結果
| 問題 | No.984 Inversion |
| ユーザー |
 Pachicobue
|
| 提出日時 | 2020-02-12 22:30:07 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
MLE
|
| 実行時間 | - |
| コード長 | 21,689 bytes |
| コンパイル時間 | 2,658 ms |
| コンパイル使用メモリ | 217,900 KB |
| 最終ジャッジ日時 | 2025-01-08 23:48:04 |
|
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 * 1 MLE * 1 |
| other | TLE * 16 MLE * 8 |
ソースコード
#include <bits/stdc++.h>
// created [2020/02/11] 13:40:33
#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 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<usize lg>
class wavelet_matrix
{
public:
using value_type = u64;
template<typename InIt>
wavelet_matrix(const InIt first, const InIt last) : sz{static_cast<usize>(std::distance(first, last))}
{
for (usize i = 0; i < lg; i++) { zero[i] = 0, table[i] = fid(sz); }
std::vector<value_type> v{first, last};
std::vector<value_type> z(sz), o(sz);
usize zn = 0, on = 0;
for (usize d = 0; d < lg; d++) {
zn = 0, on = 0;
for (usize i = 0; i < sz; i++) {
const bool b = btest(v[i], lg - d - 1);
table[d].set(i, b), (b ? o[on++] : z[zn++]) = v[i];
}
table[d].build(), zero[d] = zn, std::swap(v, z);
for (usize i = 0; i < on; i++) { v[zn + i] = o[i]; }
}
}
usize less_than(usize l, usize r, const value_type v) const
{
assert(l <= r);
usize ans = 0;
for (usize i = 0; i < lg; i++) {
const usize zl = table[i].zero(l), zr = table[i].zero(r), z = zero[i];
if (btest(v, lg - i - 1)) {
ans += zr - zl, l += z - zl, r += z - zr;
} else {
l = zl, r = zr;
}
}
return ans;
}
usize range_freq(const usize l, const usize r, const value_type vmin, const value_type vsup) const { return less_than(l, r, vsup) - less_than(l, r, vmin); }
value_type quantile(usize l, usize r, usize n) const
{
assert(l <= r), assert(r - l > n);
value_type ans = 0;
for (usize i = 0; i < lg; i++) {
const usize zl = table[i].zero(l), zr = table[i].zero(r), z = zero[i];
if (n >= zr - zl) {
ans += value_type(1) << (lg - i - 1), l += z - zl, r += z - zr, n -= (zr - zl);
} else {
l = zl, r = zr;
}
}
return ans;
}
private:
static constexpr usize bucket_size = sizeof(value_type) * 8;
static constexpr usize bslog = log2p1(bucket_size) - 1;
static constexpr usize wind(const usize n) { return n >> (bslog); }
static constexpr usize bind(const usize n) { return bcut(n, bslog); }
class fid
{
private:
usize sz, bn;
std::vector<value_type> data;
std::vector<usize> large;
public:
fid() : sz{0} {}
fid(const usize b) : sz{b}, bn{wind(sz) + 2}, data(bn, 0), large(bn, 0) {}
void build()
{
for (usize i = 1; i < large.size(); i++) { large[i] = large[i - 1] + popcount(data[i - 1]); }
}
bool operator[](const usize n) const { return btest(data[wind(n)], bind(n)); }
void set(const usize n, const bool b) { bset(data[wind(n)], bind(n), b); }
usize one(const usize n) const { return large[wind(n)] + popcount(bcut(data[wind(n)], bind(n))); }
usize zero(const usize n) const { return n - one(n); }
};
const usize sz;
std::array<usize, lg> zero;
std::array<fid, lg> table;
};
template<typename MonoidAct>
class lazyseg
{
public:
using monoid_act_type = MonoidAct;
using value_monoid_type = typename monoid_act_type::value_monoid_type;
using operator_monoid_type = typename monoid_act_type::operator_monoid_type;
using value_type = typename value_monoid_type::value_type;
using operator_type = typename operator_monoid_type::operator_type;
lazyseg(const usize sz, const value_type initial = value_monoid_type::id()) : sz{sz}, depth{clog(sz)}, half{static_cast<usize>(1) << depth}, val(half << 1, value_monoid_type::id()), op(half << 1, operator_monoid_type::id())
{
if (initial != value_monoid_type::id()) {
std::fill(val.begin() + half, val.end(), initial);
for (usize i = half - 1; i >= 1; i--) { up(i); }
}
}
template<typename InIt>
lazyseg(const InIt first, const InIt last) : sz{static_cast<usize>(std::distance(first, last))}, depth{clog(sz)}, half{static_cast<usize>(1) << depth}, val(half << 1, value_monoid_type::id()), op(half << 1, operator_monoid_type::id())
{
std::copy(first, last, val.begin() + half);
for (usize i = half - 1; i >= 1; i--) { up(i); }
}
value_type get(const usize a) { return assert(a < sz), fold(a, a + 1); }
