結果
| 問題 | No.2654 [Cherry 6th Tune] Re: start! (Black Sheep) |
| コンテスト | |
| ユーザー |
 miscalc
|
| 提出日時 | 2026-10-08 19:15:27 |
| 言語 | C++23 (gcc 15.3.0 + boost 1.92.0 + ACL) |
| 結果 |
AC
不安定
|
| 実行時間 | 222 ms / 7,000 ms |
| + 900µs | |
| コード長 | 60,435 bytes |
| 記録 | |
| コンパイル時間 | 3,518 ms |
| コンパイル使用メモリ | 378,292 KB |
| 実行使用メモリ | 25,140 KB |
| 最終ジャッジ日時 | 2026-10-08 19:15:49 |
| 合計ジャッジ時間 | 13,477 ms |
|
ジャッジサーバーID （参考情報） |
judge2_0 / judge4_0 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 40 |
ソースコード
#define SINGLE_TESTCASE
// #define MULTI_TESTCASE
// #define AOJ_TESTCASE
#define FAST_IO
// #define FAST_CIO
// #define INTERACTIVE
#define INF 4'000'000'000'000'000'037LL
#define EPS 1e-11
// https://github.com/miscalculation53/library/tree/wip/template/template_all.hpp
// https://github.com/miscalculation53/library/tree/wip/template/template_all_but_modint.hpp
// https://github.com/miscalculation53/library/tree/wip/template/template_types.hpp
#include <bits/stdc++.h>
using namespace std;
using ld = decltype(EPS);
using ll = long long;
using uint = unsigned int;
using ull = unsigned long long;
using pll = pair<ll, ll>;
using tlll = tuple<ll, ll, ll>;
using tllll = tuple<ll, ll, ll, ll>;
#define vc vector
template <class T>
using vvc = vc<vc<T>>;
template <class T>
using vvvc = vc<vc<vc<T>>>;
using vb = vc<bool>;
using vl = vc<ll>;
using vpll = vc<pll>;
using vtlll = vc<tlll>;
using vtllll = vc<tllll>;
using vstr = vc<string>;
using vvb = vvc<bool>;
using vvl = vvc<ll>;
template <class T>
using pql = priority_queue<T, vc<T>, greater<T>>;
template <class T>
using pqg = priority_queue<T>;
using i128 = __int128_t;
using u128 = __uint128_t;
i128 stoi128(const string &s)
{
const bool neg = s.front() == '-';
u128 res = 0;
for (int i = neg; i < (int)s.size(); i++)
res = 10 * res + s[i] - '0';
if (neg)
return -i128(res - 1) - 1;
return i128(res);
}
string i128tos(i128 x)
{
if (x == 0) return "0";
string sign = "", res = "";
u128 ux;
if (x < 0)
ux = u128(-(x + 1)) + 1, sign = "-";
else
ux = x;
while (ux > 0)
{
res += '0' + ux % 10;
ux /= 10;
}
reverse(res.begin(), res.end());
return sign + res;
}
istream &operator>>(istream &is, i128 &a)
{
string s;
is >> s;
a = stoi128(s);
return is;
}
ostream &operator<<(ostream &os, const i128 &a)
{
os << i128tos(a);
return os;
}
#define cauto const auto
// https://github.com/miscalculation53/library/tree/wip/template/template_rep.hpp
#define overload4(_1,_2,_3,_4,name,...) name
#define rep1(i,n) for (ll i = 0, nnnnn = ll(n); i < nnnnn; i++)
#define rep2(i,l,r) for (ll i = ll(l), rrrrr = ll(r); i < rrrrr; i++)
#define rep3(i,l,r,d) for (ll i = ll(l), rrrrr = ll(r), ddddd = ll(d); ddddd > 0 ? i < rrrrr : i > rrrrr; i += d)
#define rep(...) overload4(__VA_ARGS__, rep3, rep2, rep1)(__VA_ARGS__)
#define repi1(i,n) for (int i = 0, nnnnn = int(n); i < nnnnn; i++)
#define repi2(i,l,r) for (int i = int(l), rrrrr = int(r); i < rrrrr; i++)
#define repi3(i,l,r,d) for (int i = int(l), rrrrr = int(r), ddddd = int(d); ddddd > 0 ? i < rrrrr : i > rrrrr; i += d)
#define repi(...) overload4(__VA_ARGS__, repi3, repi2, repi1)(__VA_ARGS__)
#define fe(...) for (auto __VA_ARGS__)
#define fec(...) for (cauto &__VA_ARGS__)
#define fem(...) for (auto &__VA_ARGS__)
// https://github.com/miscalculation53/library/tree/wip/template/template_math.hpp
// https://github.com/miscalculation53/library/tree/wip/utils/is_integral_ext.hpp
template <class T>
constexpr bool is_integral_ext = is_integral_v<T> || is_same_v<T, i128> || is_same_v<T, u128>;
template <class T>
constexpr bool is_signed_ext = is_signed_v<T> || is_same_v<T, i128>;
template <class T>
constexpr bool is_unsigned_ext = is_unsigned_v<T> || is_same_v<T, u128>;
// https://github.com/miscalculation53/library/tree/wip/utils/default_infty.hpp
namespace default_infty_detail
{
template <class T, class = void>
struct has_infty : false_type {};
template <class T>
struct has_infty<T, void_t<decltype(T::infty())>> : true_type {};
template <class T>
inline constexpr bool unsupported = false;
}
template <class T, class U>
inline bool chmin(T &a, U b) { return a > b ? a = b, true : false; }
template <class T, class U>
inline bool chmax(T &a, U b) { return a < b ? a = b, true : false; }
template <class T = ll, class U, class V, typename = enable_if_t<is_integral_ext<U> && is_integral_ext<V>>>
inline constexpr T divfloor(U a, V b) { return T(a) / T(b) - (T(a) % T(b) && (T(a) ^ T(b)) < 0); }
template <class T = ll, class U, class V, typename = enable_if_t<is_integral_ext<U> && is_integral_ext<V>>>
inline constexpr T safemod(U a, V b) { return T(a) - T(b) * divfloor<T>(a, b); }
// https://github.com/miscalculation53/library/tree/wip/template/template_vector.hpp
#define ALL(a) (a).begin(), (a).end()
template <class T = ll, class V>
inline T SZ(const V &x) { return x.size(); }
#define eb emplace_back
#define LMD(x,fx) ([&](const auto &x) { return fx; })
#define GEN_VEC(n,i,fi) (gen_vec(n, LMD(i, fi)))
template <class T, class... Ts>
vc<T> concat(vc<T> v, const vc<Ts> &...vs)
{
(v.insert(v.end(), ALL(vs)), ...);
return v;
}
// https://github.com/miscalculation53/library/tree/wip/template/template_algo.hpp
// https://github.com/miscalculation53/library/tree/wip/utils/resolved_infty.hpp
// https://github.com/miscalculation53/library/tree/wip/utils/resolved_value.hpp
template <class V>
auto MAX(const V &v) { return *max_element(ALL(v)); }
template <class T>
vc<T> perminv(const vc<T> &p)
{
if (p.empty())
return {};
const int n = p.size();
vc<T> q(MAX(p) + 1);
repi(i, n) if (p[i] >= 0) q[p[i]] = i;
return q;
}
template <class V>
V reversed(const V &v) { return V(v.rbegin(), v.rend()); }
template <class T>
vvc<T> top(const vvc<T> &a)
{
if (a.empty())
return {};
const int n = a.size(), m = a[0].size();
vvc<T> b(m, vc<T>(n));
repi(i, n)
{
assert(SZ<int>(a[i]) == m);
repi(j, m) b[j][i] = a[i][j];
}
return b;
}
vstr top(const vstr &a)
{
vvc<char> a_(a.size());
repi(i, SZ<int>(a)) a_[i] = {ALL(a[i])};
vvc<char> b_ = top(a_);
vstr b(b_.size());
repi(i, SZ<int>(b)) b[i] = {ALL(b_[i])};
return b;
}
template <class T, class = void>
struct has_e0 : false_type {};
template <class T>
struct has_e0<T, void_t<decltype(T::e0())>> : true_type {};
template <class T>
inline constexpr bool has_e0_v = has_e0<T>::value;
template <class T>
struct MonoidAdd
{
using S = T;
static constexpr S op(S a, S b) { return a + b; }
static constexpr S e()
{
if constexpr (has_e0_v<S>)
return S::e0();
else
return {};
}
};
template <class T, auto infty = nullptr>
struct MonoidMin
{
using S = T;
};
template <class T, auto infty = nullptr>
struct MonoidMax
{
using S = T;
};
namespace internal
{
template <class M, class I, class = void>
struct HasMonoidPow : false_type
{
};
template <class M, class I>
struct HasMonoidPow<M, I, void_t<decltype(M::pow(declval<const typename M::S &>(), declval<I>()))>> : true_type
{
};
}
template <class M>
vc<typename M::S> cuml(const vc<typename M::S> &v, int left_index = 0)
{
const int n = v.size();
vc<typename M::S> res(n + 1);
res[0] = M::e();
repi(i, n) res[i + 1] = M::op(res[i], v[i]);
