結果
| 問題 | No.3056 量子コンピュータで素因数分解 Easy |
| ユーザー |
 Pachicobue
|
| 提出日時 | 2020-02-05 13:53:58 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
TLE
(最新)
AC
(最初)
|
| 実行時間 | - |
| コード長 | 34,504 bytes |
| コンパイル時間 | 5,295 ms |
| コンパイル使用メモリ | 236,340 KB |
| 実行使用メモリ | 24,432 KB |
| 平均クエリ数 | 2.62 |
| 最終ジャッジ日時 | 2023-08-30 06:52:41 |
| 合計ジャッジ時間 | 18,548 ms |
|
ジャッジサーバーID （参考情報） |
judge13 / judge15 |
（要ログイン）
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 | 43 ms
23,352 KB |
| testcase_01 | AC | 109 ms
23,868 KB |
| testcase_02 | AC | 834 ms
24,036 KB |
| testcase_03 | AC | 805 ms
24,192 KB |
| testcase_04 | AC | 88 ms
23,376 KB |
| testcase_05 | AC | 103 ms
23,676 KB |
| testcase_06 | AC | 116 ms
23,664 KB |
| testcase_07 | AC | 129 ms
24,348 KB |
| testcase_08 | AC | 132 ms
23,640 KB |
| testcase_09 | AC | 142 ms
23,736 KB |
| testcase_10 | AC | 171 ms
23,532 KB |
| testcase_11 | AC | 298 ms
23,400 KB |
| testcase_12 | AC | 234 ms
23,664 KB |
| testcase_13 | AC | 211 ms
24,024 KB |
| testcase_14 | TLE | - |
| testcase_15 | AC | 771 ms
23,424 KB |
| testcase_16 | AC | 302 ms
24,012 KB |
| testcase_17 | AC | 340 ms
24,432 KB |
| testcase_18 | AC | 365 ms
23,424 KB |
| testcase_19 | AC | 1,579 ms
24,192 KB |
| testcase_20 | AC | 483 ms
23,676 KB |
| testcase_21 | AC | 237 ms
24,024 KB |
| testcase_22 | AC | 522 ms
24,204 KB |
| testcase_23 | AC | 360 ms
23,376 KB |
| testcase_24 | AC | 395 ms
24,348 KB |
| testcase_25 | AC | 39 ms
23,364 KB |
ソースコード
#include <bits/stdc++.h>
// created [2020/02/05] 11:35:57
#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>
using max_heap = std::priority_queue<T>;
template<typename T>
using min_heap = std::priority_queue<T, std::vector<T>, std::greater<T>>;
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};
auto mfp = [](auto&& f) { return [=](auto&&... args) { return f(f, std::forward<decltype(args)>(args)...); }; };
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);
}
void clear()
{
std::cin.tie(), std::ios::sync_with_stdio(true);
}
} io_setting;
int out() { return 0; }
template<typename T>
int out(const T& v) { return std::cout << v, 0; }
template<typename T>
int out(const std::vector<T>& v)
{
for (usize i = 0; i < v.size(); i++) {
if (i > 0) { std::cout << ' '; }
out(v[i]);
}
return 0;
}
template<typename T1, typename T2>
int out(const std::pair<T1, T2>& v) { return out(v.first), std::cout << ' ', out(v.second), 0; }
template<typename T, typename... Args>
int out(const T& v, const Args... args) { return out(v), std::cout << ' ', out(args...), 0; }
template<typename... Args>
int outln(const Args... args) { return out(args...), std::cout << '\n', 0; }
template<typename... Args>
int outel(const Args... args) { return out(args...), std::cout << std::endl, 0; }
# 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 Real>
struct complex
{
using value_type = Real;
complex() : real{Real{0}}, imag{Real{0}} {}
complex(const complex&) = default;
complex(const Real& theta) : real(std::cos(theta)), imag(std::sin(theta)) {}
complex(const Real& r, const Real& i) : real{r}, imag{i} {}
~complex() = default;
friend complex operator+(const complex& c) { return c; }
