結果
| 問題 | No.950 行列累乗 |
| ユーザー |
 Pachicobue
|
| 提出日時 | 2019-12-13 12:36:16 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 1,073 ms / 2,000 ms |
| コード長 | 23,726 bytes |
| コンパイル時間 | 3,889 ms |
| コンパイル使用メモリ | 262,320 KB |
| 実行使用メモリ | 12,744 KB |
| 最終ジャッジ日時 | 2024-06-27 03:52:04 |
| 合計ジャッジ時間 | 12,950 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge3 |
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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 | 51 ms
6,912 KB |
| testcase_01 | AC | 56 ms
6,784 KB |
| testcase_02 | AC | 2 ms
5,376 KB |
| testcase_03 | AC | 2 ms
5,376 KB |
| testcase_04 | AC | 2 ms
5,376 KB |
| testcase_05 | AC | 37 ms
5,760 KB |
| testcase_06 | AC | 2 ms
5,376 KB |
| testcase_07 | AC | 2 ms
5,376 KB |
| testcase_08 | AC | 2 ms
5,376 KB |
| testcase_09 | AC | 2 ms
5,376 KB |
| testcase_10 | AC | 2 ms
5,376 KB |
| testcase_11 | AC | 3 ms
5,376 KB |
| testcase_12 | AC | 2 ms
5,376 KB |
| testcase_13 | AC | 2 ms
5,376 KB |
| testcase_14 | AC | 2 ms
5,376 KB |
| testcase_15 | AC | 2 ms
5,376 KB |
| testcase_16 | AC | 2 ms
5,376 KB |
| testcase_17 | AC | 2 ms
5,376 KB |
| testcase_18 | AC | 2 ms
5,376 KB |
| testcase_19 | AC | 2 ms
5,376 KB |
| testcase_20 | AC | 1 ms
5,376 KB |
| testcase_21 | AC | 48 ms
6,272 KB |
| testcase_22 | AC | 1,073 ms
11,848 KB |
| testcase_23 | AC | 82 ms
7,168 KB |
| testcase_24 | AC | 35 ms
5,376 KB |
| testcase_25 | AC | 68 ms
6,528 KB |
| testcase_26 | AC | 75 ms
7,424 KB |
| testcase_27 | AC | 38 ms
5,504 KB |
| testcase_28 | AC | 691 ms
11,140 KB |
| testcase_29 | AC | 758 ms
10,892 KB |
| testcase_30 | AC | 32 ms
5,504 KB |
| testcase_31 | AC | 62 ms
7,040 KB |
| testcase_32 | AC | 92 ms
8,832 KB |
| testcase_33 | AC | 32 ms
5,504 KB |
| testcase_34 | AC | 64 ms
7,552 KB |
| testcase_35 | AC | 45 ms
6,144 KB |
| testcase_36 | AC | 27 ms
5,376 KB |
| testcase_37 | AC | 50 ms
6,528 KB |
| testcase_38 | AC | 58 ms
6,784 KB |
| testcase_39 | AC | 29 ms
5,376 KB |
| testcase_40 | AC | 102 ms
7,808 KB |
| testcase_41 | AC | 83 ms
7,552 KB |
| testcase_42 | AC | 46 ms
6,272 KB |
| testcase_43 | AC | 954 ms
12,556 KB |
| testcase_44 | AC | 97 ms
7,808 KB |
| testcase_45 | AC | 46 ms
6,272 KB |
| testcase_46 | AC | 1,026 ms
12,744 KB |
| testcase_47 | AC | 2 ms
5,376 KB |
| testcase_48 | AC | 136 ms
9,088 KB |
| testcase_49 | AC | 1,027 ms
12,684 KB |
| testcase_50 | AC | 91 ms
8,960 KB |
| testcase_51 | AC | 88 ms
8,960 KB |
| testcase_52 | AC | 99 ms
9,088 KB |
| testcase_53 | AC | 92 ms
9,088 KB |
| testcase_54 | AC | 2 ms
5,376 KB |
| testcase_55 | AC | 2 ms
5,376 KB |
| testcase_56 | AC | 58 ms
7,168 KB |
| testcase_57 | AC | 2 ms
5,376 KB |
| testcase_58 | AC | 2 ms
5,376 KB |
| testcase_59 | AC | 79 ms
8,192 KB |
| testcase_60 | AC | 66 ms
7,424 KB |
ソースコード
#include <bits/stdc++.h>
// created [2019/12/12] 23:52:05
#pragma GCC diagnostic ignored "-Wsign-compare"
#pragma GCC diagnostic ignored "-Wsign-conversion"
using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
using uint = unsigned int;
using usize = std::size_t;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
template<typename T, usize n>
using arr = T (&)[n];
template<typename T, usize n>
using c_arr = const T (&)[n];
template<typename T> constexpr T popcount(const T u) { return u ? static_cast<T>(__builtin_popcountll(static_cast<u64>(u))) : static_cast<T>(0); }