res.erase(res.begin(), res.begin() + left_index);
return res;
}
template <class T>
vc<T> cumlsum(const vc<T> &v, int left_index = 0)
{ return cuml<MonoidAdd<T>>(v, left_index); }
constexpr array<pll, 4> DRULgrid = {{{1, 0}, {0, 1}, {-1, 0}, {0, -1}}};
constexpr array<pll, 4> DRULplane = {{{0, -1}, {1, 0}, {0, 1}, {-1, 0}}};
// https://github.com/miscalculation53/library/tree/wip/template/template_binsearch.hpp
template <class T>
struct is_random_access_iterator
{
static constexpr bool value = is_same_v<
typename iterator_traits<T>::iterator_category,
random_access_iterator_tag
>;
};
template <class T>
constexpr bool is_random_access_iterator_v = is_random_access_iterator<T>::value;
#define DEFAULT_COMP ranges::less
namespace internal
{
};
// https://github.com/miscalculation53/library/tree/wip/template/template_bit.hpp
template <class T>
inline constexpr ull MASK(T k) { return (1ULL << k) - 1ULL; }
inline constexpr ll bit_width(ll x) { return std::bit_width((ull)x); }
inline constexpr ll bit_floor(ll x) { return std::bit_floor((ull)x); }
inline constexpr ll bit_ceil(ll x) { return std::bit_ceil((ull)x); }
inline constexpr ll countr_zero(ll x) { assert(x != 0); return std::countr_zero((ull)x); }
inline constexpr ll popcount(ll x) { return std::popcount((ull)x); }
inline constexpr bool has_single_bit(ll x) { return std::has_single_bit((ull)x); }
inline constexpr ull lsb_pos(ull x) { assert(x != 0); return countr_zero(x); }
inline constexpr ull msb_pos(ull x) { assert(x != 0); return bit_width(x) - 1; }
inline constexpr ull lsb_mask(ull x) { assert(x != 0); return x & -x; }
inline constexpr ull msb_mask(ull x) { assert(x != 0); return bit_floor(x); }
inline constexpr bool btest(ull x, uint k) { return (x >> k) & 1; }
inline constexpr bool bsubset(ull x, ull y) { return (x & y) == x; }
inline constexpr bool bsupset(ull x, ull y) { return (x & y) == y; }
inline constexpr ull bsetminus(ull x, ull y) { return x & ~y; }
// https://github.com/miscalculation53/library/tree/wip/template/template_inout.hpp
// https://github.com/miscalculation53/library/tree/wip/template/template_dump.hpp
// https://github.com/miscalculation53/library/tree/wip/template/template_dump_map.hpp
#define CPP_DUMP_DEFINE_DATA(...)
#define dump(...) ((void)0)
#define local(...)
#define oj(...) __VA_ARGS__
#define local_oj(a,b) (b)
namespace fastio {
template <class T>
struct unsigned_integer
{
using type = make_unsigned_t<T>;
};
template <>
struct unsigned_integer<i128>
{
using type = u128;
};
template <>
struct unsigned_integer<u128>
{
using type = u128;
};
template <class T>
using unsigned_integer_t = typename unsigned_integer<T>::type;
static constexpr uint32_t SIZ = 1 << 17;
char ibuf[SIZ];
char obuf[SIZ];
char out[100];
uint32_t pil = 0, pir = 0, por = 0;
struct Pre {
char num[10000][4];
constexpr Pre() : num() {
for (int i = 0; i < 10000; i++) {
int n = i;
for (int j = 3; j >= 0; j--) {
num[i][j] = n % 10 | '0';
n /= 10;
}
}
}
} constexpr pre;
inline void load() {
memcpy(ibuf, ibuf + pil, pir - pil);
pir = pir - pil + fread(ibuf + pir - pil, 1, SIZ - pir + pil, stdin);
pil = 0;
if (pir < SIZ) ibuf[pir++] = '\n';
}
inline void flush() {
fwrite(obuf, 1, por, stdout);
por = 0;
}
void rd1(char &c) {
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (c <= ' ');
}
void rd1(string &x) {
x.clear();
while (true) {
if (pil == pir) load();
while (pil < pir && ibuf[pil] <= ' ') ++pil;
if (pil < pir) break;
}
while (true) {
uint32_t p = pil;
while (pil < pir && ibuf[pil] > ' ') ++pil;
x.append(ibuf + p, pil - p);
if (pil < pir) {
++pil;
return;
}
load();
}
}
template <typename T>
void rd1_real(T &x) {
string s;
rd1(s);
if constexpr (!is_same_v<T, long double>)
{
auto [p, ec] = from_chars(s.data(), s.data() + s.size(), x);
if (ec == errc{} && p == s.data() + s.size()) return;
}
if constexpr (is_same_v<T, long double>)
x = stold(s);
else
x = stod(s);
}
template <bool check_buffer = true, typename T>
void rd1_integer(T &x) {
using U = unsigned_integer_t<T>;
bool minus = false;
U val = 0;
if constexpr (check_buffer)
if (pil + 100 > pir) load();
uint32_t p = pil;
while (ibuf[p] < '-') ++p;
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (ibuf[p] == '-') minus = true, ++p;
}
while ('0' <= ibuf[p]) val = val * 10 + (ibuf[p++] & 15);
pil = p;
if constexpr (is_signed<T>::value || is_same_v<T, i128>)
{
if (minus)
{
const U min_abs = U(numeric_limits<T>::max()) + 1;
x = val == min_abs ? numeric_limits<T>::lowest() : -T(val);
}
else x = T(val);
}
else
x = T(val);
}
void rd1(int &x) { rd1_integer(x); }
void rd1(ll &x) { rd1_integer(x); }
void rd1(i128 &x) { rd1_integer(x); }
void rd1(uint &x) { rd1_integer(x); }
void rd1(ull &x) { rd1_integer(x); }
void rd1(u128 &x) { rd1_integer(x); }
void rd1(double &x) { rd1_real(x); }
void rd1(long double &x) { rd1_real(x); }
template <class T, class U>
void rd1(pair<T, U> &p) {
return rd1(p.first), rd1(p.second);
}
template <class T>
void rd1(vc<T> &x) {
for (auto &d: x) rd1(d);
}
template <class... T>
void read(T &...x) {
if constexpr (sizeof...(T) <= SIZ / 100 &&
((!is_same_v<T, char> &&
(is_integral_v<T> || is_same_v<T, i128> || is_same_v<T, u128>)) && ...)) {
if (pil + 100 * sizeof...(T) > pir) load();
(rd1_integer<false>(x), ...);
}
else
(rd1(x), ...);
}
void wt1(const char c) {
if (por == SIZ) flush();
obuf[por++] = c;
}
void wt1(string_view s) {
while (!s.empty()) {
if (por == SIZ) flush();
size_t n = min<size_t>(s.size(), SIZ - por);
memcpy(obuf + por, s.data(), n);
por += n;
s.remove_prefix(n);
}
}
template <typename T>
void wt1_integer(T x) {
if (por > SIZ - 100) flush();
using U = unsigned_integer_t<T>;
U ux;
if constexpr (is_signed<T>::value || is_same_v<T, i128>)
{
if (x < 0)
obuf[por++] = '-', ux = U(0) - U(x);
else
ux = U(x);
}
else
ux = x;
int outi;
for (outi = 96; ux >= 10000; outi -= 4) {
memcpy(out + outi, pre.num[ux % 10000], 4);
ux /= 10000;
}
if (ux >= 1000) {
memcpy(obuf + por, pre.num[ux], 4);
por += 4;
} else if (ux >= 100) {
memcpy(obuf + por, pre.num[ux] + 1, 3);
por += 3;
} else if (ux >= 10) {
int q = (ux * 103) >> 10;
obuf[por] = q | '0';
obuf[por + 1] = (ux - q * 10) | '0';
por += 2;
} else
obuf[por++] = ux | '0';
memcpy(obuf + por, out + outi + 4, 96 - outi);
por += 96 - outi;
}
template <typename T>
void wt1_real(T x) {
if constexpr (!is_same_v<T, long double>)
{
auto [p, ec] = to_chars(out, out + sizeof(out), x, chars_format::fixed, 15);
if (ec == errc{}) {
wt1(string_view(out, p));
return;
}
}
ostringstream oss;
oss << fixed << setprecision(15) << x;
wt1(oss.str());
}
void wt1(int x) { wt1_integer(x); }
template <class T, enable_if_t<is_integral_v<T>, int> = 0>
void wt1(T x) { wt1_integer(x); }
void wt1(i128 x) { wt1_integer(x); }
void wt1(u128 x) { wt1_integer(x); }
void wt1(double x) { wt1_real(x); }
void wt1(long double x) { wt1_real(x); }
template <class T, class U>
void wt1(const pair<T, U> &val);
template <class... T>
void wt1(const tuple<T...> &tpl);
template <class T, size_t S>
void wt1(const array<T, S> &val);
template <class T>
void wt1(const vector<T> &val);