friend complex operator-(const complex& c) { return complex{-c.real, -c.imag}; }
friend complex operator+(const complex& c1, const complex& c2) { return complex{c1.real + c2.real, c1.imag + c2.imag}; }
friend complex operator-(const complex& c1, const complex& c2) { return complex{c1.real - c2.real, c1.imag - c2.imag}; }
friend complex operator*(const complex& c1, const complex& c2) { return complex{c1.real * c2.real - c1.imag * c2.imag, c1.real * c2.imag + c1.imag * c2.real}; }
friend complex operator*(const complex& c, const Real& r) { return complex{c.real * r, c.imag * r}; }
friend complex operator/(complex& c1, complex& c2) { c1* c2.conj() / c2.norm(); }
friend bool operator==(const complex& c1, const complex& c2) { return c1.real == c2.real and c1.imag == c2.imag; }
friend bool operator!=(const complex& c1, const complex& c2) { return not(c1 == c2); }
friend complex& operator+=(complex& c1, const complex& c2) { return c1.real += c2.real, c1.imag += c2.imag, c1; }
friend complex& operator-=(complex& c1, const complex& c2) { return c1.real += c2.real, c1.imag += c2.imag, c1; }
friend complex& operator*=(complex& c1, const complex& c2) { return c1 = c1 * c2; }
friend complex& operator*=(complex& c, const Real& r) { return c = c * r; }
friend complex& operator/=(complex& c1, const complex& c2) { return c1 = c1 / c2; }
complex conj() const { return complex{real, -imag}; }
Real norm() const { return real * real + imag * imag; }
Real abs() const { return std::sqrt(norm()); }
Real arg() const { return std::atan2(imag, real); }
friend std::ostream& operator<<(std::ostream& os, const complex& c) { return os << c.real << "+" << c.imag << "i"; }
Real real, imag;
};
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();
}
std::pair<ll, ll> quad() const
{
const auto ans = quad_r(v, mod());
ll x = std::get<0>(ans), y = std::get<1>(ans);
if (y < 0) { x = -x, y = -y; }
return {x, y};
}
private:
static std::tuple<ll, ll, ll> quad_r(const ll r, const ll p) // r = x/y (mod p), (x,y,z) s.t. x=yr+pz
{
if (std::abs(r) <= 1000) { return {r, 1, 0}; }
ll nr = p % r, q = p / r;
if (nr * 2LL >= r) { nr -= r, q++; }
if (nr * 2LL <= -r) { nr += r, q--; }
const auto sub = quad_r(nr, r);
const ll x = std::get<0>(sub), z = std::get<1>(sub), y = std::get<2>(sub);
return {x, y - q * z, z};
}
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 <= 2000000 ? 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 Real = double>
class fft
{
private:
static constexpr usize depth = 30;
static constexpr Real pi = pi_v<Real>;
static void transform(std::vector<complex<Real>>& a, const usize lg, const bool rev)
{
static std::vector<complex<Real>> root[depth];
const usize sz = a.size();
assert((1UL << lg) == sz);
if (root[lg].empty()) {
root[lg].reserve(sz), root[lg].resize(sz);
for (usize i = 0; i < sz; i++) { root[lg][i] = complex<Real>(pi * Real(2 * i) / Real(sz)); }
}
std::vector<complex<Real>> tmp(sz);
for (usize w = (sz >> 1); w > 0; w >>= 1) {
for (usize y = 0; y < (sz >> 1); y += w) {
const complex<Real> r = rev ? root[lg][y].conj() : root[lg][y];
for (usize x = 0; x < w; x++) {
