結果
| 問題 |
No.1232 2^x = x
|
| コンテスト | |
| ユーザー |
 kkishi
|
| 提出日時 | 2021-03-10 11:35:17 |
| 言語 | C++17(clang) (17.0.6 + boost 1.87.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 14,301 bytes |
| コンパイル時間 | 3,144 ms |
| コンパイル使用メモリ | 164,480 KB |
| 実行使用メモリ | 191,616 KB |
| 最終ジャッジ日時 | 2024-10-12 02:39:49 |
| 合計ジャッジ時間 | 7,144 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | WA * 1 TLE * 1 -- * 1 |
ソースコード
#include <bits/stdc++.h>
#ifndef ATCODER_MATH_HPP
#define ATCODER_MATH_HPP 1
#ifndef ATCODER_INTERNAL_MATH_HPP
#define ATCODER_INTERNAL_MATH_HPP 1
namespace atcoder {
namespace internal {
// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
unsigned int _m;
unsigned long long im;
// @param m `1 <= m < 2^31`
barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
// @return m
unsigned int umod() const { return _m; }
// @param a `0 <= a < m`
// @param b `0 <= b < m`
// @return `a * b % m`
unsigned int mul(unsigned int a, unsigned int b) const {
// [1] m = 1
// a = b = im = 0, so okay
// [2] m >= 2
// im = ceil(2^64 / m)
// -> im * m = 2^64 + r (0 <= r < m)
// let z = a*b = c*m + d (0 <= c, d < m)
// a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
// c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
// ((ab * im) >> 64) == c or c + 1
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x =
(unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned int v = (unsigned int)(z - x * _m);
if (_m <= v) v += _m;
return v;
}
};
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
constexpr long long bases[3] = {2, 7, 61};
for (long long a : bases) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);
// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
// Contracts:
// [1] s - m0 * a = 0 (mod b)
// [2] t - m1 * a = 0 (mod b)
// [3] s * |m1| + t * |m0| <= b
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b
// [3]:
// (s - t * u) * |m1| + t * |m0 - m1 * u|
// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
// = s * |m1| + t * |m0| <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
// by [3]: |m0| <= b/g
// by g != b: |m0| < b/g
if (m0 < 0) m0 += b / s;
return {s, m0};
}
// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (long long)(i)*i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) {
x /= i;
}
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
} // namespace internal
} // namespace atcoder
#endif // ATCODER_INTERNAL_MATH_HPP
namespace atcoder {
long long pow_mod(long long x, long long n, int m) {
assert(0 <= n && 1 <= m);
if (m == 1) return 0;
internal::barrett bt((unsigned int)(m));
unsigned int r = 1, y = (unsigned int)(internal::safe_mod(x, m));
while (n) {
if (n & 1) r = bt.mul(r, y);
y = bt.mul(y, y);
n >>= 1;
}
return r;
}
long long inv_mod(long long x, long long m) {
assert(1 <= m);
auto z = internal::inv_gcd(x, m);
assert(z.first == 1);
return z.second;
}
// (rem, mod)
std::pair<long long, long long> crt(const std::vector<long long>& r,
const std::vector<long long>& m) {
assert(r.size() == m.size());
int n = int(r.size());
// Contracts: 0 <= r0 < m0
long long r0 = 0, m0 = 1;
