QOJ.ac
QOJ
| ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
|---|---|---|---|---|---|---|---|---|---|
| #288956 | #7864. Random Tree Parking | ucup-team1516# | AC ✓ | 240ms | 37204kb | C++20 | 26.2kb | 2023-12-23 14:27:05 | 2024-11-20 09:58:48 |
Judging History
answer
#include<bits/stdc++.h>
#include <algorithm>
#include <array>
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (unsigned int)(n)) x++;
return x;
}
// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n) {
#ifdef _MSC_VER
unsigned long index;
_BitScanForward(&index, n);
return index;
#else
return __builtin_ctz(n);
#endif
}
} // namespace internal
} // namespace atcoder
#include <utility>
namespace atcoder {
namespace internal {
// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
unsigned int _m;
unsigned long long im;
// @param m `1 <= m < 2^31`
barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
// @return m
unsigned int umod() const { return _m; }
// @param a `0 <= a < m`
// @param b `0 <= b < m`
// @return `a * b % m`
unsigned int mul(unsigned int a, unsigned int b) const {
// [1] m = 1
// a = b = im = 0, so okay
// [2] m >= 2
// im = ceil(2^64 / m)
// -> im * m = 2^64 + r (0 <= r < m)
// let z = a*b = c*m + d (0 <= c, d < m)
// a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
// c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
// ((ab * im) >> 64) == c or c + 1
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x =
(unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned int v = (unsigned int)(z - x * _m);
if (_m <= v) v += _m;
return v;
}
};
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
constexpr long long bases[3] = {2, 7, 61};
for (long long a : bases) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);
// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
// Contracts:
// [1] s - m0 * a = 0 (mod b)
// [2] t - m1 * a = 0 (mod b)
// [3] s * |m1| + t * |m0| <= b
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b
// [3]:
// (s - t * u) * |m1| + t * |m0 - m1 * u|
// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
// = s * |m1| + t * |m0| <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
// by [3]: |m0| <= b/g
// by g != b: |m0| < b/g
if (m0 < 0) m0 += b / s;
return {s, m0};
}
// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (long long)(i)*i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) {
x /= i;
}
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
} // namespace internal
} // namespace atcoder
#include <cassert>
#include <numeric>
#include <type_traits>
namespace atcoder {
namespace internal {
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value &&
std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
} // namespace atcoder
#include <cassert>
#include <numeric>
#include <type_traits>
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;
} // namespace internal
template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
static_modint(T v) {
_v = (unsigned int)(v % umod());
}
static_modint(bool v) { _v = ((unsigned int)(v) % umod()); }
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = internal::inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
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;
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = internal::is_prime<m>;
};
template <int id> struct dynamic_modint : internal::modint_base {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = internal::barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
dynamic_modint(T v) {
long long x = (long long)(v % (long long)(mod()));
if (x < 0) x += mod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
dynamic_modint(T v) {
_v = (unsigned int)(v % mod());
}
dynamic_modint(bool v) { _v = ((unsigned int)(v) % mod()); }
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v += mod() - rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator*=(const mint& rhs) {
_v = bt.mul(_v, rhs._v);
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
auto eg = internal::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
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;
}
private:
unsigned int _v;
static internal::barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt = 998244353;
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
} // namespace internal
} // namespace atcoder
#include <cassert>
#include <type_traits>
#include <vector>
namespace atcoder {
namespace internal {
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly(std::vector<mint>& a) {