const auto u = a[y << 1 | x], v = a[y << 1 | x | w] * r;
tmp[y | x] = u + v, tmp[y | x | (sz >> 1)] = u - v;
}
}
std::swap(tmp, a);
}
}
public:
using value_type = Real;
fft() = delete;
template<typename T = ll, typename I = int>
static std::vector<T> simple_convolute(const std::vector<I>& a, const std::vector<I>& b)
{
const usize need = a.size() + b.size() - 1, lg = clog(need), sz = 1UL << lg;
std::vector<complex<Real>> x(sz), y(sz);
for (usize i = 0; i < a.size(); i++) { x[i] = {(Real)a[i], (Real)0}; }
for (usize i = 0; i < b.size(); i++) { y[i] = {(Real)b[i], (Real)0}; }
transform(x, lg, false), transform(y, lg, false);
for (usize i = 0; i < sz; i++) { x[i] *= y[i]; }
transform(x, lg, true);
std::vector<T> ans(need);
for (usize i = 0; i < need; i++) { ans[i] = (T)std::round(x[i].real / (Real)sz); }
return ans;
}
template<typename T = ll, usize division = 2, typename I = int>
static std::vector<T> convolute(const std::vector<I>& a, const std::vector<I>& b)
{
constexpr usize bitnum = (depth + division - 1) / division;
const usize need = a.size() + b.size() - 1, lg = clog(need), sz = 1UL << lg;
std::vector<complex<value_type>> x[division], y[division], tmp(sz);
for (usize i = 0; i < division; i++) {
x[i].reserve(sz), x[i].resize(sz), y[i].reserve(sz), y[i].resize(sz);
std::fill(tmp.begin() + std::min(a.size(), b.size()), tmp.end(), complex<value_type>{});
for (usize j = 0; j < a.size(); j++) { tmp[j].real = value_type((a[j] >> (bitnum * i)) & ((1 << bitnum) - 1)); }
for (usize j = 0; j < b.size(); j++) { tmp[j].imag = value_type((b[j] >> (bitnum * i)) & ((1 << bitnum) - 1)); }
transform(tmp, lg, false);
for (usize j = 0; j < sz; j++) { tmp[j] *= value_type(0.5); }
for (usize j = 0; j < sz; j++) {
const usize k = j == 0 ? 0UL : sz - j;
x[i][j] = complex<value_type>{tmp[j].real + tmp[k].real, tmp[j].imag - tmp[k].imag}, y[i][j] = complex<value_type>{tmp[j].imag + tmp[k].imag, -tmp[j].real + tmp[k].real};
}
}
std::vector<complex<value_type>> z[division];
for (usize i = 0; i < division; i++) { z[i].reserve(sz), z[i].resize(sz); }
for (usize a = 0; a < division; a++) {
for (usize b = 0; b < division; b++) {
for (usize i = 0; i < sz; i++) {
if (a + b < division) {
z[a + b][i] += x[a][i] * y[b][i];
} else {
z[a + b - division][i] += x[a][i] * y[b][i] * complex<value_type>(0, 1);
}
}
}
}
for (usize i = 0; i < division; i++) { transform(z[i], lg, true); }
std::vector<T> ans(need);
T base = 1;
for (usize k = 0; k < 2 * division - 1; k++, base *= (1LL << bitnum)) {
for (usize i = 0; i < need; i++) {
if (k < division) {
ans[i] += base * T(std::round(z[k][i].real / value_type(sz)));
} else {
ans[i] += base * T(std::round(z[k - division][i].imag / value_type(sz)));
}
}
}
return ans;
}
template<uint mod, bool dynamic = false, usize division = 2>
static std::vector<modint_base<mod, dynamic>> convolute(const std::vector<modint_base<mod, dynamic>>& a, const std::vector<modint_base<mod, dynamic>>& b)
{
using mint = modint_base<mod, dynamic>;
constexpr usize bitnum = (depth + division - 1) / division;
const usize need = a.size() + b.size() - 1, lg = clog(need), sz = 1UL << lg;
