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ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#279966 | #7774. 基础寄术练习题 | georgeyucjr | 100 ✓ | 73ms | 8376kb | C++23 | 16.2kb | 2023-12-09 13:03:02 | 2023-12-09 13:03:03 |
Judging History
answer
# include <bits/stdc++.h>
# pragma GCC optimize(2,3,"Ofast","unroll-loops","inline")
# pragma GCC target("avx2")
#ifndef ATCODER_MODINT_HPP
#define ATCODER_MODINT_HPP 1
#include <type_traits>
#ifdef _MSC_VER
#include <intrin.h>
#endif
#ifndef ATCODER_INTERNAL_MATH_HPP
#define ATCODER_INTERNAL_MATH_HPP 1
#include <utility>
#ifdef _MSC_VER
#include <intrin.h>
#endif
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
#endif // ATCODER_INTERNAL_MATH_HPP
#ifndef ATCODER_INTERNAL_TYPE_TRAITS_HPP
#define ATCODER_INTERNAL_TYPE_TRAITS_HPP 1
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
#endif // ATCODER_INTERNAL_TYPE_TRAITS_HPP
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()); }
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()); }
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
#endif // ATCODER_MODINT_HPP
using mint = atcoder :: dynamic_modint < -1 >;
using namespace std;
# define ll long long
# define ull unsigned long long
# define rep(i, f, t, ...) for (int i = f, ##__VA_ARGS__; i <= t; ++i)
# define red(i, f, t, ...) for (int i = f, ##__VA_ARGS__; i >= t; --i)
# define emb emplace_back
# define pb push_back
# define pii pair<int, int>
# define mkp make_pair
# define arr3 array<int, 3>
# define arr4 array<int, 4>
# define FILEIO(filename) freopen (filename".in", "r", stdin), freopen (filename ".out", "w", stdout)
# define N
template < class T > constexpr static T inf = numeric_limits < T > :: max ( ) / 2;
# ifdef MACOS
# include "/Users/yzw/GeorgeYuOI/codes/cpp/georgeyucjr/debug/debug.hpp"
using namespace georgeyucjr;
# else
# define write(...) void ( 36 )
# define bug(...) void ( 36 )
# endif
bool Mst;
int n, m, k, mod;
struct Binom {
int lim ;
vector < mint > fac, ifac, inv;
inline void Init () {
fac[0] = inv[1] = 1; rep (i, 1, lim) fac[i] = fac[i - 1] * i;
ifac[lim] = fac[lim].inv () ; red (i, lim, 1)ifac[i - 1] = ifac[i] * i;
rep (i, 2, lim)inv[i] = -( mod / i ) *inv[mod % i];
}
inline void resize (int _){
lim = _;
fac.resize ( lim + 5 );
ifac.resize ( lim + 5 );
inv.resize ( lim + 5 );
Init ();
}
inline mint C (int n, int m) {
if (n < 0 || m < 0 || n < m) return 0;
assert(n <= lim);
return fac[n] * ifac[n - m ] *ifac[m];
}
} binom;
mint f[105][5505], g[105][5505];
bool Med;
signed main() {
ios_base :: sync_with_stdio ( false ), cin.tie ( nullptr ), cout.tie (nullptr);
cin >> n >> m >> k >> mod;
mint :: set_mod(mod);
binom.resize ( 10000 );
// rep (i, 1, 10) cerr << binom.inv[i].val ( ) << " "; cerr << endl;
memset(f, 0, sizeof f);
memset(g, 0, sizeof g);
fill ( f[0], f[0] + ( m * (m + 1) >> 1 ) + 1, 1 );
red (i, m, 1) {
int s = ( i - 1 ) * i >> 1;
red (j, m - i, 1) rep (x, 0, s) {
g[j + 1][x] += 2 * f[j][x + i];
g[j + 1][x] += binom.inv[i] * (g[j][x] - g[j][x + i]);
}
rep (x, 0 , s) ++g[1][x];
red (j, m - i, 0) rep (x, 0, s) {
f[j + 1][x] += binom.inv[x + i] * f[j][x + i];
f[j + 1][x] += binom.inv[i] * (f[j][x] - f[j][x + i]);
}
}
cout << ( k == 1 ? f[n][0] : g[n][0] ) .val () << endl;
# ifdef MACOS
cerr << "Memory & Time Information : " << endl;
cerr << "Memory : " << ( ( &Med ) - ( &Mst ) ) * 1. / 1024. / 1024. << "MB" << endl;
cerr << "Time : " << clock ( ) * 1. / CLOCKS_PER_SEC * 1000. << "ms" << endl;
# endif
return 0;
}
Details
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Subtask #1:
score: 10
Accepted
Test #1:
score: 10
Accepted
time: 3ms
memory: 8304kb
input:
9 16 1 327134593
output:
162102742
result:
ok single line: '162102742'
Test #2:
score: 0
Accepted
time: 3ms
memory: 8368kb
input:
11 18 1 834359503
output:
256188485
result:
ok single line: '256188485'
Test #3:
score: 0