static constexpr int g = internal::primitive_root<mint::mod()>;
int n = int(a.size());
int h = internal::ceil_pow2(n);
static bool first = true;
static mint sum_e[30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
if (first) {
first = false;
mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1
int cnt2 = bsf(mint::mod() - 1);
mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
for (int i = cnt2; i >= 2; i--) {
// e^(2^i) == 1
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
mint now = 1;
for (int i = 0; i <= cnt2 - 2; i++) {
sum_e[i] = es[i] * now;
now *= ies[i];
}
}
for (int ph = 1; ph <= h; ph++) {
int w = 1 << (ph - 1), p = 1 << (h - ph);
mint now = 1;
for (int s = 0; s < w; s++) {
int offset = s << (h - ph + 1);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p] * now;
a[i + offset] = l + r;
a[i + offset + p] = l - r;
}
now *= sum_e[bsf(~(unsigned int)(s))];
}
}
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly_inv(std::vector<mint>& a) {
static constexpr int g = internal::primitive_root<mint::mod()>;
int n = int(a.size());
int h = internal::ceil_pow2(n);
static bool first = true;
static mint sum_ie[30]; // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]
if (first) {
first = false;
mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1
int cnt2 = bsf(mint::mod() - 1);
mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
for (int i = cnt2; i >= 2; i--) {
// e^(2^i) == 1
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
mint now = 1;
for (int i = 0; i <= cnt2 - 2; i++) {
sum_ie[i] = ies[i] * now;
now *= es[i];
}
}
for (int ph = h; ph >= 1; ph--) {
int w = 1 << (ph - 1), p = 1 << (h - ph);
mint inow = 1;
for (int s = 0; s < w; s++) {
int offset = s << (h - ph + 1);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p];
a[i + offset] = l + r;
a[i + offset + p] =
(unsigned long long)(mint::mod() + l.val() - r.val()) *
inow.val();
}
inow *= sum_ie[bsf(~(unsigned int)(s))];
}
}
}
} // namespace internal
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(std::vector<mint> a, std::vector<mint> b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
if (std::min(n, m) <= 60) {
if (n < m) {
std::swap(n, m);
std::swap(a, b);
}
std::vector<mint> ans(n + m - 1);
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
ans[i + j] += a[i] * b[j];
}
}
return ans;
}
int z = 1 << internal::ceil_pow2(n + m - 1);
a.resize(z);
internal::butterfly(a);
b.resize(z);
internal::butterfly(b);
for (int i = 0; i < z; i++) {
a[i] *= b[i];
}
internal::butterfly_inv(a);
a.resize(n + m - 1);
mint iz = mint(z).inv();
for (int i = 0; i < n + m - 1; i++) a[i] *= iz;
return a;
}
template <unsigned int mod = 998244353,
class T,
std::enable_if_t<internal::is_integral<T>::value>* = nullptr>
std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
using mint = static_modint<mod>;
std::vector<mint> a2(n), b2(m);
for (int i = 0; i < n; i++) {
a2[i] = mint(a[i]);
}
for (int i = 0; i < m; i++) {
b2[i] = mint(b[i]);
}
auto c2 = convolution(move(a2), move(b2));
std::vector<T> c(n + m - 1);
for (int i = 0; i < n + m - 1; i++) {
c[i] = c2[i].val();
}
return c;
}
std::vector<long long> convolution_ll(const std::vector<long long>& a,
const std::vector<long long>& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
static constexpr unsigned long long MOD1 = 754974721; // 2^24
static constexpr unsigned long long MOD2 = 167772161; // 2^25
static constexpr unsigned long long MOD3 = 469762049; // 2^26
static constexpr unsigned long long M2M3 = MOD2 * MOD3;
static constexpr unsigned long long M1M3 = MOD1 * MOD3;
static constexpr unsigned long long M1M2 = MOD1 * MOD2;
static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;
static constexpr unsigned long long i1 =
internal::inv_gcd(MOD2 * MOD3, MOD1).second;
static constexpr unsigned long long i2 =
internal::inv_gcd(MOD1 * MOD3, MOD2).second;
static constexpr unsigned long long i3 =
internal::inv_gcd(MOD1 * MOD2, MOD3).second;
auto c1 = convolution<MOD1>(a, b);
auto c2 = convolution<MOD2>(a, b);
auto c3 = convolution<MOD3>(a, b);
std::vector<long long> c(n + m - 1);
for (int i = 0; i < n + m - 1; i++) {
unsigned long long x = 0;
x += (c1[i] * i1) % MOD1 * M2M3;
x += (c2[i] * i2) % MOD2 * M1M3;
x += (c3[i] * i3) % MOD3 * M1M2;
// B = 2^63, -B <= x, r(real value) < B
// (x, x - M, x - 2M, or x - 3M) = r (mod 2B)
// r = c1[i] (mod MOD1)
// focus on MOD1
// r = x, x - M', x - 2M', x - 3M' (M' = M % 2^64) (mod 2B)
// r = x,
// x - M' + (0 or 2B),
// x - 2M' + (0, 2B or 4B),
// x - 3M' + (0, 2B, 4B or 6B) (without mod!)