std::vector<complex<value_type>> x[division], y[division], tmp(sz);
for (usize i = 0; i < division; i++) {
x[i].reserve(sz), x[i].resize(sz), y[i].reserve(sz), y[i].resize(sz);
std::fill(tmp.begin() + std::min(a.size(), b.size()), tmp.end(), complex<value_type>{});
for (usize j = 0; j < a.size(); j++) { tmp[j].real = value_type((a[j]() >> (bitnum * i)) & ((1 << bitnum) - 1)); }
for (usize j = 0; j < b.size(); j++) { tmp[j].imag = value_type((b[j]() >> (bitnum * i)) & ((1 << bitnum) - 1)); }
transform(tmp, lg, false);
for (usize j = 0; j < sz; j++) { tmp[j] *= value_type(0.5); }
for (usize j = 0; j < sz; j++) {
const usize k = j == 0 ? 0UL : sz - j;
x[i][j] = complex<value_type>{tmp[j].real + tmp[k].real, tmp[j].imag - tmp[k].imag}, y[i][j] = complex<value_type>{tmp[j].imag + tmp[k].imag, -tmp[j].real + tmp[k].real};
}
}
std::vector<complex<value_type>> z[division];
for (usize i = 0; i < division; i++) { z[i].reserve(sz), z[i].resize(sz); }
for (usize a = 0; a < division; a++) {
for (usize b = 0; b < division; b++) {
for (usize i = 0; i < sz; i++) {
if (a + b < division) {
z[a + b][i] += x[a][i] * y[b][i];
} else {
z[a + b - division][i] += x[a][i] * y[b][i] * complex<value_type>(0, 1);
}
}
}
}
for (usize i = 0; i < division; i++) { transform(z[i], lg, true); }
std::vector<mint> ans(need);
mint base = 1;
for (usize k = 0; k < 2 * division - 1; k++, base *= (1LL << bitnum)) {
for (usize i = 0; i < need; i++) {
if (k < division) {
ans[i] += int((base * ll(std::round(z[k][i].real / value_type(sz))))());
} else {
ans[i] += int((base * ll(std::round(z[k - division][i].imag / value_type(sz))))());
}
}
}
return ans;
}
};
template<usize bucket_digits = 7, usize fft_division = 2>
class bigint
{
public:
using bucket_type = ll;
static constexpr bucket_type bucket_value = TEN(bucket_digits);
bigint() {}
bigint(const bucket_type x) : sign(x >= 0), d(x == 0 ? 0 : 1, x < 0 ? -x : x) { normalize(); }
bigint(const bool sign, const std::vector<bucket_type>& d) : sign(sign), d(d) { normalize(); }
bigint(const bigint& n) : sign(n.sign), d(n.d) {}
bigint(const std::string& str)
{
assert(not str.empty());
sign = str[0] != '-';
for (usize i = 0; i < str.size(); i += bucket_digits) {
const usize r = str.size() - i, l = (sign ? (r >= bucket_digits ? r - bucket_digits : 0) : (r > bucket_digits ? r - bucket_digits : 1));
if (r > l) { d.push_back(static_cast<bucket_type>(std::stoll(str.substr(l, r - l)))); }
}
}
friend bigint operator+(const bigint& m) { return m; }
friend bigint operator-(const bigint& m) { return bigint{not m.sign, m.d}; }
explicit operator bool() const { return not d.empty(); }
bool operator!() const { return not static_cast<bool>(*this); }
friend bigint operator+(const bigint& m, const bigint& n)
{
if (m.sign == n.sign) {
usize sz = std::max(m.d.size(), n.d.size());
std::vector<bucket_type> v(sz, 0);
for (usize i = 0; i < m.d.size(); i++) { v[i] += m.d[i]; }
for (usize i = 0; i < n.d.size(); i++) { v[i] += n.d[i]; }
return bigint{m.sign, v};
} else {
usize sz = std::max(m.d.size(), n.d.size());
std::vector<bucket_type> v(sz, 0);
if (abs_comp(m, n) == -1) {
for (usize i = 0; i < m.d.size(); i++) { v[i] -= m.d[i]; }