template <class... T>
void write(T &&...x) {
(wt1(std::forward<T>(x)), ...);
}
template <class... T>
void print(T &&...x) {
if constexpr (sizeof...(T))
{
int i = 0;
((i++ ? wt1(' ') : void(), wt1(std::forward<T>(x))), ...);
}
wt1('\n');
}
}
struct Dummy {
Dummy() { atexit(fastio::flush); }
} dummy;
namespace internal
{
template <class... Ts>
void READnodump(Ts &...a) { fastio::read(a...); }
template <class... T>
void READVECnodump(int n, vc<T> &...v)
{
(v.resize(n), ...);
READnodump(v...);
}
};
#define READ(...) internal::READnodump(__VA_ARGS__); dump(__VA_ARGS__)
#define IN(T,...) T __VA_ARGS__; READ(__VA_ARGS__)
#define CHAR(...) IN(char, __VA_ARGS__)
#define INT(...) IN(int, __VA_ARGS__)
#define LL(...) IN(ll, __VA_ARGS__)
#define STR(...) IN(string, __VA_ARGS__)
#define ARR(T,n,...) array<T, n> __VA_ARGS__; READ(__VA_ARGS__)
#define READVEC(...) internal::READVECnodump(__VA_ARGS__); dump(__VA_ARGS__)
#define READVEC2(...) internal::READVEC2nodump(__VA_ARGS__); dump(__VA_ARGS__)
#define VEC(T,n,...) vc<T> __VA_ARGS__; READVEC(n, __VA_ARGS__)
#define VEC2(T,n,m,...) vvc<T> __VA_ARGS__; READVEC2(n, m, __VA_ARGS__)
#define READJAG(...) internal::READJAGnodump(__VA_ARGS__); dump(__VA_ARGS__)
#define JAG(T,n,...) vvc<T> __VA_ARGS__; READJAG(n, __VA_ARGS__)
#define ENDL '\n'
#define WRITE fastio::write
#define PRINT fastio::print
#define PRINTEXIT(...) do { PRINT(__VA_ARGS__); exit(0); } while (false)
#define PRINTRETURN(...) do { PRINT(__VA_ARGS__); return; } while (false)
template <class T>
void PRINTV(const vc<T> &v) { for (auto &vi : v) PRINT(vi); }
#define PRINTVEXIT(...) do { PRINTV(__VA_ARGS__); exit(0); } while (false)
#define PRINTVRETURN(...) do { PRINTV(__VA_ARGS__); return; } while (false)
namespace internal
{
};
namespace internal
{
};
namespace internal
{
};
#define UNZIP(vt,...) auto [__VA_ARGS__] = unzip(vt)
#define ZIP(vt,...) auto vt = internal::zip_vectors(__VA_ARGS__)
// https://github.com/miscalculation53/library/tree/wip/template/template_random.hpp
mt19937_64 mt;
bool randbool(double p)
{
assert(0 <= p && p <= 1);
return bernoulli_distribution(p)(mt);
}
namespace internal
{
};
// https://github.com/miscalculation53/library/tree/wip/math/modint/template_modint.hpp
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint.hpp
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_static.hpp
// https://github.com/miscalculation53/library/tree/wip/utils/larger_int.hpp
namespace larger_int_detail
{
}
template <class T>
struct larger_int
{
private:
static constexpr bool check();
static_assert(check());
public:
using type = T;
};
#define LARGER_INT(T,U) template <> struct larger_int<T> { using type = U; };
LARGER_INT(signed char, short)
LARGER_INT(short, int)
LARGER_INT(int, long long)
LARGER_INT(long, __int128_t)
LARGER_INT(long long, __int128_t)
LARGER_INT(unsigned char, unsigned short)
LARGER_INT(unsigned short, unsigned int)
LARGER_INT(unsigned int, unsigned long long)
LARGER_INT(unsigned long, __uint128_t)
LARGER_INT(unsigned long long, __uint128_t)
#undef LARGER_INT
template <class T>
struct Rational;
template <class T>
struct larger_int<Rational<T>>
{
using type = Rational<typename larger_int<T>::type>;
};
template <class T>
using larger_int_t = typename larger_int<T>::type;
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_isprime.hpp
namespace internal
{
template <class T>
constexpr ll powmod_constexpr(ll x, ll n, T m)
{
if (m == 1)
return 0;
using U = make_unsigned_t<T>;
using L = larger_int_t<U>;
U r = 1, y = safemod(x, m);
while (n)
{
if (n & 1)
r = L(r) * y % m;
y = L(y) * y % m;
n >>= 1;
}
return r;
}
template <auto n>
constexpr bool isprime = isprime_constexpr(n);
};
namespace internal
{
template <auto M>
struct policy_static
{
using mod_type = decltype(M);
using value_type = make_unsigned_t<mod_type>;
using calc_type = conditional_t<(M <= UINT_MAX), ull, larger_int_t<value_type>>;
static constexpr bool is_prime = isprime_constexpr(M);
static constexpr value_type init(value_type v) { return v; }
static constexpr mod_type val(value_type v);
};
};
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_barrett32.hpp
namespace internal
{
struct barrett32
{
uint m = 0;
ull im = 0;
barrett32() = default;
explicit barrett32(uint m) : m(m), im((ull)(-1) / m + 1) {}
uint umod() const { return m; }
uint mul(uint a, uint b) const
{
ull z = a;
z *= b;
ull x = ull((u128(z) * im) >> 64);
ull y = x * m;
return uint(z - y + (z < y ? m : 0));
}
};
template <int id>
struct policy_barrett32
{
using value_type = uint;
using calc_type = ull;
using mod_type = int;
static constexpr bool is_prime = false;
static inline barrett32 reducer{};
static value_type init(value_type v) { return v; }
static mod_type val(value_type v);
};
};
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_montgomery64.hpp
namespace internal
{
inline constexpr ull inv64(ull a)
{
ull x = a;
while (a * x != 1) x *= 2 - a * x;
return x;
}
struct montgomery64odd
{
ull m = 0, im = 0, sq = 0;
montgomery64odd() = default;
explicit montgomery64odd(ull m) : m(m), im(inv64(m)), sq(-u128(m) % m) {}
ull umod() const { return m; }
ull reduce(u128 x) const
{
auto t = (x + u128(m) * (-im * ull(x))) >> 64;
if (t >= m) t -= m;
return (ull)t;
}
ull inv_reduce(i128 v) const { return reduce(u128(v % m + m) * sq); }
};
struct montgomery64
{
ull m = 0, mx = 0, imx = 0, d = 0, q = 0;
uint b = 0;
montgomery64() = default;
explicit montgomery64(ull m) : m(m)
{
b = countr_zero(m), mx = m >> b;
imx = inv64(mx);
d = powmod_constexpr((mx + 1) / 2, b, mx);
u128 sq = -u128(mx) % mx;
q = (1 + (((sq - 1) * d) << b)) % m;
}
ull umod() const { return m; }
ull reduce(u128 x) const
{
if (b == 0)
{
auto t = (x + u128(mx) * (-imx * ull(x))) >> 64;
if (t >= m) t -= m;
return (ull)t;
}
ull p = x & MASK(b);
x = (x >> b) + p * d;
ull y = p << (64 - b);
auto t = (x + u128(mx) * (imx * (y - ull(x)))) >> (64 - b);
if (t >= m) { t -= m; if (t >= m) t -= m; }
return (ull)t;
}
ull inv_reduce(i128 v) const { return reduce(u128(v % m + m) * q); }
};
template <int id>
struct policy_montgomery64_odd
{
using value_type = ull;
using calc_type = u128;
using mod_type = ll;
static constexpr bool is_prime = false;
static inline montgomery64odd reducer{};
static value_type init(value_type v) { return reducer.inv_reduce(v); }
static mod_type val(value_type v);
};
template <int id>
struct policy_montgomery64
{
using value_type = ull;
using calc_type = u128;
using mod_type = ll;
static constexpr bool is_prime = false;
static inline montgomery64 reducer{};
static value_type init(value_type v) { return reducer.inv_reduce(v); }
static mod_type val(value_type v);
};
};
// https://github.com/miscalculation53/library/tree/wip/math/extgcd.hpp
namespace internal
{
template <class Policy, class PowInv = void>
struct modint_impl
{
using V = typename Policy::value_type;
using M = typename Policy::mod_type;
using mint = modint_impl;
private:
V _v;
public:
modint_impl();
template <class T, typename = enable_if_t<is_integral_ext<T>>>
modint_impl(T v);
M val() const;