template<typename T> constexpr T log2p1(const T u) { return u ? static_cast<T>(64 - __builtin_clzll(static_cast<u64>(u))) : static_cast<T>(0); }
template<typename T> constexpr T msbp1(const T u) { return log2p1(u); }
template<typename T> constexpr T lsbp1(const T u) { return __builtin_ffsll(u); }
template<typename T> constexpr T clog(const T u) { return u ? log2p1(u - 1) : static_cast<T>(u); }
template<typename T> constexpr bool ispow2(const T u) { return u and (static_cast<u64>(u) & static_cast<u64>(u - 1)) == 0; }
template<typename T> constexpr T ceil2(const T u) { return static_cast<T>(1) << clog(u); }
template<typename T> constexpr T floor2(const T u) { return u == 0 ? static_cast<T>(0) : static_cast<T>(1) << (log2p1(u) - 1); }
template<typename T> constexpr bool btest(const T mask, const usize ind) { return static_cast<bool>((static_cast<u64>(mask) >> ind) & static_cast<u64>(1)); }
template<typename T> void bset(T& mask, const usize ind) { mask |= (static_cast<T>(1) << ind); }
template<typename T> void breset(T& mask, const usize ind) { mask &= ~(static_cast<T>(1) << ind); }
template<typename T> void bflip(T& mask, const usize ind) { mask ^= (static_cast<T>(1) << ind); }
template<typename T> void bset(T& mask, const usize ind, const bool b) { (b ? bset(mask, ind) : breset(mask, ind)); }
template<typename T> constexpr T bcut(const T mask, const usize ind) { return ind == 0 ? static_cast<T>(0) : static_cast<T>((static_cast<u64>(mask) << (64 - ind)) >> (64 - ind)); }
template<typename T> bool chmin(T& a, const T& b) { return (a > b ? a = b, true : false); }
template<typename T> bool chmax(T& a, const T& b) { return (a < b ? a = b, true : false); }
constexpr unsigned int mod = 1000000007;
template<typename T> constexpr T inf_v = std::numeric_limits<T>::max() / 4;
template<typename Real> constexpr Real pi_v = Real{3.141592653589793238462643383279502884};
template<typename T>
T in()
{
T v;
return std::cin >> v, v;
}
template<typename T, typename Uint, usize n, usize i>
T in_v(typename std::enable_if<(i == n), c_arr<Uint, n>>::type) { return in<T>(); }
template<typename T, typename Uint, usize n, usize i>
auto in_v(typename std::enable_if<(i < n), c_arr<Uint, n>>::type& szs)
{
const usize s = (usize)szs[i];
std::vector<decltype(in_v<T, Uint, n, i + 1>(szs))> ans(s);
for (usize j = 0; j < s; j++) { ans[j] = in_v<T, Uint, n, i + 1>(szs); }
return ans;
}
template<typename T, typename Uint, usize n>
auto in_v(c_arr<Uint, n> szs) { return in_v<T, Uint, n, 0>(szs); }
template<typename... Types>
auto in_t() { return std::tuple<std::decay_t<Types>...>{in<Types>()...}; }
struct io_init
{
io_init()
{
std::cin.tie(nullptr), std::ios::sync_with_stdio(false);
std::cout << std::fixed << std::setprecision(20);
}
} hogechan;
template<typename T>
void out(const T& v) { std::cout << v << '\n'; } // Reactiveではstd::flushを忘れない
template<typename T, typename... Args>
void out(const T& v, const Args... args) { std::cout << v << ' ', out(args...); }
# define SHOW(...) static_cast<void>(0)
constexpr ull TEN(const usize n) { return n == 0 ? 1ULL : TEN(n - 1) * 10ULL; }
template<typename T, typename Uint, usize n, usize i>
auto make_v(typename std::enable_if<(i == n), c_arr<Uint, n>>::type, const T& v = T{}) { return v; }