for (int i = 0; i < n; i++) {
assert(1 <= m[i]);
long long r1 = internal::safe_mod(r[i], m[i]), m1 = m[i];
if (m0 < m1) {
std::swap(r0, r1);
std::swap(m0, m1);
}
if (m0 % m1 == 0) {
if (r0 % m1 != r1) return {0, 0};
continue;
}
// assume: m0 > m1, lcm(m0, m1) >= 2 * max(m0, m1)
// (r0, m0), (r1, m1) -> (r2, m2 = lcm(m0, m1));
// r2 % m0 = r0
// r2 % m1 = r1
// -> (r0 + x*m0) % m1 = r1
// -> x*u0*g % (u1*g) = (r1 - r0) (u0*g = m0, u1*g = m1)
// -> x = (r1 - r0) / g * inv(u0) (mod u1)
// im = inv(u0) (mod u1) (0 <= im < u1)
long long g, im;
std::tie(g, im) = internal::inv_gcd(m0, m1);
long long u1 = (m1 / g);
// |r1 - r0| < (m0 + m1) <= lcm(m0, m1)
if ((r1 - r0) % g) return {0, 0};
// u1 * u1 <= m1 * m1 / g / g <= m0 * m1 / g = lcm(m0, m1)
long long x = (r1 - r0) / g % u1 * im % u1;
// |r0| + |m0 * x|
// < m0 + m0 * (u1 - 1)
// = m0 + m0 * m1 / g - m0
// = lcm(m0, m1)
r0 += x * m0;
m0 *= u1; // -> lcm(m0, m1)
if (r0 < 0) r0 += m0;
}
return {r0, m0};
}
long long floor_sum(long long n, long long m, long long a, long long b) {
long long ans = 0;
if (a >= m) {
ans += (n - 1) * n * (a / m) / 2;
a %= m;
}
if (b >= m) {
ans += n * (b / m);
b %= m;
}
long long y_max = (a * n + b) / m, x_max = (y_max * m - b);
if (y_max == 0) return ans;
ans += (n - (x_max + a - 1) / a) * y_max;
ans += floor_sum(y_max, a, m, (a - x_max % a) % a);
return ans;
}
} // namespace atcoder
#endif // ATCODER_MATH_HPP
#include <boost/hana/functional/fix.hpp>
template <typename T, typename = void>
struct is_dereferenceable : std::false_type {};
template <typename T>
struct is_dereferenceable<T, std::void_t<decltype(*std::declval<T>())>>
: std::true_type {};
template <typename T, typename = void>
struct is_iterable : std::false_type {};
template <typename T>
struct is_iterable<T, std::void_t<decltype(std::begin(std::declval<T>())),
decltype(std::end(std::declval<T>()))>>
: std::true_type {};
template <typename T, typename = void>
struct is_applicable : std::false_type {};
template <typename T>
struct is_applicable<T, std::void_t<decltype(std::tuple_size<T>::value)>>
: std::true_type {};
template <typename T, typename... Ts>
void debug(const T& value, const Ts&... args);
template <typename T>
void debug(const T& v) {
if constexpr (is_dereferenceable<T>::value) {
std::cerr << "{";
if (v) {
debug(*v);
} else {
std::cerr << "nil";
}
std::cerr << "}";
} else if constexpr (is_iterable<T>::value &&
!std::is_same<T, std::string>::value) {
std::cerr << "{";
for (auto it = std::begin(v); it != std::end(v); ++it) {
if (it != std::begin(v)) std::cerr << ", ";
debug(*it);
}
std::cerr << "}";
} else if constexpr (is_applicable<T>::value) {
std::cerr << "{";
std::apply([](const auto&... args) { debug(args...); }, v);
std::cerr << "}";
} else {
std::cerr << v;
}
}
template <typename T, typename... Ts>
void debug(const T& value, const Ts&... args) {
debug(value);
std::cerr << ", ";
debug(args...);
}
#if DEBUG
#define dbg(...) \
do { \
cerr << #__VA_ARGS__ << ": "; \
debug(__VA_ARGS__); \
cerr << " (L" << __LINE__ << ")\n"; \
} while (0)
#else
#define dbg(...)