friend mint operator+(const mint &lhs, const mint &rhs) { return mint(lhs) += rhs; }
friend mint operator-(const mint &lhs, const mint &rhs) { return mint(lhs) -= rhs; }
friend mint operator*(const mint &lhs, const mint &rhs) { return mint(lhs) *= rhs; }
friend mint operator/(const mint &lhs, const mint &rhs) { return mint(lhs) /= rhs; }
friend bool operator==(const mint &lhs, const mint &rhs) { return lhs._v == rhs._v; }
friend bool operator!=(const mint &lhs, const mint &rhs) { return lhs._v != rhs._v; }
friend M safe_hash_key(const mint &x) { return x.val(); }
friend void rd1(mint &x)
{
long long a;
fastio::rd1(a);
x = a;
}
friend void wt1(const mint &x)
{
fastio::wt1(x.val());
}
};
};
template <int mod>
using static_modint32 = internal::modint_impl<internal::policy_static<mod>>;
template <int id>
using dynamic_modint32 = internal::modint_impl<internal::policy_barrett32<id>>;
template <ll mod>
using static_modint64 = internal::modint_impl<internal::policy_static<mod>>;
template <int id>
using dynamic_modint64_odd = internal::modint_impl<internal::policy_montgomery64_odd<id>>;
template <int id>
using dynamic_modint64 = internal::modint_impl<internal::policy_montgomery64<id>>;
using modint998244353 = static_modint32<998244353>;
using modint1000000007 = static_modint32<1000000007>;
using modint = dynamic_modint32<-1>;
using modint61 = static_modint64<(1LL << 61) - 1>;
using modint64 = dynamic_modint64<-1>;
template <class T>
struct is_modint : std::false_type
{
};
template <class Policy, class PowInv>
struct is_modint<internal::modint_impl<Policy, PowInv>> : std::true_type
{
};
template <class T>
inline constexpr bool is_modint_v = is_modint<T>::value;
template <class T>
struct is_static_modint : false_type {};
template <int m, class PowInv>
struct is_static_modint<internal::modint_impl<internal::policy_static<m>, PowInv>> : true_type {};
template <ll m, class PowInv>
struct is_static_modint<internal::modint_impl<internal::policy_static<m>, PowInv>> : true_type {};
template <class T>
inline constexpr bool is_static_modint_v = is_static_modint<T>::value;
template <class T>
struct is_dynamic_modint : false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint32<id>> : true_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint64_odd<id>> : true_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint64<id>> : true_type {};
template <class T>
inline constexpr bool is_dynamic_modint_v = is_dynamic_modint<T>::value;
template <typename, typename = void>
struct has_mod : std::false_type
{
};
template <typename T>
struct has_mod<T, std::void_t<decltype(T::mod())>> : std::true_type
{
};
template <class mint>
struct modint_less
{
};
template <class mint>
struct modint_hash
{
};
// https://github.com/miscalculation53/library/tree/wip/math/modint/power_table.hpp
template <class mint>
struct PowerTable
{
private:
decltype(mint::mod()) mod;
mint base;
vc<mint> pw;
public:
};
// https://github.com/miscalculation53/library/tree/wip/math/modint/binomial.hpp
template <class T>
struct Binomial
{
private:
inline static decltype(T::mod()) mod;
public:
inline static vc<T> fac_, finv_, inv_;
};
// https://github.com/miscalculation53/library/tree/wip/math/modint/stom.hpp
// https://github.com/miscalculation53/library/tree/wip/math/modint/to_rational.hpp
// https://github.com/miscalculation53/library/tree/wip/math/svp2d.hpp
namespace cpp_dump
{
template <class T>
struct rat_value
{
T p, q;
friend ostream &operator<<(ostream &os, const rat_value &x)
{
os << x.p;
if (x.q != 1)
os << '/' << x.q;
return os;
}
};
struct mint_to_rat_fn
{
};
template <class T>
struct rat_object
{
T value;
};
template <class T>
inline constexpr bool rat_is_map = false;
template <class... Args>
inline constexpr bool rat_is_map<std::map<Args...>> = true;
template <class... Args>
inline constexpr bool rat_is_map<std::multimap<Args...>> = true;
template <class... Args>
inline constexpr bool rat_is_map<std::unordered_map<Args...>> = true;
template <class... Args>
inline constexpr bool rat_is_map<std::unordered_multimap<Args...>> = true;
struct rat_closure : std::ranges::range_adaptor_closure<rat_closure>
{
};
constexpr rat_closure rat()
{
return rat_closure{};
}
}
using mint = modint998244353;
// using mint = modint1000000007;
// using mint = static_modint<1000000000>;
// using mint = modint;
using bi = Binomial<mint>;
void init()
{
oj(mt.seed(random_device()()));
}
// https://github.com/miscalculation53/library/tree/wip/graph/tree/rooted_tree.hpp
struct RootedTree
{
protected:
static const int MSK = 1 << 30;
int n;
vc<int> p_head, dep, pre, post, preinv;
inline int internal_head(int v) const { return (p_head[v] & MSK) ? v : p_head[v]; }
inline int parent_of_head(int hv) const { return p_head[hv] & ~MSK; }
void build(int rt, const vc<int> &siz, vc<int> &max_chi_siz)
{
vc<int> ord(n);
{
vc<int> cnt(n + 1);
repi(i, n) cnt[siz[i]]++;
cnt = cumlsum(cnt);
repi(i, n) ord[n - 1 - (cnt[siz[i]]++)] = i;
}
{
p_head[rt] = rt | MSK, post[rt] = n;
vc<int> add(n, 1);
repi(i, 1, n)
{
int v = ord[i];
int p = p_head[v];
dep[v] = dep[p] + 1;
pre[v] = pre[p] + add[p];
add[p] += siz[v];
post[v] = pre[v] + siz[v];
if (max_chi_siz[p] == siz[v])
{
max_chi_siz[p] = 0;
p_head[v] = internal_head(p_head[v]);
}
else
p_head[v] |= MSK;
}
preinv = perminv(pre);
}
}
public:
RootedTree() {}
template <class P>
RootedTree(int n, const vc<P> &es, int rt)
: n(n), p_head(n), dep(n), pre(n), post(n), preinv(n)
{
assert(n >= 1);
assert(SZ(es) == n - 1);
assert(0 <= rt && rt < n);
vc<int> deg(n), siz(n, 1), max_chi_siz(n);
fec([ u, v ] : es)
{
deg[u]++, deg[v]++;
p_head[u] ^= v, p_head[v] ^= u;
}
deg[rt] = 0;
repi(i, n)
{
int v = i;
while (deg[v] == 1)
{
int p = p_head[v];
deg[p]--, deg[v]--, p_head[p] ^= v;
siz[p] += siz[v];
chmax(max_chi_siz[p], siz[v]);
v = p;
}
}
build(rt, siz, max_chi_siz);
}
int root() const { return preinv[0]; }
int parent(int v) const
{
assert(0 <= v && v < n);
assert(v != root());
int ph = p_head[v];
if (ph & MSK)
return ph & ~MSK;
else
return preinv[pre[v] - 1];
}
int head(int v) const
{
assert(0 <= v && v < n);
return internal_head(v);
}
int preorder(int v) const
{
assert(0 <= v && v < n);
return pre[v];
}
int postorder(int v) const
{
assert(0 <= v && v < n);
return post[v];
}
int preorder_select(int i) const
{
assert(0 <= i && i < n);
return preinv[i];
}
vc<int> path_to_root(int v) const
{
assert(0 <= v && v < n);
vc<int> res = {v};
res.reserve(dep[v] + 1);
int rt = root();
while (v != rt)
{
int p = parent(v);
res.eb(p);
v = p;
}
return res;
}
vc<int> path(int u, int v) const
{
assert(0 <= u && u < n);
assert(0 <= v && v < n);
vc<int> pu = {u}, pv = {v};
while (u != v)
{
if (dep[u] > dep[v])
{
int p = parent(u);
pu.eb(p);
u = p;
}
else
{
int p = parent(v);
pv.eb(p);
v = p;
}
}
pv.pop_back();
return concat(pu, reversed(pv));
}
const vc<int> &top_down_vertices() const { return preinv; }
vc<int> bottom_up_vertices() const { return reversed(top_down_vertices()); }
pair<string, vc<int>> dfs_ordered_vertices() const
{
string bp(2 * (n - 1), '?');
vc<int> vs(2 * (n - 1) + 1);
int rt = root();