template<typename T, typename Uint, usize n, usize i>
auto make_v(typename std::enable_if<(i < n), c_arr<Uint, n>>::type szs, const T& v = T{})
{
const usize s = (usize)szs[i];
return std::vector<decltype(make_v<T, Uint, n, i + 1>(szs, v))>(s, make_v<T, Uint, n, i + 1>(szs, v));
}
template<typename T, typename Uint, usize n>
auto make_v(c_arr<Uint, n> szs, const T& t = T{}) { return make_v<T, Uint, n, 0>(szs, t); }
template<typename T> T gcd(const T& a, const T& b) { return a < 0 ? gcd(-a, b) : b < 0 ? gcd(a, -b) : (a > b ? gcd(b, a) : a == 0 ? b : gcd(b % a, a)); }
template<typename T> T lcm(const T& a, const T& b) { return a / gcd(a, b) * b; }
template<typename T>
constexpr std::pair<T, T> extgcd(const T a, const T b)
{
if (b == 0) { return std::pair<T, T>{1, 0}; }
const auto g = gcd(a, b), da = std::abs(b) / g;
const auto p = extgcd(b, a % b);
const auto x = (da + p.second % da) % da, y = (g - a * x) / b;
return {x, y};
}
template<typename T>
constexpr T inverse(const T a, const T mod) { return extgcd(a, mod).first; }
template<uint mod_value, bool dynamic = false>
class modint_base
{
public:
template<typename UInt = uint>
static std::enable_if_t<dynamic, const UInt> mod() { return mod_ref(); }
template<typename UInt = uint>
static constexpr std::enable_if_t<not dynamic, const UInt> mod() { return mod_value; }
template<typename UInt = uint>
static void set_mod(const std::enable_if_t<dynamic, const UInt> mod) { mod_ref() = mod, inv_ref() = {1, 1}; }
modint_base() : v{0} {}
modint_base(const ll val) : v{norm(static_cast<uint>(val % static_cast<ll>(mod()) + static_cast<ll>(mod())))} {}
modint_base(const modint_base& n) : v{n()} {}
explicit operator bool() const { return v != 0; }
bool operator!() const { return not static_cast<bool>(*this); }
modint_base& operator=(const modint_base& m) { return v = m(), (*this); }
modint_base& operator=(const ll val) { return v = norm(uint(val % static_cast<ll>(mod()) + static_cast<ll>(mod()))), (*this); }
friend modint_base operator+(const modint_base& m) { return m; }
friend modint_base operator-(const modint_base& m) { return make(norm(mod() - m.v)); }
friend modint_base operator+(const modint_base& m1, const modint_base& m2) { return make(norm(m1.v + m2.v)); }
friend modint_base operator-(const modint_base& m1, const modint_base& m2) { return make(norm(m1.v + mod() - m2.v)); }
friend modint_base operator*(const modint_base& m1, const modint_base& m2) { return make(static_cast<uint>(static_cast<ll>(m1.v) * static_cast<ll>(m2.v) % static_cast<ll>(mod()))); }
friend modint_base operator/(const modint_base& m1, const modint_base& m2) { return m1 * inv(m2.v); }
friend modint_base operator+(const modint_base& m, const ll val) { return modint_base{static_cast<ll>(m.v) + val}; }
friend modint_base operator-(const modint_base& m, const ll val) { return modint_base{static_cast<ll>(m.v) - val}; }
friend modint_base operator*(const modint_base& m, const ll val) { return modint_base{static_cast<ll>(m.v) * (val % static_cast<ll>(mod()))}; }
friend modint_base operator/(const modint_base& m, const ll val) { return modint_base{static_cast<ll>(m.v) * inv(val)}; }
friend modint_base operator+(const ll val, const modint_base& m) { return modint_base{static_cast<ll>(m.v) + val}; }