for (usize i = 0; i < n.d.size(); i++) { v[i] += n.d[i]; }
return bigint{n.sign, v};
} else {
for (usize i = 0; i < m.d.size(); i++) { v[i] += m.d[i]; }
for (usize i = 0; i < n.d.size(); i++) { v[i] -= n.d[i]; }
return bigint{m.sign, v};
}
}
}
friend bigint operator-(const bigint& m, const bigint& n) { return m + (-n); }
friend bigint operator*(const bigint& m, const bigint& n) { return bigint{not(m.sign ^ n.sign), fft<>::convolute<bucket_type, fft_division, bucket_type>(m.d, n.d)}; }
friend bigint operator/(const bigint& m, const bigint& n) { return div(m, n).first; }
friend bigint operator%(const bigint& m, const bigint& n) { return div(m, n).second; }
friend bigint operator^(const bigint& m, const bigint& n) { return n == 0 ? bigint{1} : n % 2 == 1 ? (m ^ (n - 1)) * m : (m * m) ^ (n / 2); }
friend bool operator<(const bigint& m, const bigint& n) { return comp(m, n) == -1; }
friend bool operator>(const bigint& m, const bigint& n) { return comp(m, n) == 1; }
friend bool operator==(const bigint& m, const bigint& n) { return comp(m, n) == 0; }
friend bool operator!=(const bigint& m, const bigint& n) { return not(m == n); }
friend bool operator<=(const bigint& m, const bigint& n) { return not(m > n); }
friend bool operator>=(const bigint& m, const bigint& n) { return not(m < n); }
friend bigint operator<<(const bigint& m, const usize n) // *(B^n)
{
std::vector<bucket_type> ans(m.d.size() + n, 0);
for (usize i = 0; i < m.d.size(); i++) { ans[i + n] = m.d[i]; }
return bigint{m.sign, ans};
}
friend bigint operator>>(const bigint& m, const usize n) // /(B^n)
{
if (m.d.size() <= n) { return 0; }
std::vector<bucket_type> ans(m.d.size() - n, 0);
for (usize i = 0; i < m.d.size() - n; i++) { ans[i] = m.d[i + n]; }
return bigint{m.sign, ans};
}
bigint& operator=(const bigint& n) { return sign = n.sign, d = n.d, *this; }
bigint& operator=(const bucket_type n) { return *this = bigint{n}; }
friend bigint& operator+=(bigint& m, const bigint& n) { return m = m + n; }
friend bigint& operator-=(bigint& m, const bigint& n) { return m = m - n; }
friend bigint& operator*=(bigint& m, const bigint& n) { return m = m * n; }
friend bigint& operator/=(bigint& m, const bigint& n) { return m = m / n; }
friend bigint& operator%=(bigint& m, const bigint& n) { return m = m % n; }
friend bigint& operator^=(bigint m, const bigint& n) { return m = m ^ n; }
friend bigint& operator<<=(bigint& m, const usize n) { return m = m << n; }
friend bigint& operator>>=(bigint& m, const usize n) { return m = m >> n; }
friend bigint operator+(const bigint& m, const bucket_type n) { return m + bigint{n}; }
friend bigint operator-(const bigint& m, const bucket_type n) { return m - bigint{n}; }
friend bigint operator*(const bigint& m, const bucket_type n) { return small_multiply(m, n); }
friend bigint operator/(const bigint& m, const bucket_type n) { return m / bigint{n}; }
friend bigint operator%(const bigint& m, const bucket_type n) { return m % bigint{n}; }
friend bool operator<(const bigint& m, const bucket_type n) { return comp(m, bigint{n}) == -1; }
friend bool operator>(const bigint& m, const bucket_type n) { return comp(m, bigint{n}) == 1; }