vs[0] = rt;
repi(v, n)
{
if (v == rt)
continue;
int p = parent(v);
int in_idx = 2 * pre[v] - dep[v] - 1;
int out_idx = 2 * post[v] - dep[v] - 2;
bp[in_idx] = '(', vs[in_idx + 1] = v;
bp[out_idx] = ')', vs[out_idx + 1] = p;
}
return {bp, vs};
}
class ChildIterator;
class ChildRange;
class ChildIterator
{
private:
const RootedTree* t;
int cur;
friend class RootedTree;
friend class ChildRange;
ChildIterator(const RootedTree* t, int cur) : t(t), cur(cur) {}
public:
using iterator_category = std::input_iterator_tag;
using value_type = int;
using difference_type = std::ptrdiff_t;
using pointer = int*;
using reference = int;
int operator*() const { return t->preinv[cur]; }
void operator++() { cur = t->post[t->preinv[cur]]; }
bool operator!=(const ChildIterator& r) const { return cur != r.cur; }
bool operator==(const ChildIterator& r) const { return cur == r.cur; }
};
class ChildRange
{
private:
const RootedTree* t;
int cur, end_pos;
friend class RootedTree;
ChildRange(const RootedTree* t, int cur, int end_pos) : t(t), cur(cur), end_pos(end_pos) {}
public:
ChildIterator begin() const { return ChildIterator(t, cur); }
ChildIterator end() const { return ChildIterator(t, end_pos); }
bool empty() const { return cur == end_pos; }
vc<int> to_v() const { return vc<int>(begin(), end()); }
};
int heavy_child(int v) const
{
assert(0 <= v && v < n);
if (post[v] - pre[v] == 1)
return -1;
return preinv[pre[v] + 1];
}
ChildRange children(int v) const
{
assert(0 <= v && v < n);
return {this, pre[v] + 1, post[v]};
}
ChildRange light_children(int v) const
{
assert(0 <= v && v < n);
int cur = pre[v] + 1;
if (cur < post[v])
{
cur = post[preinv[cur]];
}
return {this, cur, post[v]};
}
pair<int, int> parent_child(int u, int v) const
{
assert(0 <= u && u < n);
assert(0 <= v && v < n);
return dep[u] < dep[v] ? pair{u, v} : pair{v, u};
}
int lca(int u, int v) const
{
assert(0 <= u && u < n);
assert(0 <= v && v < n);
while (true)
{
int hu = internal_head(u), hv = internal_head(v);
if (hu == hv)
break;
if (dep[hu] > dep[hv])
swap(u, v), swap(hu, hv);
v = parent_of_head(hv);
}
return dep[u] < dep[v] ? u : v;
}
bool is_ancestor(int u, int v) const
{
assert(0 <= u && u < n);
assert(0 <= v && v < n);
return pre[u] <= pre[v] && pre[v] < post[u];
}
int la(int v, int k) const
{
assert(0 <= v && v < n);
assert(0 <= k);
if (k > dep[v])
return -1;
while (true)
{
int hv = internal_head(v);
if (k <= dep[v] - dep[hv])
break;
k -= dep[v] - dep[hv] + 1;
v = parent_of_head(hv);
}
return preinv[pre[v] - k];
}
int jump(int u, int v, int k) const
{
assert(0 <= u && u < n);
assert(0 <= v && v < n);
assert(0 <= k);
int l = lca(u, v);
int d_ul = dep[u] - dep[l];
int d_vl = dep[v] - dep[l];
if (k > d_ul + d_vl)
return -1;
if (k <= d_ul)
return la(u, k);
return la(v, d_ul + d_vl - k);
}
pair<int, int> subtree_interval(int v, bool edge = false) const
{
return {pre[v] + edge, post[v]};
}
class PathRange
{
private:
static constexpr int capacity = 2 * numeric_limits<int>::digits;
array<tuple<int, int, bool>, capacity> intervals;
int count = 0;
friend class RootedTree;
PathRange() = default;
public:
using iterator = decltype(intervals)::const_iterator;
iterator begin() const { return intervals.begin(); }
iterator end() const { return intervals.begin() + count; }
int size() const { return count; }
bool empty() const { return count == 0; }
vc<tuple<int, int, bool>> to_v() const { return {begin(), end()}; }
};
PathRange path_query(int u, int v, bool edge = false) const
{
assert(0 <= u && u < n);
assert(0 <= v && v < n);
PathRange res;
int down_begin = PathRange::capacity;
while (true)
{
int hu = internal_head(u), hv = internal_head(v);
if (hu == hv)
break;
if (dep[hu] > dep[hv])
{
res.intervals[res.count++] = {pre[hu], pre[u] + 1, true};
u = parent_of_head(hu);
}
else
{
res.intervals[--down_begin] = {pre[hv], pre[v] + 1, false};
v = parent_of_head(hv);
}
}
if (dep[u] > dep[v])
{
int l = pre[v] + edge;
int r = pre[u] + 1;
if (l < r)
res.intervals[res.count++] = {l, r, true};
}
else
{
int l = pre[u] + edge;
int r = pre[v] + 1;
if (l < r)
res.intervals[res.count++] = {l, r, false};
}
while (down_begin < PathRange::capacity)
res.intervals[res.count++] = res.intervals[down_begin++];
return res;
}
};
// https://github.com/miscalculation53/library/tree/wip/ds/two_multisets.hpp
// https://github.com/miscalculation53/library/tree/wip/ds/priority_container/all.hpp
// https://github.com/miscalculation53/library/tree/wip/ds/priority_container/multiset.hpp
// https://github.com/miscalculation53/library/tree/wip/ds/priority_container/common.hpp
// https://github.com/miscalculation53/library/tree/wip/ds/priority_container/aggregate.hpp
// https://github.com/miscalculation53/library/tree/wip/algebra/algebra_base.hpp
template <class S_, auto op_, auto e_>
struct Monoid
{
using S = S_;
static constexpr auto op = op_;
static constexpr auto e = e_;
};
template <class S_, auto op_, auto e_, auto inv_>
struct Group
{
using S = S_;
static constexpr auto op = op_;
static constexpr auto e = e_;
static constexpr auto inv = inv_;
};
template <class S_, auto add_, auto e0_, auto mul_, auto e1_>
struct SemiRing
{
using S = S_;
static constexpr auto add = add_;
static constexpr auto e0 = e0_;
static constexpr auto mul = mul_;
static constexpr auto e1 = e1_;
};
template <class S_, auto add_, auto e0_, auto minus_, auto mul_, auto e1_>
struct Ring
{
using S = S_;
static constexpr auto add = add_;
static constexpr auto e0 = e0_;
static constexpr auto minus = minus_;
static constexpr auto mul = mul_;
static constexpr auto e1 = e1_;
};
template <class S_, auto add_, auto e0_, auto minus_, auto mul_, auto e1_, auto inv_>
struct Field
{
using S = S_;
static constexpr auto add = add_;
static constexpr auto e0 = e0_;
static constexpr auto minus = minus_;
static constexpr auto mul = mul_;
static constexpr auto e1 = e1_;
static constexpr auto inv = inv_;
};
template <class M, class = void>
struct HasInverse : false_type {};
template <class M>
struct HasInverse<M, void_t<decltype(M::inv(declval<const typename M::S &>()))>> : true_type {};
template <class M>
struct OppositeMonoid
{
using S = typename M::S;
static constexpr auto e = M::e;
};
template <class G>
struct OppositeGroup
{
using S = typename G::S;
static constexpr auto e = G::e;
static constexpr auto inv = G::inv;
};
template <class M>
struct NormalAndOppositeMonoid
{
struct S
{
typename M::S normal;
typename M::S opposite;
};
};
template <class G>
struct NormalAndOppositeGroup
{
struct S
{
typename G::S normal;
typename G::S opposite;
};
};
template <class SR>
using MonoidOfSemiRingAdd = Monoid<typename SR::S, SR::add, SR::e0>;
template <class SR>
using MonoidOfSemiRingMul = Monoid<typename SR::S, SR::mul, SR::e1>;
template <class R>
using GroupOfRingAdd = Group<typename R::S, R::add, R::e0, R::minus>;
template <class K>
using GroupOfFieldMul = Group<typename K::S, K::mul, K::e1, K::inv>;
template <class Madd, class Mmul>
struct SemiRingFromMonoidMonoid
{
static_assert(is_same_v<typename Madd::S, typename Mmul::S>, "Madd::S and Mmul::S must be identical");