friend modint_base operator-(const ll val, const modint_base& m) { return modint_base{-static_cast<ll>(m.v) + val}; }
friend modint_base operator*(const ll val, const modint_base& m) { return modint_base{static_cast<ll>(m.v) * (val % static_cast<ll>(mod()))}; }
friend modint_base operator/(const ll val, const modint_base& m) { return modint_base{val * inv(static_cast<ll>(m.v))}; }
friend modint_base& operator+=(modint_base& m1, const modint_base& m2) { return m1 = m1 + m2; }
friend modint_base& operator-=(modint_base& m1, const modint_base& m2) { return m1 = m1 - m2; }
friend modint_base& operator*=(modint_base& m1, const modint_base& m2) { return m1 = m1 * m2; }
friend modint_base& operator/=(modint_base& m1, const modint_base& m2) { return m1 = m1 / m2; }
friend modint_base& operator+=(modint_base& m, const ll val) { return m = m + val; }
friend modint_base& operator-=(modint_base& m, const ll val) { return m = m - val; }
friend modint_base& operator*=(modint_base& m, const ll val) { return m = m * val; }
friend modint_base& operator/=(modint_base& m, const ll val) { return m = m / val; }
friend modint_base operator^(const modint_base& m, const ll n) { return power(m.v, n); }
friend modint_base& operator^=(modint_base& m, const ll n) { return m = m ^ n; }
friend bool operator==(const modint_base& m1, const modint_base& m2) { return m1.v == m2.v; }
friend bool operator!=(const modint_base& m1, const modint_base& m2) { return not(m1 == m2); }
friend bool operator==(const modint_base& m, const ll val) { return m.v == norm(static_cast<uint>(static_cast<ll>(mod()) + val % static_cast<ll>(mod()))); }
friend bool operator!=(const modint_base& m, const ll val) { return not(m == val); }
friend bool operator==(const ll val, const modint_base& m) { return m.v == norm(static_cast<uint>(static_cast<ll>(mod()) + val % static_cast<ll>(mod()))); }
friend bool operator!=(const ll val, const modint_base& m) { return not(m == val); }
friend std::istream& operator>>(std::istream& is, modint_base& m)
{
ll v;
return is >> v, m = v, is;
}
friend std::ostream& operator<<(std::ostream& os, const modint_base& m) { return os << m(); }
uint operator()() const { return v; }
static modint_base small_inv(const usize n)
{
auto& in = inv_ref();
if (n < in.size()) { return in[n]; }
for (usize i = in.size(); i <= n; i++) { in.push_back(-in[modint_base::mod() % i] * (modint_base::mod() / i)); }
return in.back();
}
private:
template<typename UInt = uint>
static std::enable_if_t<dynamic, UInt&> mod_ref()
{
static UInt mod = 0;
return mod;
}
static uint norm(const uint x) { return x < mod() ? x : x - mod(); }
static modint_base make(const uint x)
{
modint_base m;
return m.v = x, m;
}
static modint_base power(modint_base x, ull n)
{
modint_base ans = 1;
for (; n; n >>= 1, x *= x) {
if (n & 1) { ans *= x; }
}
return ans;
}
static modint_base inv(const ll v) { return v < 1000000 ? small_inv(static_cast<usize>(v)) : modint_base{inverse(v, static_cast<ll>(mod()))}; }
static std::vector<modint_base>& inv_ref()
{
static std::vector<modint_base> in{1, 1};
return in;
}
uint v;
};
template<uint mod>
using modint = modint_base<mod, false>;
template<uint id>
using dynamic_modint = modint_base<id, true>;
template<typename T>
std::vector<T> divisors(const T n)
{
std::vector<T> head, tail;
for (T i = 1; i * i <= n; i++) {