// (r - x) = 0, (0)
// - M' + (0 or 2B), (1)
// -2M' + (0 or 2B or 4B), (2)
// -3M' + (0 or 2B or 4B or 6B) (3) (mod MOD1)
// we checked that
// ((1) mod MOD1) mod 5 = 2
// ((2) mod MOD1) mod 5 = 3
// ((3) mod MOD1) mod 5 = 4
long long diff =
c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));
if (diff < 0) diff += MOD1;
static constexpr unsigned long long offset[5] = {
0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};
x -= offset[diff % 5];
c[i] = x;
}
return c;
}
} // namespace atcoder
using namespace std;
using namespace atcoder;
#define ll long long
#define ull unsigned long long
#define db double
#define pii pair<int,int>
#define pli pair<ll,int>
#define pil pair<int,ll>
#define pll pair<ll,ll>
#define ti3 tuple<int,int,int>
#define int128 __int128_t
#define pii128 pair<int128,int128>
const int inf = 1 << 30;
const ll linf = 1e18;
const ll mod = 998244353;
const db EPS = 1e-10;
const db pi = acos(-1);
template<class T> bool chmin(T& x, T y){
if(x > y) {
x = y;
return true;
} else return false;
}
template<class T> bool chmax(T& x, T y){
if(x < y) {
x = y;
return true;
} else return false;
}
// overload macro
#define CAT( A, B ) A ## B
#define SELECT( NAME, NUM ) CAT( NAME, NUM )
#define GET_COUNT( _1, _2, _3, _4, _5, _6 /* ad nauseam */, COUNT, ... ) COUNT
#define VA_SIZE( ... ) GET_COUNT( __VA_ARGS__, 6, 5, 4, 3, 2, 1 )
#define VA_SELECT( NAME, ... ) SELECT( NAME, VA_SIZE(__VA_ARGS__) )(__VA_ARGS__)
// rep(overload)
#define rep( ... ) VA_SELECT(rep, __VA_ARGS__)
#define rep2(i, n) for (int i = 0; i < int(n); i++)
#define rep3(i, a, b) for (int i = a; i < int(b); i++)
#define rep4(i, a, b, c) for (int i = a; i < int(b); i += c)
// repll(overload)
#define repll( ... ) VA_SELECT(repll, __VA_ARGS__)
#define repll2(i, n) for (ll i = 0; i < (ll)(n); i++)
#define repll3(i, a, b) for (ll i = a; i < (ll)(b); i++)
#define repll4(i, a, b, c) for (ll i = a; i < (ll)(b); i += c)
// rrep(overload)
#define rrep( ... ) VA_SELECT(rrep, __VA_ARGS__)
#define rrep2(i, n) for (int i = n - 1; i >= 0; i--)
#define rrep3(i, a, b) for (int i = b - 1; i >= a; i--)
#define rrep4(i, a, b, c) for (int i = b - 1; i >= a; i -= c)
// rrepll(overload)
#define rrepll( ... ) VA_SELECT(rrepll, __VA_ARGS__)
#define rrepll2(i, n) for (ll i = (ll)(n) - 1; i >= 0ll; i--)
#define rrepll3(i, a, b) for (ll i = b - 1; i >= (ll)(a); i--)
#define rrepll4(i, a, b, c) for (ll i = b - 1; i >= (ll)(a); i -= c)
// for_earh
#define fore(e, v) for (auto&& e : v)
// vector
#define all(v) v.begin(), v.end()
#define rall(v) v.rbegin(), v.rend()
using mint = modint998244353;
int n, sz[100010];
vector<int> G[100010];