using S = typename Madd::S;
static constexpr auto add = Madd::op;
static constexpr auto e0 = Madd::e;
static constexpr auto mul = Mmul::op;
static constexpr auto e1 = Mmul::e;
};
template <class Gadd, class Mmul>
struct RingFromGroupMonoid
{
static_assert(is_same_v<typename Gadd::S, typename Mmul::S>, "Gadd::S and Mmul::S must be identical");
using S = typename Gadd::S;
static constexpr auto add = Gadd::op;
static constexpr auto e0 = Gadd::e;
static constexpr auto minus = Gadd::inv;
static constexpr auto mul = Mmul::op;
static constexpr auto e1 = Mmul::e;
};
template <class Gadd, class Gmul>
struct FieldFromGroupGroup
{
static_assert(is_same_v<typename Gadd::S, typename Gmul::S>, "Gadd::S and Gmul::S must be identical");
using S = typename Gadd::S;
static constexpr auto add = Gadd::op;
static constexpr auto e0 = Gadd::e;
static constexpr auto minus = Gadd::inv;
static constexpr auto mul = Gmul::op;
static constexpr auto e1 = Gmul::e;
static constexpr auto inv = Gmul::inv;
};
// https://github.com/miscalculation53/library/tree/wip/algebra/trivial.hpp
struct GroupTrivial
{
using S = monostate;
static constexpr S e() { return {}; }
static constexpr S op(S, S) { return {}; }
static constexpr S inv(S) { return {}; }
};
// https://github.com/miscalculation53/library/tree/wip/utils/identity.hpp
struct Identity
{
template <class T>
constexpr T &&operator()(T &&x) const noexcept { return std::forward<T>(x); }
};
namespace priority_container_detail
{
template <class C, class = void>
struct NativeMonoid { using type = GroupTrivial; };
template <class C>
struct NativeMonoid<C, void_t<typename C::monoid_type>> { using type = typename C::monoid_type; };
template <class C, class = void>
struct NativeProjection
{
using type = Identity;
};
template <class C>
struct NativeProjection<C, void_t<typename C::projection_type,
decltype(declval<const C &>().projection())>>
{
using type = typename C::projection_type;
};
template <class C, class M, class Projection = typename NativeProjection<C>::type, class = void>
struct HasNativeAggregate : false_type {};
template <class C, class M, class Projection>
struct HasNativeAggregate<C, M, Projection, void_t<typename C::monoid_type,
decltype(declval<const C &>().all_prod())>>
: bool_constant<is_same_v<typename C::monoid_type, M> &&
is_same_v<typename NativeProjection<C>::type, Projection>> {};
template <class M, bool Native>
struct AggregateCache {};
template <class M>
struct AggregateCache<M, false> { typename M::S product = M::e(); };
template <>
struct AggregateCache<GroupTrivial, false> {};
}
// https://github.com/miscalculation53/library/tree/wip/utils/reverse_compare.hpp
template <class Compare>
struct ReverseCompare
{
Compare comp;
};
template <class Compare>
struct reverse_compare_type { using type = ReverseCompare<Compare>; };
template <class Compare>
struct reverse_compare_type<ReverseCompare<Compare>> { using type = Compare; };
template <class T>
struct reverse_compare_type<less<T>> { using type = greater<T>; };
template <class T>
struct reverse_compare_type<greater<T>> { using type = less<T>; };
template <class Compare>
using reverse_compare_t = typename reverse_compare_type<Compare>::type;
namespace priority_container_detail
{
template <class C, class = void>
struct HasErase : false_type {};
template <class C>
struct HasErase<C, void_t<decltype(declval<C &>().erase(declval<const typename C::value_type &>()))>> : true_type {};
template <class C, class = void>
struct HasContains : false_type {};
template <class C>
struct HasContains<C, void_t<decltype(declval<const C &>().contains(declval<const typename C::value_type &>()))>> : true_type {};
template <class C, class = void>
struct HasFront : false_type {};
template <class C>
struct HasFront<C, void_t<decltype(declval<const C &>().front()), decltype(declval<C &>().pop_front())>> : true_type {};
template <class C, class = void>
struct HasBack : false_type {};
template <class C>
struct HasBack<C, void_t<decltype(declval<const C &>().back()), decltype(declval<C &>().pop_back())>> : true_type {};
template <class C, class = void>
struct HasClear : false_type {};
template <class C>
struct HasClear<C, void_t<decltype(declval<C &>().clear())>> : true_type {};
template <class C, class = void>
struct HasContent : false_type {};
template <class C>
struct HasContent<C, void_t<decltype(declval<const C &>().content())>> : true_type {};
template <class C>
struct Access
{
using T = typename C::value_type;
static constexpr bool can_erase = HasErase<C>::value;
static constexpr bool can_contains = HasContains<C>::value;
static constexpr bool can_front = HasFront<C>::value, can_back = HasBack<C>::value;
};
template <class C, class Compare, bool Back, bool ReverseInput>
struct SingleEndedQueue
{
using value_type = typename C::value_type;
private:
C data;
public:
};
template <class C, class Compare, bool Back>
struct ContainerForEnd { using type = C; };
template <class C, class Order, bool CurrentBack, bool ReverseInput, class Compare, bool Back>
struct ContainerForEnd<SingleEndedQueue<C, Order, CurrentBack, ReverseInput>, Compare, Back>
: ContainerForEnd<C, Compare, Back> {};
}
template <class Container,
class M = typename priority_container_detail::NativeMonoid<Container>::type,
class Projection = typename priority_container_detail::NativeProjection<Container>::type>
struct PriorityContainer : private priority_container_detail::AggregateCache<M,
priority_container_detail::HasNativeAggregate<Container, M, Projection>::value>
{
using value_type = typename Container::value_type;
using monoid_type = M;
using projection_type = Projection;
using S = typename M::S;
static_assert(is_same_v<M, GroupTrivial> ||
is_same_v<decay_t<invoke_result_t<const Projection &, const value_type &>>, S>,
"The projection result and M::S must have the same type");
static constexpr bool supports_erase = priority_container_detail::Access<Container>::can_erase;
static constexpr bool supports_contains = priority_container_detail::Access<Container>::can_contains;
static constexpr bool supports_front = priority_container_detail::Access<Container>::can_front;
static constexpr bool supports_back = priority_container_detail::Access<Container>::can_back;
static_assert(supports_front || supports_back, "A priority container needs front/pop_front or back/pop_back");
private:
using Access = priority_container_detail::Access<Container>;
static constexpr bool native = priority_container_detail::HasNativeAggregate<Container, M, Projection>::value;
static_assert(native || HasInverse<M>::value,
"Aggregation needs M::inv or a container with the same monoid and projection and all_prod");
Container data;
Projection proj{};
void initialize_aggregate()
{
if constexpr (!native && !is_same_v<M, GroupTrivial>)
{
auto copy = data;
while (!copy.empty())
{
if constexpr (supports_front) { add(Access::front(copy)); Access::pop_front(copy); }
else { add(Access::back(copy)); Access::pop_back(copy); }
}
}
}
void add(const value_type &x)
{
