << endl << " ] ";
}
void dbg_out() { cerr << endl; }
template <typename T, class... U>
void dbg_out(const T &t, const U &... u) {
_cout(t);
if (sizeof...(u)) cerr << ", ";
dbg_out(u...);
}
template <typename T>
void array_out(const T &v, int s) {
cerr << "{ ";
for (int i = 0; i < s; i++) {
cerr << (i ? ", " : "");
_cout(v[i]);
}
cerr << " } " << endl;
}
template <typename T>
void array_out(const T &v, int H, int W) {
cerr << "[ ";
for (int i = 0; i < H; i++) {
cerr << (i ? ", " : "");
array_out(v[i], W);
}
cerr << " ] " << endl;
}
#else
#define trc(...)
#define trca(...)
#define trcc(...)
#endif
inline int popcnt(unsigned long long a) { return __builtin_popcountll(a); }
inline int lsb(unsigned long long a) { return __builtin_ctzll(a); }
inline int msb(unsigned long long a) { return 63 - __builtin_clzll(a); }
template <typename T>
inline int getbit(T a, int i) {
return (a >> i) & 1;
}
template <typename T>
inline void setbit(T &a, int i) {
a |= (1LL << i);
}
template <typename T>
inline void delbit(T &a, int i) {
a &= ~(1LL << i);
}
template <typename T>
int lb(const vector<T> &v, const T &a) {
return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
return upper_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int btw(T a, T x, T b) {
return a <= x && x < b;
}
template <typename T, typename U>
T ceil(T a, U b) {
return (a + b - 1) / b;
}
constexpr long long TEN(int n) {
long long ret = 1, x = 10;
while (n) {
if (n & 1) ret *= x;
x *= x;
n >>= 1;
}
return ret;
}
template <typename T>
vector<T> mkrui(const vector<T> &v) {
vector<T> ret(v.size() + 1);
for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
return ret;
};
template <typename T>
vector<T> mkuni(const vector<T> &v) {
vector<T> ret(v);
sort(ret.begin(), ret.end());
ret.erase(unique(ret.begin(), ret.end()), ret.end());
return ret;
}
template <typename F>
vector<int> mkord(int N, F f) {
vector<int> ord(N);
iota(begin(ord), end(ord), 0);
sort(begin(ord), end(ord), f);
return ord;
}
template <typename T = int>
vector<T> mkiota(int N) {
vector<T> ret(N);
iota(begin(ret), end(ret), 0);
return ret;
}
template <typename T>
vector<int> mkinv(vector<T> &v) {
vector<int> inv(v.size());
for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
return inv;
}
struct IoSetupNya {
IoSetupNya() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
cerr << fixed << setprecision(7);
}
} iosetupnya;
void solve();
int main() { solve(); }
#pragma endregion
using namespace std;
using namespace std;
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;
using namespace std;
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;
using namespace std;
using namespace std;
namespace my_rand {
uint64_t rng() {
#ifdef NyaanDebug
static uint64_t x_ =
chrono::duration_cast<chrono::nanoseconds>(
chrono::high_resolution_clock::now().time_since_epoch())
.count();
#else
static uint64_t x_ = 88172645463325252ULL;
#endif
x_ = x_ ^ (x_ << 7);
return x_ = x_ ^ (x_ >> 9);
}
// [l, r)
int64_t randint(int64_t l, int64_t r) {
assert(l < r);
return l + rng() % (r - l);
}
//
vector<int64_t> randset(int64_t l, int64_t r, int64_t n) {
assert(l <= r && n <= r - l);
unordered_set<int64_t> s;
for (int64_t i = n; i; --i) {
int64_t m = randint(l, r + 1 - i);
if (s.find(m) != s.end()) m = r - i;
s.insert(m);
}
vector<int64_t> ret;
for (auto& x : s) ret.push_back(x);
return ret;
}
} // namespace my_rand
using my_rand::randint;
using my_rand::randset;
using my_rand::rng;
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;
}
using i64 = int64_t;
map<u64, i64> factor_count(u64 n) {
map<u64, i64> mp;
for (auto &x : factorize(n)) mp[x]++;
return mp;
}
vector<u64> divisors(u64 n) {
if (n == 0) return {};
vector<pair<u64, i64>> v;
for (auto &p : factor_count(n)) v.push_back(p);
vector<u64> ret;
auto f = [&](auto rec, int i, u64 x) -> void {
if (i == (int)v.size()) {
ret.push_back(x);
return;
}
for (int j = v[i].second;; --j) {
rec(rec, i + 1, x);
if (j == 0) break;
x *= v[i].first;
}
};
f(f, 0, 1);
sort(begin(ret), end(ret));
return ret;
}
} // namespace fast_factorize
using fast_factorize::divisors;
using fast_factorize::factor_count;
using fast_factorize::factorize;
using fast_factorize::is_prime;
/**
* @brief (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;
/**
* @brief kth root(Tonelli-Shanks algorithm)
* @docs docs/modulo/mod-kth-root.md
*/
void solve(){
ini(T);
rep(_,T){
ini(x,k);
out(kth_root(x,k,1000000007));
}
}
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