vector<mint> dp[100010];
mint inv[100010], frac;
void dfs(int v, int d) {
sz[v]++;
rep (i, d + 1) {
dp[v].emplace_back(inv[i]);
}
for (auto u : G[v]) {
dfs(u, d + 1);
sz[v] += sz[u];
}
G[v].push_back(v);
sort(all(G[v]), [&](int a, int b) {
return dp[a].size() < dp[b].size();
});
rep (i, G[v].size() - 1) {
dp[G[v][i + 1]] = convolution(dp[G[v][i]], dp[G[v][i + 1]]);
if (dp[G[v][i + 1]].size() > sz[v] + d) dp[G[v][i + 1]].resize(sz[v] + d);
}
dp[v] = dp[G[v].back()];
rep (i, sz[v]) dp[v][i] = 0;
}
int main() {
cin.tie(nullptr);
ios_base::sync_with_stdio(false);
cout << fixed << setprecision(20);
cin >> n;
rep (i, 2, n + 1) {
int p;
cin >> p;
G[p].push_back(i);
}
frac = 1;
inv[0] = 1;
rep (i, 1, n + 1) {
frac *= i;
}
inv[n] = (mint)1 / frac;
rrep (i, n) inv[i] = inv[i + 1] * (i + 1);
dfs(1, 1);
cout << (dp[1][n] * frac).val() << endl;
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 0ms
memory: 6040kb
input:
3 1 1
output:
12
result:
ok 1 number(s): "12"
Test #2:
score: 0
Accepted
time: 1ms
memory: 5940kb
input:
3 1 2
output:
16
result:
ok 1 number(s): "16"
Test #3:
score: 0
Accepted
time: 1ms
memory: 4040kb
input:
4 1 2 3
output:
125
result:
ok 1 number(s): "125"
Test #4:
score: 0
Accepted
time: 1ms
memory: 3972kb
input:
8 1 2 3 1 3 4 3
output:
1198736
result:
ok 1 number(s): "1198736"
Test #5:
score: 0
Accepted
time: 0ms
memory: 5964kb
input:
15 1 2 2 2 2 3 3 2 7 7 3 10 3 13
output:
938578089
result:
ok 1 number(s): "938578089"
Test #6:
score: 0
Accepted
time: 1ms
memory: 5948kb
input:
100 1 1 1 3 5 5 5 5 9 9 3 2 11 14 9 8 16 8 18 18 20 10 12 2 22 21 27 28 29 6 2 21 2 20 21 11 16 19 9 25 39 8 14 19 6 38 22 19 25 13 3 27 19 51 23 18 45 30 30 22 24 16 12 61 42 24 3 3 53 40 59 72 6 23 1 64 41 13 71 75 30 64 11 55 70 60 32 84 25 4 69 49 15 42 72 31 71 23 58
output:
426063005
result:
ok 1 number(s): "426063005"
Test #7:
score: 0
Accepted
time: 1ms
memory: 4132kb
input:
500 1 1 3 3 3 4 3 5 2 5 8 4 12 11 8 14 1 12 7 16 7 7 17 10 8 26 7 4 13 21 6 7 20 34 35 24 25 23 25 39 20 30 13 43 43 35 45 34 7 4 11 23 11 43 35 27 6 2 3 11 37 42 27 37 62 42 41 43 63 4 57 17 18 8 11 23 72 74 41 49 76 44 50 81 46 18 45 5 8 88 77 27 35 11 52 18 32 85 57 25 32 22 39 35 43 26 63 7 62 2...
output:
105022837
result:
ok 1 number(s): "105022837"
Test #8:
score: 0
Accepted
time: 0ms
memory: 6520kb
input:
2000 1 1 2 4 4 4 1 5 9 4 5 9 9 4 15 1 11 18 11 2 4 22 10 23 18 15 6 25 25 19 15 28 32 17 29 24 35 11 32 20 25 8 7 12 27 29 40 21 23 47 24 8 6 24 53 43 9 10 48 18 16 16 10 45 42 33 20 27 33 47 41 22 37 4 38 23 8 29 14 54 49 74 60 56 45 32 11 4 58 16 71 29 49 32 31 95 38 2 89 73 91 65 26 12 94 35 1 73...