#endif
void read_from_cin() {}
template <typename T, typename... Ts>
void read_from_cin(T& value, Ts&... args) {
std::cin >> value;
read_from_cin(args...);
}
#define rd(type, ...) \
type __VA_ARGS__; \
read_from_cin(__VA_ARGS__);
#define ints(...) rd(int, __VA_ARGS__);
#define strings(...) rd(string, __VA_ARGS__);
template <typename T>
void write_to_cout(const T& value) {
if constexpr (std::is_same<T, bool>::value) {
std::cout << (value ? "Yes" : "No");
} else if constexpr (is_iterable<T>::value &&
!std::is_same<T, std::string>::value) {
for (auto it = std::begin(value); it != std::end(value); ++it) {
if (it != std::begin(value)) std::cout << " ";
std::cout << *it;
}
} else {
std::cout << value;
}
}
template <typename T, typename... Ts>
void write_to_cout(const T& value, const Ts&... args) {
write_to_cout(value);
std::cout << ' ';
write_to_cout(args...);
}
#define wt(...) \
do { \
write_to_cout(__VA_ARGS__); \
cout << '\n'; \
} while (0)
#define all(x) (x).begin(), (x).end()
#define eb(...) emplace_back(__VA_ARGS__)
#define pb(...) push_back(__VA_ARGS__)
#define dispatch(_1, _2, _3, name, ...) name
#define as_i64(x) \
( \
[] { \
static_assert( \
std::is_integral< \
typename std::remove_reference<decltype(x)>::type>::value, \
"rep macro supports std integral types only"); \
}, \
static_cast<std::int64_t>(x))
#define rep3(i, a, b) for (std::int64_t i = as_i64(a); i < as_i64(b); ++i)
#define rep2(i, n) rep3(i, 0, n)
#define rep1(n) rep2(_loop_variable_, n)
#define rep(...) dispatch(__VA_ARGS__, rep3, rep2, rep1)(__VA_ARGS__)
#define rrep3(i, a, b) for (std::int64_t i = as_i64(b) - 1; i >= as_i64(a); --i)
#define rrep2(i, n) rrep3(i, 0, n)
#define rrep1(n) rrep2(_loop_variable_, n)
#define rrep(...) dispatch(__VA_ARGS__, rrep3, rrep2, rrep1)(__VA_ARGS__)
#define each3(k, v, c) for (auto&& [k, v] : c)
#define each2(e, c) for (auto&& e : c)
#define each(...) dispatch(__VA_ARGS__, each3, each2)(__VA_ARGS__)
template <typename T>
std::istream& operator>>(std::istream& is, std::vector<T>& v) {
for (T& vi : v) is >> vi;
return is;
}
template <typename T, typename U>
std::istream& operator>>(std::istream& is, std::pair<T, U>& p) {
is >> p.first >> p.second;
return is;
}
template <typename T, typename U>
bool chmax(T& a, U b) {
if (a < b) {
a = b;
return true;
}
return false;
}
template <typename T, typename U>
bool chmin(T& a, U b) {
if (a > b) {
a = b;
return true;
}
return false;
}
template <typename T, typename U>
auto max(T a, U b) {
return a > b ? a : b;
}
template <typename T, typename U>
auto min(T a, U b) {
return a < b ? a : b;
}
template <typename T>
std::int64_t sz(const T& v) {
return std::size(v);
}
template <typename T>
std::int64_t popcount(T i) {
return std::bitset<std::numeric_limits<T>::digits>(i).count();
}
template <typename T>
bool hasbit(T s, int i) {
return std::bitset<std::numeric_limits<T>::digits>(s)[i];
}
template <typename T, typename U>
auto div_floor(T n, U d) {
if (d < 0) {
n = -n;
d = -d;
}
if (n < 0) {
return -((-n + d - 1) / d);
}
return n / d;
};
template <typename T, typename U>
auto div_ceil(T n, U d) {
if (d < 0) {
n = -n;
d = -d;
}
if (n < 0) {
return -(-n / d);
}
return (n + d - 1) / d;
}
template <typename T>
bool even(T x) {
return x % 2 == 0;
}
const std::int64_t big = std::numeric_limits<std::int64_t>::max() / 4;
using i64 = std::int64_t;
using i32 = std::int32_t;
template <typename T>
using low_priority_queue =
std::priority_queue<T, std::vector<T>, std::greater<T>>;
template <typename T>
using V = std::vector<T>;
template <typename T>
using VV = V<V<T>>;
void Main();
int main() {
std::ios_base::sync_with_stdio(false);
std::cin.tie(NULL);
std::cout << std::fixed << std::setprecision(20);
Main();
return 0;
}
const auto& Fix = boost::hana::fix;
using namespace std;
#define int i64
// x y p=3
// 0 1 0 1
// 1 2 1 2
// 2 4 2 1
// 3 8 0 2
// 4 16 1 1
// 5 32
int Solve() {
ints(p);
map<int, int> seen;
int x = 0;
int y = 1;
while (true) {
if (x == y) {
return x;
}
if (seen.count(y)) {
int l = x - seen[y];
int z = (y - x % p + p) * atcoder::inv_mod(l, p) % p;
dbg(x, l, z);
return x + l * z % p;
}
seen[y] = x;
++x;
(y *= 2) %= p;
}
}
void Main() {
ints(n);
rep(n) wt(Solve());
}