if (n % i == 0) {
head.push_back(i);
if (i * i != n) { tail.push_back(n / i); }
}
}
for (auto it = tail.rbegin(); it != tail.rend(); it++) { head.push_back(*it); }
return head;
}
template<typename T>
std::vector<std::pair<T, usize>> prime_factors(T n)
{
std::vector<std::pair<T, usize>> ans;
for (T i = 2; i * i <= n; i++) {
usize cnt = 0;
for (; n % i == 0; n /= i, cnt++) {}
if (cnt > 0) { ans.push_back({i, cnt}); }
}
if (n > 1) { ans.push_back({n, 1}); }
return ans;
}
template<uint mod_value, bool dynamic>
ull period(const modint_base<mod_value, dynamic>& x)
{
using mint = modint_base<mod_value, dynamic>;
const ull p = mint::mod(); // constexprにしたいね
const auto ds = divisors(p - 1);
for (const ull d : ds) {
if ((x ^ d) == 1) { return d; }
}
return p - 1;
}
template<typename mint>
mint primal_root()
{
const ull p = mint::mod(); // constexprにしたいね
const auto fs = prime_factors(p - 1);
mint g = 1;
for (;; g += 1) {
bool ok = true;
for (const auto& q : fs) {
const ull per = (p - 1) / q.first;
if ((g ^ per) == 1) {
ok = false;
break;
}
}
if (ok) { return g; }
}
return p;
}
template<typename T, typename InIt>
std::pair<T, T> crt(const InIt first, const InIt last)
{
using P = std::pair<T, T>;
return std::accumulate(first, last, P{0, 1}, [](const P& a1, const P& a2) -> P {
T r1 = a1.first, m1 = a1.second, r2 = a2.first, m2 = a2.second;
const T g = gcd(m1, m2);
if (r1 % g != r2 % g) { return P{0, 0}; }
const T m = m1 / g * m2;
if (r1 == r2) { return {r1, m}; }
const auto k1 = extgcd(m1, m2).first * ((r2 - r1) / g) % m;
return P{(m + (__int128_t(m1) * k1 % m) + r1) % m, m};
});
}
template<typename Ring>
class discrete_log
{
public:
discrete_log(const Ring x, const ull period) : x{x}, period{period}
{
for (; bs * bs < period; bs++) {}
for (ull i = 0; i * bs < period; i++) { giant[x ^ (i * bs)] = i * bs; }
}
ull operator()(Ring y)
{
for (ull i = 0; i < bs; i++) {
if (giant.count(y)) { return (giant[y] + period - i) % period; }
y = y * x;
}
return period;
}
private:
const Ring x;
ull period;
ull bs = 1;
std::map<Ring, ull> giant;
};
using mint = dynamic_modint<0>;
bool operator<(const mint& m1, const mint& m2) { return m1() < m2(); }
mint g;
template<typename T = mint>
struct mat
{
mat()
{
table[0][0] = T{0};
table[0][1] = T{0};
table[1][0] = T{0};
table[1][1] = T{0};
}
mat(const T& a00, const T& a01, const T& a10, const T& a11)
{
table[0][0] = a00;
table[0][1] = a01;
table[1][0] = a10;
table[1][1] = a11;
}
std::array<T, 2>& operator[](const int i) { return table[i]; }
const std::array<T, 2>& operator[](const int i) const { return table[i]; }
friend bool operator==(const mat& m1, const mat& m2) { return m1.table == m2.table; }
friend mat operator+(const mat& m1, const mat& m2)
{
mat ans;
for (int i = 0; i < 2; i++) {
for (int j = 0; j < 2; j++) { ans[i][j] = m1[i][j] + m2[i][j]; }
}
return ans;
}
friend mat operator-(const mat& m1, const mat& m2)
{
mat ans;
for (int i = 0; i < 2; i++) {
for (int j = 0; j < 2; j++) { ans[i][j] = m1[i][j] - m2[i][j]; }
}
return ans;
}
friend mat operator*(const mat& m1, const mat& m2)
{
mat ans;
for (int i = 0; i < 2; i++) {
for (int j = 0; j < 2; j++) {
for (int k = 0; k < 2; k++) { ans[i][j] = ans[i][j] + m1[i][k] * m2[k][j]; }
}
}
return ans;
}
friend mat operator*(const mat& m, const T& v)
{
mat ans;
for (int i = 0; i < 2; i++) {