void set(usize a, const value_type& v)
{
assert(a < sz);
top_down(a += half), top_down(a + 1), op[a] = operator_monoid_type::id(), val[a] = v;
while (a >>= 1) { up(a); }
}
value_type fold(usize l, usize r)
{
assert(l < r), assert(r <= sz);
top_down(l += half), top_down(r += half);
value_type accl = value_monoid_type::id(), accr = value_monoid_type::id();
for (; l < r; l >>= 1, r >>= 1) {
if (l & 1) { accl = value_monoid_type::merge(accl, val[l++]); }
if (r & 1) { accr = value_monoid_type::merge(val[--r], accr); }
}
return value_monoid_type::merge(accl, accr);
}
void act(usize l, usize r, const operator_type& f)
{
assert(l < r), assert(r <= sz);
const usize lin = l + half, rin = r + half;
top_down(l += half), top_down(r += half);
for (usize ls = 1, rs = 1; l < r; l >>= 1, r >>= 1, ls <<= 1, rs <<= 1) {
if (l & 1) { update(l++, f, ls); }
if (r & 1) { update(--r, f, rs); }
}
bottom_up(lin), bottom_up(rin);
}
usize size() const { return sz; }
friend std::ostream& operator<<(std::ostream& os, const lazyseg& lseg)
{
auto lseg2 = lseg;
os << "[";
for (usize i = 0; i < lseg.sz; i++) { os << lseg2.get(i) << (i + 1 == lseg2.sz ? "" : ","); }
return (os << "]\n");
}
private:
void up(const usize i) { val[i] = value_monoid_type::merge(val[i << 1], val[i << 1 | 1]); }
void update(const usize a, const operator_type& f, const usize l) { op[a] = operator_monoid_type::compose(f, op[a]), val[a] = monoid_act_type::apply(f, val[a], l); }
void down(const usize a, const usize l) { update(a << 1, op[a], l >> 1), update(a << 1 | 1, op[a], l >> 1), op[a] = operator_monoid_type::id(); }
void top_down(const usize a)
{
const usize b = (a / (a & -a)) >> 1;
for (usize i = 0, l = half; i < depth; i++, l >>= 1) {
const usize v = a >> (depth - i);
if (v > b) { break; }
down(v, l);
}
}
void bottom_up(usize a)
{
a = (a / (a & -a)) >> 1;
for (; a >= 1; a >>= 1) { up(a); }
}
const usize sz, depth, half;
std::vector<value_type> val;
std::vector<operator_type> op;
};
struct accum_sum // a_l+2*a_{l+1}+3*a_{l+2}+...+(r-l)*a_{r-1}
{
struct value_type
{
ll asum = 0;
ll sum = 0;
ll len = 0;
friend std::ostream& operator<<(std::ostream& os, const value_type& v)
{
os << "[asum=" << v.asum << ",sum=" << v.sum << "]";
return os;
}
};
accum_sum() = delete;
static value_type merge(const value_type& a, const value_type& b)
{
value_type ans;
ans.len = a.len + b.len;
ans.sum = a.sum + b.sum;
ans.asum = a.asum + b.asum + b.sum * a.len;
return ans;
}
static value_type id() { return value_type{}; }
};
struct plus
{
using operator_type = ll;
plus() = delete;
static operator_type compose(const operator_type& a, const operator_type& b) { return a + b; }
static constexpr operator_type id() { return operator_type{}; }
};
struct mact
{
using value_monoid_type = accum_sum;
using operator_monoid_type = plus;
using value_type = typename value_monoid_type::value_type;
using operator_type = typename operator_monoid_type::operator_type;
mact() = delete;
static value_type apply(const operator_type& f, const value_type& x, const usize)
{
value_type ans;
ans.len = x.len;
ans.sum = x.sum + f * x.len;
ans.asum = x.asum + f * x.len * (x.len + 1) / 2;
return ans;
}
};
int main()
{
const auto P = in<uint>();
using mint = dynamic_modint<0>;
mint::set_mod(P);
auto N = in<ll>();
if (N == 1) { return outln(0); }
bool inv = false;
if (N * N < P) {
inv = true;
N = (mint(1) / N)();
}
std::vector<ll> bs;
for (ll i = 0, q = 1; i < P; q++) {
bs.push_back(i * N % P);
i = (P * q - 1) / N + 1;
}
wavelet_matrix<33> wm(bs.begin(), bs.end());
const ll L = P / N + 1; // 0-N-2N-...-(L-1)N
std::vector<accum_sum::value_type> vs(L);
for (int i = 0; i < L; i++) { vs[i] = {0, 0, 1}; }
lazyseg<mact> seg(vs.begin(), vs.end());
ll ans = 0;
for (int i = 0; i < bs.size(); i++) {
SHOW(seg);
const ll b = bs[i];
const ll l = (P - b - 1) / N + 1;
SHOW(i, b, l);
ll plus = seg.fold(0, L).asum + (l >= L ? 0LL : seg.fold(l, L).asum);
SHOW(plus);
plus -= wm.less_than(0, i, bs[i]) * l;
ans += plus;
seg.act(0, l, 1LL);
}
if (inv) { ans = P * (P - 1) / 2 - ans; }
outln(ans % 2);
return 0;
}