friend bool operator==(const bigint& m, const bucket_type n) { return comp(m, bigint{n}) == 0; }
friend bool operator!=(const bigint& m, const bucket_type n) { return not(m == n); }
friend bool operator<=(const bigint& m, const bucket_type n) { return not(m > n); }
friend bool operator>=(const bigint& m, const bucket_type n) { return not(m < n); }
friend bigint& operator+=(const bigint& m, const bucket_type n) { return m += bigint{n}; }
friend bigint& operator-=(const bigint& m, const bucket_type n) { return m -= bigint{n}; }
friend bigint& operator*=(const bigint& m, const bucket_type n) { return m *= bigint{n}; }
friend bigint& operator/=(const bigint& m, const bucket_type n) { return m /= bigint{n}; }
friend bigint& operator%=(const bigint& m, const bucket_type n) { return m %= bigint{n}; }
friend bigint operator+(const bucket_type m, const bigint& n) { return bigint{m} + n; }
friend bigint operator-(const bucket_type m, const bigint& n) { return bigint{m} - n; }
friend bigint operator*(const bucket_type m, const bigint& n) { return bigint{m} * n; }
friend bigint operator/(const bucket_type m, const bigint& n) { return bigint{m} / n; }
friend bigint operator%(const bucket_type m, const bigint& n) { return bigint{m} % n; }
friend bool operator<(const bucket_type m, const bigint& n) { return comp(bigint{m}, n) == -1; }
friend bool operator>(const bucket_type m, const bigint& n) { return comp(bigint{m}, n) == 1; }
friend bool operator==(const bucket_type m, const bigint& n) { return comp(bigint{m}, n) == 0; }
friend bool operator!=(const bucket_type m, const bigint& n) { return not(m == n); }
friend bool operator<=(const bucket_type m, const bigint& n) { return not(m > n); }
friend bool operator>=(const bucket_type m, const bigint& n) { return not(m < n); }
bigint& operator++() { return *this += bigint{1}; }
bigint operator++(int) { return std::exchange(*this, *this + bigint{1}); }
bigint& operator--() { return *this -= bigint{1}; }
bigint operator--(int) { return std::exchange(*this, *this - bigint{1}); }
friend std::pair<bigint, bigint> div(bigint m, bigint n)
{
assert(not n.d.empty());
if (abs_comp(m, n) == -1) { return {0, m}; }
const bool ms = m.sign, ns = n.sign;
m.sign = n.sign = true;
const usize sho_size = m.d.size() - n.d.size();
std::vector<bucket_type> sho(sho_size + 1);
for (usize i = 0; i <= sho_size; i++) {
const usize ind = sho_size - i;
const auto L = m >> ind;
bucket_type inf = -1, sup = bucket_value;
while (sup - inf > 1) {
const bucket_type mid = (sup + inf) >> 1;
(abs_comp(L, small_multiply(n, mid)) == -1 ? sup : inf) = mid;
}
sho[ind] = inf, m -= (small_multiply(n, inf) << ind);
}
return m.sign = ms, std::pair<bigint, bigint>{bigint{not(ms ^ ns), sho}, m};
}
friend std::istream& operator>>(std::istream& is, bigint& n)
{
std::string str;
is >> str;
return n = bigint{str}, is;
}
friend std::ostream& operator<<(std::ostream& os, const bigint& n)
{
if (n.d.empty()) { return os << '0'; }
if (n.sign == false) { os << '-'; }
const usize sz = n.d.size();
for (usize i = 0; i < sz; i++) {
if (i == 0) {
os << n.d[sz - i - 1];
} else {
usize nz = 0;