if constexpr (!native && !is_same_v<M, GroupTrivial>) this->product = M::op(this->product, std::invoke(projection(), x));
}
void remove(const value_type &x)
{
if constexpr (!native && !is_same_v<M, GroupTrivial>) this->product = M::op(this->product, M::inv(std::invoke(projection(), x)));
}
template <bool Back>
value_type get_end() const
{
assert(!empty());
if constexpr (Back) return Access::back(data);
else return Access::front(data);
}
template <bool Back>
void pop_data_end()
{
if constexpr (Back) Access::pop_back(data);
else Access::pop_front(data);
}
template <bool Back>
value_type extract_end()
{
auto x = get_end<Back>();
pop_data_end<Back>();
remove(x);
return x;
}
public:
PriorityContainer() = default;
template <bool Native = native, enable_if_t<!Native && !native, int> = 0>
PriorityContainer(Container data, Projection projection)
: data(std::move(data)), proj(std::move(projection)) { initialize_aggregate(); }
PriorityContainer(const PriorityContainer &) = default;
PriorityContainer &operator=(const PriorityContainer &) = default;
template <class Compare>
static PriorityContainer with_compare(const Compare &comp, Projection projection = Projection())
{
if constexpr (native)
{
if constexpr (is_constructible_v<Container, const Compare &, const Projection &>)
return PriorityContainer(Container(comp, projection));
else
{
static_assert(is_same_v<Projection, Identity>, "The native container must accept the projection");
return PriorityContainer(Access::make(comp));
}
}
else return PriorityContainer(Access::make(comp), std::move(projection));
}
int size() const { return data.size(); }
bool empty() const { return data.empty(); }
void push(const value_type &x)
{
if constexpr (!native && !is_same_v<M, GroupTrivial>)
{
S value = std::invoke(projection(), x);
Access::push(data, x);
this->product = M::op(this->product, value);
}
else Access::push(data, x);
}
template <bool Enabled = supports_front, enable_if_t<Enabled && supports_front, int> = 0>
value_type front() const { return get_end<false>(); }
template <bool Enabled = supports_back, enable_if_t<Enabled && supports_back, int> = 0>
value_type back() const { return get_end<true>(); }
template <bool Enabled = supports_front, enable_if_t<Enabled && supports_front, int> = 0>
value_type extract_front() { return extract_end<false>(); }
template <bool Enabled = supports_back, enable_if_t<Enabled && supports_back, int> = 0>
value_type extract_back() { return extract_end<true>(); }
template <bool Enabled = supports_erase, enable_if_t<Enabled && supports_erase, int> = 0>
void erase(const value_type &x)
{
if constexpr (!native && !is_same_v<M, GroupTrivial>)
{
S value = std::invoke(projection(), x);
Access::erase(data, x);
this->product = M::op(this->product, M::inv(value));
}
else Access::erase(data, x);
}
template <bool Enabled = supports_contains, enable_if_t<Enabled && supports_contains, int> = 0>
bool contains(const value_type &x) const { return Access::contains(data, x); }
S all_prod() const
{
if constexpr (native) return data.all_prod();
else if constexpr (is_same_v<M, GroupTrivial>) return {};
else return this->product;
}
const Projection &projection() const { return proj; }
};
namespace priority_container_detail
{
template <class T, class Compare, class Allocator>
struct Access<multiset<T, Compare, Allocator>>
{
using C = multiset<T, Compare, Allocator>;
static constexpr bool can_erase = true, can_contains = true, can_front = true, can_back = true;
static T front(const C &c) { return *c.begin(); }
static T back(const C &c) { return *c.rbegin(); }
static void push(C &c, const T &x) { c.insert(x); }
static void pop_front(C &c) { c.erase(c.begin()); }
static void pop_back(C &c) { c.erase(prev(c.end())); }
static bool contains(const C &c, const T &x) { return c.find(x) != c.end(); }
static void erase(C &c, const T &x)
{
auto it = c.find(x);
assert(it != c.end());
c.erase(it);
}
template <class Comp>
static C make(const Comp &comp) { return C(comp); }
};
}
// https://github.com/miscalculation53/library/tree/wip/ds/priority_container/priority_queue.hpp
template <class T, class Compare = less<T>, class Sequence = vector<T>>
using MinPriorityQueue = priority_container_detail::SingleEndedQueue<
priority_queue<T, Sequence, reverse_compare_t<Compare>>, Compare, false, true>;
template <class T, class Compare = less<T>, class Sequence = vector<T>>
using MaxPriorityQueue = priority_container_detail::SingleEndedQueue<
priority_queue<T, Sequence, Compare>, Compare, true, false>;
namespace priority_container_detail
{
template <class T, class Sequence, class Compare>
struct Access<priority_queue<T, Sequence, Compare>>
{
using C = priority_queue<T, Sequence, Compare>;
static constexpr bool can_erase = false, can_contains = false, can_front = false, can_back = true;
};
template <class T, class Sequence, class RawCompare, class Compare, bool Back>
struct ContainerForEnd<priority_queue<T, Sequence, RawCompare>, Compare, Back>
{
using type = conditional_t<Back, MaxPriorityQueue<T, Compare, Sequence>, MinPriorityQueue<T, Compare, Sequence>>;
};
}
// https://github.com/miscalculation53/library/tree/wip/ds/priority_container/erasable_priority_queue.hpp
// https://github.com/miscalculation53/library/tree/wip/ds/erasable_priority_queue.hpp
template <class T, class Compare = less<T>>
struct ErasablePriorityQueue
{
using value_type = T;
using compare_type = Compare;
private:
struct ReverseCompare
{
Compare comp;
};
Compare comp;
priority_queue<T, vc<T>, ReverseCompare> body, era;
public:
};
template <class T, class Compare = less<T>>
using MinErasablePriorityQueue = priority_container_detail::SingleEndedQueue<
ErasablePriorityQueue<T, Compare>, Compare, false, false>;
template <class T, class Compare = less<T>>
using MaxErasablePriorityQueue = priority_container_detail::SingleEndedQueue<
ErasablePriorityQueue<T, reverse_compare_t<Compare>>, Compare, true, true>;
namespace priority_container_detail
{
template <class T, class Compare>
struct Access<ErasablePriorityQueue<T, Compare>>
{
using C = ErasablePriorityQueue<T, Compare>;
static constexpr bool can_erase = true, can_contains = false, can_front = true, can_back = false;
};
template <class T, class RawCompare, class Compare, bool Back>
struct ContainerForEnd<ErasablePriorityQueue<T, RawCompare>, Compare, Back>
{
using type = conditional_t<Back, MaxErasablePriorityQueue<T, Compare>, MinErasablePriorityQueue<T, Compare>>;
};
}
// https://github.com/miscalculation53/library/tree/wip/ds/priority_container/double_ended_priority_queue.hpp
// https://github.com/miscalculation53/library/tree/wip/ds/double_ended_priority_queue.hpp
template <class T, class Compare = less<T>>
struct DoubleEndedPriorityQueue
{
using value_type = T;
using compare_type = Compare;
private:
ErasablePriorityQueue<T, Compare> mn;
ErasablePriorityQueue<T, reverse_compare_t<Compare>> mx;
public:
};
namespace priority_container_detail
{
template <class T, class Compare>
struct Access<DoubleEndedPriorityQueue<T, Compare>>
{
using C = DoubleEndedPriorityQueue<T, Compare>;