output:
510693456
result:
ok 1 number(s): "510693456"
Test #9:
score: 0
Accepted
time: 12ms
memory: 8852kb
input:
10000 1 2 1 1 2 1 4 3 5 6 1 8 8 3 2 15 4 14 10 9 9 15 17 5 21 9 11 24 17 20 17 16 4 13 10 10 36 2 8 29 34 40 8 13 27 5 1 18 16 4 40 47 4 8 9 1 54 40 38 41 46 52 31 21 21 14 49 49 46 22 14 59 71 37 30 18 37 30 36 56 24 56 48 17 75 68 68 6 65 87 48 52 8 26 94 89 29 32 40 77 51 6 9 78 1 48 100 69 85 89...
output:
158503783
result:
ok 1 number(s): "158503783"
Test #10:
score: 0
Accepted
time: 240ms
memory: 37204kb
input:
100000 1 1 1 2 4 4 7 8 6 9 7 8 12 10 15 15 9 12 9 16 9 13 11 18 11 8 6 23 22 28 8 29 12 24 14 9 33 5 17 4 33 29 41 19 37 34 19 41 15 21 20 13 36 25 34 38 2 56 33 53 40 36 26 28 34 7 19 66 35 43 52 47 53 32 61 11 55 10 78 75 43 80 71 16 20 68 27 41 80 33 69 50 71 7 5 26 24 78 62 17 76 15 10 11 56 64 ...
output:
937583571
result:
ok 1 number(s): "937583571"
Test #11:
score: 0
Accepted
time: 205ms
memory: 34728kb
input:
100000 1 2 1 2 5 3 5 4 6 8 2 1 6 2 5 5 1 6 12 12 15 11 23 3 4 13 3 22 8 5 13 12 10 9 6 27 37 22 14 24 12 26 15 30 2 27 43 4 47 9 42 5 33 26 13 54 17 32 23 15 34 36 14 49 41 25 14 35 22 35 51 50 17 22 38 54 71 41 69 44 61 18 77 3 78 53 74 70 67 8 18 10 88 2 1 74 36 15 76 62 7 70 89 24 72 77 15 44 49 ...
output:
264669337
result:
ok 1 number(s): "264669337"
Test #12:
score: 0
Accepted
time: 211ms
memory: 35136kb
input:
100000 1 1 3 2 2 6 7 6 3 4 10 1 2 14 12 16 3 2 19 20 3 2 12 17 6 17 16 9 27 18 23 21 2 31 18 13 6 17 39 13 25 18 29 11 42 17 10 34 22 9 33 31 52 45 5 54 43 52 56 4 5 47 63 51 41 54 28 65 31 70 2 63 59 53 53 40 39 5 46 71 13 6 41 31 57 4 82 62 78 59 87 72 92 9 5 69 90 92 19 15 78 41 39 23 12 1 47 49 ...
output:
399299126
result:
ok 1 number(s): "399299126"
Test #13:
score: 0
Accepted
time: 210ms
memory: 35596kb
input:
100000 1 1 1 4 5 5 3 7 6 1 7 8 8 11 11 13 7 7 1 1 13 20 21 22 22 19 8 2 29 28 4 27 8 16 30 4 5 14 21 35 29 32 35 22 14 23 41 24 33 12 31 39 4 40 24 5 38 46 20 23 37 5 27 39 32 41 26 50 33 15 50 40 40 23 52 58 31 16 25 60 36 72 29 33 48 1 82 1 25 57 15 69 5 78 29 81 36 46 97 38 15 7 39 51 19 80 29 77...
output:
58289876
result:
ok 1 number(s): "58289876"
Test #14:
score: 0
Accepted
time: 197ms
memory: 34108kb
input:
100000 1 1 1 1 4 1 7 2 4 8 6 3 2 9 15 15 5 5 7 1 12 15 4 19 7 8 15 21 26 28 13 20 14 21 30 27 21 2 3 14 1 33 33 8 41 25 11 38 35 35 35 5 16 29 16 9 24 39 13 12 3 58 20 44 3 43 53 57 13 23 44 43 14 4 23 69 27 73 22 55 25 64 52 40 71 48 56 56 8 68 27 30 92 46 18 7 58 30 65 69 61 55 38 92 33 102 80 2 2...