for (int j = 0; j < 2; j++) { ans[i][j] = m[i][j] * v; }
}
return ans;
}
friend mat operator^(const mat& m, const ll k) { return k == 0 ? I() : k % 2 == 0 ? (m * m) ^ (k / 2) : (m ^ (k - 1)) * m; }
friend std::ostream& operator<<(std::ostream& os, const mat& m)
{
os << "[";
for (int i = 0; i < 2; i++) {
os << "[";
for (int j = 0; j < 2; j++) { os << m[i][j] << ","; }
os << "]\n";
}
return os << "]\n";
}
static mat I()
{
mat ans;
ans[0][0] = T{1}, ans[1][1] = T{1};
return ans;
}
static T tr(const mat& m) { return m[0][0] + m[1][1]; }
static T det(const mat& m) { return m[0][0] * m[1][1] - m[0][1] * m[1][0]; }
static mat inv(const mat& m)
{
const T d = det(m);
mat<T> ans;
ans[0][0] = m[1][1] / d;
ans[0][1] = -m[0][1] / d;
ans[1][0] = -m[1][0] / d;
ans[1][1] = m[0][0] / d;
return ans;
}
std::array<std::array<T, 2>, 2> table;
};
struct C
{
C() : x{0}, y{0} {}
C(const mint& x) : x{x}, y{0} {}
C(const mint& x, const mint& y) : x{x}, y{y} {}
friend bool operator==(const C& c1, const C& c2) { return c1.x == c2.x and c1.y == c2.y; }
friend bool operator!=(const C& c1, const C& c2) { return not(c1 == c2); }
friend bool operator<(const C& c1, const C& c2) { return c1.x != c2.x ? c1.x < c2.x : c1.y < c2.y; }
friend C operator-(const C& c) { return C{-c.x, -c.y}; }
friend C operator+(const C& c1, const C& c2) { return C{c1.x + c2.x, c1.y + c2.y}; }
friend C operator-(const C& c1, const C& c2) { return C{c1.x - c2.x, c1.y - c2.y}; }
friend C operator*(const C& c1, const C& c2) { return C{c1.x * c2.x + g * c1.y * c2.y, c1.x * c2.y + c1.y * c2.x}; }
friend C operator/(const C& c1, const C& c2) { return c1 * conj(c2); }
friend C operator*(const C& c, const mint& v) { return C{c.x * v, c.y * v}; }
friend C operator/(const C& c, const mint& v) { return C{c.x / v, c.y / v}; }
friend C operator^(const C& c, const ll k)
{
const mint a = c.x;
const mint b = c.y;
const auto m = (mat<mint>(a, b * g, b, a)) ^ k;
return C{m[0][0], m[1][0]};
}
static mint normSq(const C& c) { return c.x * c.x - g * c.y * c.y; }
static C conj(const C& c) { return C{c.x, -c.y} / normSq(c); }
friend std::ostream& operator<<(std::ostream& os, const C& c) { return os << c.x << "+" << c.y << "\\sqrt(g)"; }
mint x, y; // x+y\sqrt{g}
};
int main()
{
const uint p = in<uint>();
mint::set_mod(p);
g = primal_root<mint>();
const auto as = in_v<mint>({4});
const auto bs = in_v<mint>({4});
mat<mint> A(as[0], as[1], as[2], as[3]);
mat<mint> B(bs[0], bs[1], bs[2], bs[3]);
for (int i = 1; i <= 100; i++) {
if ((A ^ i) == B) { return std::cout << i << std::endl, 0; }
}
discrete_log<mint> pr_dlog(g, p - 1);
auto sqrt = [&](const mint x) -> C {
if (x == 0) { return {0, 0}; }
const ll y = pr_dlog(x);
if (y % 2 == 0) {
return {g ^ (y / 2), 0};
} else {
return {0, g ^ ((y - 1) / 2)};
}
};
auto eigens = [&](const mat<mint>& A) -> std::array<C, 2> {
const auto s = mat<mint>::tr(A);
const auto t = mat<mint>::det(A);
const auto d = s * s - 4 * t;
const auto sq = sqrt(d);
return {(C{s, 0} + sq) / 2, (C{s, 0} - sq) / 2};
};
auto eigen_vecs = [&](const auto& A) -> mat<C> { // D=S^(-1)ASのS
if (A[0][1] == 0 and A[1][0] == 0) { return mat<C>(C{1}, C{0}, C{0}, C{1}); }
const auto es = eigens(A);
if (es[0] == es[1]) { // ジョルダン標準形
const mint l = es[0].x;
const auto N = A - mat<mint>::I() * l;
SHOW(N);