for (bucket_type base = 1; n.d[sz - i - 1] >= base; nz++, base *= bucket_type(10)) {}
for (usize i = 0; i + nz < bucket_digits; i++) { os << '0'; }
if (n.d[sz - i - 1] != 0LL) { os << n.d[sz - i - 1]; }
}
}
return os;
}
friend usize log10p1(const bigint& m)
{
if (m.d.empty()) { return 0; }
assert(m.sign);
return (m.d.size() - 1) * bucket_digits + log10p1(m.d.back());
}
friend bigint abs(const bigint& m)
{
auto ans = m;
return ans.sign = true, ans;
}
long long to_ll() const
{
long long ans = 0, base = 1;
for (usize i = 0; i < d.size(); i++, base *= bucket_value) { ans += base * d[i]; }
return sign ? ans : -ans;
}
std::string to_string() const
{
if (d.empty()) { return "0"; }
std::string ans;
if (sign == false) { ans.push_back('-'); }
const usize N = d.size();
for (usize i = 0; i < N; i++) {
if (i == 0) {
ans += std::to_string(d[N - i - 1]);
} else {
usize nz = 0;
for (bucket_type U = 1; d[N - i - 1] >= U; nz++, U *= bucket_type(10)) {}
for (usize i = 0; i + nz < bucket_digits; i++) { ans.push_back('0'); }
if (d[N - i - 1] != 0LL) { ans += std::to_string(d[N - i - 1]); }
}
}
return ans;
}
private:
friend bigint small_multiply(const bigint& m, bucket_type n) // [TODO] karatsuba
{
const bool s = n < 0 ? not m.sign : m.sign;
n = n < 0 ? -n : n;
assert(n < bucket_value);
std::vector<bucket_type> ans(m.d.size());
for (usize i = 0; i < m.d.size(); i++) { ans[i] = m.d[i] * n; }
return bigint{s, ans};
}
friend int comp(const bigint& m, const bigint& n)
{
if (m.sign != n.sign) {
return m.sign ? 1 : -1;
} else {
return m.sign ? abs_comp(m, n) : -abs_comp(m, n);
}
}
static usize log10p1(const bucket_type n)
{
usize ans = 0;
for (bucket_type base = 1; base <= n; base *= static_cast<bucket_type>(10), ans++) {}
return ans;
}
friend int abs_comp(const bigint& m, const bigint& n) // m<n:-1 m=n:0 m>n:1
{
if (m.d.size() != n.d.size()) {
return m.d.size() < n.d.size() ? -1 : 1;
} else {
for (usize i = 0; i < m.d.size(); i++) {
const auto m_back = m.d[m.d.size() - i - 1], n_back = n.d[n.d.size() - i - 1];
if (m_back != n_back) { return m_back < n_back ? -1 : 1; }
}
}
return 0;
}
void normalize()
{
for (usize i = 0; i < d.size(); i++) {
if (d[i] >= bucket_value) {
if (i + 1 == d.size()) {
d.push_back(d[i] / bucket_value);
} else {
d[i + 1] += d[i] / bucket_value;
}
d[i] %= bucket_value;
} else if (d[i] < 0) {
assert(i + 1 != d.size());
while (d[i] < 0) { d[i + 1]--, d[i] += bucket_value; }
}
}
for (; not d.empty() and d.back() == 0; d.pop_back()) {}
}
bool sign = true;
std::vector<bucket_type> d;
};
int main()
{
const auto N = in<bigint<>>();
auto pow = mfp([&](auto&& self, const bigint<>& x, const bigint<>& n) -> bigint<> {
if (n == 0) { return 1; }
if (n % 2 == 1) {
return self(self, x, n - 1) * x % N;
} else {
return self(self, x * x % N, n / 2);
}
});
if (N % 2 == 0) { return outel('!', N / 2, 2); }
for (bigint a = 2; a * a <= N; a++) {
if (N % a == 0) { return outel('!', N / a, a); }
outel('?', a);
const auto p = in<bigint<>>();
if (p % 2 == 1) { continue; }
const auto b = pow(a, p / 2) + 1;
if (b == N) { continue; }
const auto g = gcd(N, b);
if (g != 1) { return outel('!', N / g, g); }
}
return 0;
}