output:
861492056
result:
ok 1 number(s): "861492056"
Test #15:
score: 0
Accepted
time: 206ms
memory: 34956kb
input:
100000 1 1 2 3 2 2 5 8 7 4 1 3 5 11 15 2 9 8 19 5 19 11 15 19 19 11 26 3 13 15 30 1 18 28 16 33 9 23 15 2 3 36 7 11 44 31 40 15 46 7 8 5 23 36 22 12 2 28 23 14 11 40 21 18 60 24 32 42 50 57 21 27 60 54 9 63 76 56 22 59 40 41 31 58 27 68 10 45 70 54 46 29 68 6 4 61 11 7 60 56 69 92 69 5 88 71 46 21 7...
output:
528382031
result:
ok 1 number(s): "528382031"
Test #16:
score: 0
Accepted
time: 201ms
memory: 34496kb
input:
100000 1 1 3 1 1 5 4 5 3 3 6 4 1 8 10 15 5 14 5 16 9 13 14 13 8 15 26 17 1 21 11 31 18 16 21 27 14 32 9 27 30 30 3 41 33 26 47 25 26 6 24 15 11 15 6 49 48 25 23 56 3 38 31 28 54 14 17 45 60 64 24 21 14 30 20 30 38 8 13 43 37 11 83 78 75 12 30 66 37 85 24 77 72 71 49 78 88 73 25 68 19 51 79 43 93 21 ...
output:
316789948
result:
ok 1 number(s): "316789948"
Test #17:
score: 0
Accepted
time: 210ms
memory: 35616kb
input:
100000 1 2 1 2 5 4 3 8 5 8 7 6 3 10 15 12 10 4 17 15 16 13 11 1 15 10 4 16 21 11 25 11 15 4 9 21 18 16 17 29 39 3 39 1 34 5 1 14 44 5 15 16 12 15 42 28 45 32 8 33 7 32 61 9 8 34 54 66 59 61 51 51 37 40 30 61 36 36 45 18 75 27 27 45 45 53 50 77 26 89 72 41 15 18 56 53 64 6 34 33 9 90 41 50 8 4 58 101...
output:
846732448
result:
ok 1 number(s): "846732448"
Test #18:
score: 0
Accepted
time: 196ms
memory: 33636kb
input:
100000 1 1 1 3 3 6 5 7 1 3 11 6 3 2 4 4 12 1 6 10 15 8 8 20 24 10 3 5 25 4 10 13 18 30 19 11 9 6 8 24 16 5 17 2 42 33 35 3 26 42 7 42 30 17 6 41 57 53 8 19 41 50 4 16 13 45 28 50 53 22 20 2 9 30 62 25 43 76 2 41 67 74 16 2 43 64 17 28 61 15 35 33 12 60 29 64 51 33 16 18 16 15 45 18 77 40 10 87 70 72...
output:
994347719
result:
ok 1 number(s): "994347719"
Test #19:
score: 0
Accepted
time: 210ms
memory: 35076kb
input:
100000 1 1 1 4 3 3 5 8 8 1 4 9 9 14 6 12 5 3 2 9 14 4 15 11 14 14 12 18 3 22 25 1 23 1 15 8 21 35 31 34 15 23 30 13 32 18 22 33 32 18 36 46 36 27 45 16 4 35 48 12 29 1 59 64 33 12 4 1 53 8 29 16 18 67 75 7 54 18 74 21 55 69 47 54 42 56 2 85 3 90 81 42 15 90 9 41 72 68 43 58 28 87 38 22 39 29 26 44 2...
output:
946042832
result:
ok 1 number(s): "946042832"
Test #20:
score: 0
Accepted
time: 65ms
memory: 15384kb
input:
40000 1 2 2 4 1 6 5 3 3 6 3 3 4 6 10 12 1 18 18 4 11 3 9 14 25 13 14 18 4 3 1 6 13 16 9 17 37 13 38 7 10 36 13 8 22 3 17 1 20 12 33 37 8 10 25 35 41 52 10 35 36 59 20 25 32 62 18 5 3 22 66 13 2 52 38 30 62 18 35 77 51 58 32 34 44 2 70 85 46 2 80 84 67 91 91 80 19 13 42 99 75 36 38 51 62 93 96 37 96 ...
output:
599775439
result:
ok 1 number(s): "599775439"
Extra Test:
score: 0
Extra Test Passed