if (N[0][1] != 0 or N[1][1] != 0) {
return mat<C>(C{N[0][1]}, C{0}, C{N[1][1]}, C{1});
} else {
return mat<C>(C{N[0][0]}, C{1}, C{N[1][0]}, C{0});
}
} else { // 対角化可能
std::array<std::array<C, 2>, 2> ans;
for (int i = 0; i < 2; i++) {
std::array<C, 2> v1{{C{A[0][0], 0} - es[i], C{A[0][1], 0}}};
if (v1[0] == C{} and v1[1] == C{}) {
v1 = {{C{A[1][0], 0}, C{A[1][1], 0} - es[i]}};
}
SHOW(i, v1);
ans[i] = {{-v1[1], v1[0]}};
}
return mat<C>(ans[0][0], ans[1][0], ans[0][1], ans[1][1]);
}
};
auto normal = [&](const C& c) {
if (c == C{0}) { return c; }
if (c.y == 0) { return C{1, 0}; }
return C{c.x / c.y, 1};
};
SHOW(eigens(A));
SHOW(eigens(B));
const auto AS = eigen_vecs(A);
SHOW(AS);
mat<C> CA(C{A[0][0]}, C{A[0][1]}, C{A[1][0]}, C{A[1][1]});
mat<C> CB(C{B[0][0]}, C{B[0][1]}, C{B[1][0]}, C{B[1][1]});
CA = mat<C>::inv(AS) * CA * AS;
CB = mat<C>::inv(AS) * CB * AS;
SHOW(CA, CB); // ここまでが間違っていたらマジで終了
auto lg = [&](const C& c1, const C& c2) -> std::pair<ll, ll> {
// c1=a+b\sqrt{g}について
// c1^(p+1) = a^2-(b^2)g (特にF_pの元)
// なのでF_q倍を無視した同値類の周期Pは(p+1)の約数
// [c1^rの同値類]=[c2]の同値類となるrをBSGSで見つける
// 残りは n=c1^P と (c2/c1^r) が整数なので (mod p)での普通の離散対数
if (c1 == C{0}) {
if (c2 == C{0}) {
return {0, 1};
} else {
return {0, 0};
}
}
if (c2 == C{0}) { return {0, 0}; }
static std::vector<uint> ds;
if (ds.empty()) { ds = divisors(p + 1); }
ll per = p + 1;
for (const ll d : ds) {
if ((c1 ^ d).y == 0) {
per = d;
break;
}
}
const mint c = c2.x;
const mint d = c2.y;
const mint n = (c1 ^ per).x;
assert(n != 0);
SHOW(n);
if (d == 0) {
const ull per2 = period(n);
const ull lg2 = discrete_log<mint>(n, per2)(c);
return {lg2 * per, per * per2};
} else {
auto res = [&]() {
ll bs = 1;
for (; bs * bs < per; bs++) {}
std::map<C, ll> giant;
for (ll i = 0; i * bs < per; i++) {
const C n = normal(c1 ^ (i * bs));
giant[n] = i * bs;
}
C c2_ = normal(c2);
for (ll i = 0; i < bs; i++) {
if (giant.count(c2_)) { return (per + giant[c2_] - i) % per; }
c2_ = normal(c2_ * c1);
}
return per;
}();
if (res == per) { return {0, 0}; }
const C cr = c1 ^ res;
const C d = c2 / cr;
assert(d.y == 0);
const mint r = d.x;
const ull per2 = period(n);
const ull lg2 = discrete_log<mint>(n, per2)(r);
return {lg2 * per + res, per2 * per};
}
};
if (CB[1][0] != C{0}) { return std::cout << -1 << std::endl, 0; }
if (CA[0][1] == C{0}) { // 対角
if (CB[0][1] != C{0}) { return std::cout << -1 << std::endl, 0; }
const auto p1 = lg(CA[0][0], CB[0][0]);
const auto p2 = lg(CA[1][1], CB[1][1]);
if (p1.second == 0 or p2.second == 0) { return std::cout << -1 << std::endl, 0; }
std::vector<std::pair<ll, ll>> mods{p1, p2};
SHOW(mods);
const auto ans = crt<ll>(mods.begin(), mods.end());
ll n = ans.first;
if (n == 0) { n = ans.second; }
std::cout << ((A ^ n) == B ? n : -1LL) << std::endl;
} else { // 非対角
if (CB[0][0] != CB[1][1]) { return std::cout << -1 << std::endl, 0; }
const mint l = CA[0][0].x;
const mint m = (CB[0][1].x * l) / CB[0][0].x;
const auto p1 = lg(CA[0][0], CB[0][0]);
const auto p2 = std::pair<ll, ll>{(ll)m(), (ll)p};
if (p1.second == 0 or p2.second == 0) { return std::cout << -1 << std::endl, 0; }
std::vector<std::pair<ll, ll>> mods{p1, p2};
SHOW(mods);
const auto ans = crt<ll>(mods.begin(), mods.end());
SHOW(ans);
ll n = ans.first;
if (n == 0) { n = ans.second; }
std::cout << ((A ^ n) == B ? n : -1LL) << std::endl;
}
return 0;
}