static constexpr bool can_erase = true, can_contains = false, can_front = true, can_back = true;
};
}
// https://github.com/miscalculation53/library/tree/wip/ds/priority_container/monotone_deque.hpp
template <class T, class Compare = less<T>>
struct MonotonePriorityDeque
{
using value_type = T;
private:
deque<T> data;
Compare comp;
public:
MonotonePriorityDeque() = default;
};
// https://github.com/miscalculation53/library/tree/wip/algebra/algebra_basic_ops.hpp
template <class T, class = void>
struct has_e1 : false_type {};
template <class T>
struct has_e1<T, void_t<decltype(T::e1())>> : true_type {};
template <class T>
inline constexpr bool has_e1_v = has_e1<T>::value;
template <class T>
struct MonoidMul
{
using S = T;
};
template <class T>
struct GroupAddSub
{
using S = T;
static constexpr S op(S a, S b) { return a + b; }
static constexpr S e()
{
if constexpr (has_e0_v<S>)
return S::e0();
else
return S{};
}
static constexpr S inv(S a) { return -a; }
};
template <class T>
struct GroupMulDiv
{
using S = T;
};
template <class T, auto infty = nullptr>
using SemiRingMinPlus = SemiRingFromMonoidMonoid<MonoidMin<T, infty>, MonoidAdd<T>>;
template <class T, auto infty = nullptr>
using SemiRingMaxPlus = SemiRingFromMonoidMonoid<MonoidMax<T, infty>, MonoidAdd<T>>;
template <class T>
using RingAddSubMul = RingFromGroupMonoid<GroupAddSub<T>, MonoidMul<T>>;
template <class T>
using FieldAddSubMulDiv = FieldFromGroupGroup<GroupAddSub<T>, GroupMulDiv<T>>;
template <class T, class M, class Compare, class Projection>
struct OrderedMultisetTree;
template <class S>
struct TwoMultisetsState
{
int left_size, right_size;
S left_prod, right_prod;
int size() const { return left_size + right_size; }
};
struct PartitionByMedian
{
template <class S>
bool operator()(const TwoMultisetsState<S> &s) const { return s.left_size <= (s.size() + 1) / 2; }
};
struct PartitionBySize
{
int k = 0;
};
template <class S>
struct PartitionBySum
{
S limit;
};
namespace two_multisets_detail
{
template <template <class...> class Base, class T, class Compare, class M, class Projection, bool Back>
struct ContainerType
{
using type = typename priority_container_detail::ContainerForEnd<Base<T, Compare>, Compare, Back>::type;
};
template <class T, class Compare, class M, class Projection, bool Back>
struct ContainerType<priority_queue, T, Compare, M, Projection, Back>
{
using type = conditional_t<Back, MaxPriorityQueue<T, Compare>, MinPriorityQueue<T, Compare>>;
};
template <class T, class Compare, class M, class Projection, bool Back>
struct ContainerType<OrderedMultisetTree, T, Compare, M, Projection, Back>
{
using type = OrderedMultisetTree<T, M, Compare, Projection>;
};
}
template <class T, template <class...> class Base = multiset,
class Condition = PartitionByMedian, class M = GroupTrivial,
class Compare = less<T>, class Projection = Identity>
struct TwoMultisets
{
using value_type = T;
using monoid_type = M;
using projection_type = Projection;
using S = typename M::S;
using State = TwoMultisetsState<S>;
using Left = typename two_multisets_detail::ContainerType<Base, T, Compare, M, Projection, true>::type;
using Right = typename two_multisets_detail::ContainerType<Base, T, Compare, M, Projection, false>::type;
using LeftContainer = PriorityContainer<Left, M, Projection>;
using RightContainer = PriorityContainer<Right, M, Projection>;
static_assert(LeftContainer::supports_back && RightContainer::supports_front,
"TwoMultisets needs a back endpoint on the left and a front endpoint on the right");
static constexpr bool supports_erase = LeftContainer::supports_erase && RightContainer::supports_erase;
static constexpr bool supports_contains = LeftContainer::supports_contains && RightContainer::supports_contains;
private:
optional<Condition> cond;
Compare comp;
LeftContainer lo;
RightContainer hi;
State state() const { return {lo.size(), hi.size(), lo.all_prod(), hi.all_prod()}; }
void move_left_to_right() { hi.push(lo.extract_back()); }
void move_right_to_left() { lo.push(hi.extract_front()); }
void check_empty_prefix() const
{
assert((*cond)(State{0, size(), M::e(), all_prod()}));
}
void balance()
{
check_empty_prefix();
while (!(*cond)(state())) move_left_to_right();
while (!hi.empty())
{
if constexpr (HasInverse<M>::value)
{
auto s = state();
++s.left_size;
--s.right_size;
if constexpr (!is_same_v<M, GroupTrivial>)
{
auto x = std::invoke(hi.projection(), hi.front());
s.left_prod = M::op(s.left_prod, x);
s.right_prod = M::op(s.right_prod, M::inv(x));
}
if (!(*cond)(s)) break;
move_right_to_left();
}
else
{
move_right_to_left();
if (!(*cond)(state())) { move_left_to_right(); break; }
}
}
}
public:
explicit TwoMultisets(Condition cond = Condition(), Compare comp = Compare(), Projection projection = Projection())
: cond(std::move(cond)), comp(comp),
lo(LeftContainer::with_compare(comp, projection)),
hi(RightContainer::with_compare(comp, projection))
{
check_empty_prefix();
}
int size() const { return lo.size() + hi.size(); }
S all_prod() const { return M::op(lo.all_prod(), hi.all_prod()); }
const LeftContainer &left() const { return lo; }
const RightContainer &right() const { return hi; }
void insert(const T &x)
{
if (lo.empty() ? (hi.empty() || !comp(hi.front(), x)) : !comp(lo.back(), x)) lo.push(x);
else hi.push(x);
balance();
}
template <bool Enabled = supports_erase, enable_if_t<Enabled && supports_erase, int> = 0>
void erase(const T &x)
{
if constexpr (supports_contains)
{
if (lo.contains(x)) lo.erase(x);
else hi.erase(x);
}
else
{
if (!lo.empty() && !comp(lo.back(), x)) lo.erase(x);
else hi.erase(x);
}
balance();
}
};
template <class T, template <class...> class Base = multiset,
class Condition = PartitionByMedian, class Compare = less<T>, class Projection = Identity>
using SumTwoMultisets = TwoMultisets<T, Base, Condition,
GroupAddSub<decay_t<invoke_result_t<const Projection &, const T &>>>, Compare, Projection>;
void main2()
{
LL(N);
VEC(ll, N + 1, A);
VEC(pll, N, UV);
RootedTree G(N + 1, UV, 0);
SumTwoMultisets<ll> ms;
ms.insert(A[0]);
auto [bp, vs] = G.dfs_ordered_vertices();
vl ans(N + 1, INF);
rep(i, 2 * N)
{
if (bp[i] == '(')
{
ms.insert(A[vs[i + 1]]);
if (SZ(ms) >= 3)
{
dump(vs[i + 1]);
dump(ms);
ll mn = ms.left().front(), mx = ms.right().back();
dump(mn, mx);
if (mn == mx)
ans[vs[i + 1]] = 1;
else
{
fe(val : {mn, mx})
{
ms.erase(val);
ll med = ms.left().back();
ll opt = (med * ms.left().size() - ms.left().all_prod()) + (ms.right().all_prod() - med * ms.right().size());
dump(med, opt);
chmin(ans[vs[i + 1]], opt);
ms.insert(val);
}
}
}
}
else
{
ms.erase(A[vs[i]]);
}
}
ans.erase(ans.begin());
fem(ansi : ans) if (ansi == INF) ansi = -1;
PRINTV(ans);
}
void test()
{
}
// https://github.com/miscalculation53/library/tree/wip/template/template_main.hpp
template <auto init, auto main2, auto test>
struct Main
{
Main()
{
cauto CERR = [](string val, string color)
{
string s = "\033[" + color + "m" + val + "\033[m";
};
CERR("\n[FAST_IO]\n\n", "32");
cout << fixed << setprecision(20);
init();
CERR("\n[SINGLE_TESTCASE]\n\n", "36");
main2();
}
};
Main<init, main2, test> main_dummy;
int main() {}