Accepted
time: 0ms
memory: 8364kb
input:
18 18 1 614802701
output:
552168146
result:
ok single line: '552168146'
Test #4:
score: 0
Accepted
time: 3ms
memory: 8368kb
input:
7 16 2 861918403
output:
306693876
result:
ok single line: '306693876'
Test #5:
score: 0
Accepted
time: 3ms
memory: 8224kb
input:
11 17 2 617904383
output:
393900291
result:
ok single line: '393900291'
Subtask #2:
score: 25
Accepted
Test #6:
score: 25
Accepted
time: 66ms
memory: 8240kb
input:
60 98 1 715015339
output:
690737273
result:
ok single line: '690737273'
Test #7:
score: 0
Accepted
time: 68ms
memory: 8240kb
input:
96 97 1 507892589
output:
481151247
result:
ok single line: '481151247'
Test #8:
score: 0
Accepted
time: 59ms
memory: 8328kb
input:
90 95 1 621080027
output:
255353202
result:
ok single line: '255353202'
Test #9:
score: 0
Accepted
time: 57ms
memory: 8312kb
input:
85 94 1 297115421
output:
122254364
result:
ok single line: '122254364'
Test #10:
score: 0
Accepted
time: 54ms
memory: 8296kb
input:
81 91 1 460412027
output:
148037986
result:
ok single line: '148037986'
Subtask #3:
score: 15
Accepted
Test #11:
score: 15
Accepted
time: 3ms
memory: 8248kb
input:
29 29 2 545875273
output:
171843225
result:
ok single line: '171843225'
Test #12:
score: 0
Accepted
time: 0ms
memory: 8244kb
input:
29 29 2 342070607
output:
291380196
result:
ok single line: '291380196'
Test #13:
score: 0
Accepted
time: 3ms
memory: 8248kb
input:
30 30 2 293965439
output:
148471965
result:
ok single line: '148471965'
Test #14:
score: 0
Accepted
time: 4ms
memory: 8324kb
input:
30 30 2 528219961
output:
203632962
result:
ok single line: '203632962'
Test #15:
score: 0
Accepted
time: 0ms
memory: 8296kb
input:
30 30 1 202836509
output:
158493990
result:
ok single line: '158493990'
Subtask #4:
score: 10
Accepted
Test #16:
score: 10
Accepted
time: 3ms
memory: 8324kb
input:
27 30 2 360712453
output:
80987914
result:
ok single line: '80987914'
Test #17:
score: 0
Accepted
time: 3ms
memory: 8256kb
input:
26 29 2 377615957
output:
278812897
result:
ok single line: '278812897'
Test #18:
score: 0
Accepted
time: 3ms
memory: 8248kb
input:
22 30 2 163686233
output:
19517828
result:
ok single line: '19517828'
Test #19:
score: 0
Accepted
time: 3ms
memory: 8248kb
input:
20 29 2 785657729
output:
713061509
result:
ok single line: '713061509'
Test #20:
score: 0
Accepted
time: 3ms
memory: 8300kb
input:
24 29 1 374090597
output:
312615700
result:
ok single line: '312615700'
Subtask #5:
score: 15
Accepted
Test #21:
score: 15
Accepted
time: 0ms
memory: 8308kb
input:
29 38 2 909155077
output:
745973305
result:
ok single line: '745973305'
Test #22:
score: 0
Accepted
time: 0ms
memory: 8244kb
input:
40 40 2 1067474879
output:
995503334
result:
ok single line: '995503334'
Test #23:
score: 0
Accepted
time: 0ms
memory: 8304kb
input:
32 37 2 751116719
output:
699924081
result:
ok single line: '699924081'
Test #24:
score: 0
Accepted
time: 4ms
memory: 8376kb
input:
33 37 2 496100951
output:
21741458
result:
ok single line: '21741458'
Test #25:
score: 0
Accepted
time: 4ms
memory: 8308kb
input:
34 38 1 499914887
output:
386116226
result:
ok single line: '386116226'
Subtask #6:
score: 10
Accepted
Test #26:
score: 10
Accepted
time: 13ms
memory: 8372kb
input:
57 66 2 767174999
output:
315351738
result:
ok single line: '315351738'
Test #27:
score: 0
Accepted
time: 20ms
memory: 8312kb
input:
52 69 2 399947623
output:
237685494
result:
ok single line: '237685494'
Test #28:
score: 0
Accepted
time: 12ms
memory: 8308kb
input:
63 64 2 903693961
output:
520250635
result:
ok single line: '520250635'
Test #29:
score: 0
Accepted
time: 21ms
memory: 8372kb
input:
65 70 2 268454909
output:
255864893
result:
ok single line: '255864893'
Test #30:
score: 0
Accepted
time: 19ms
memory: 8320kb
input:
58 68 1 562105223
output:
175445185
result:
ok single line: '175445185'
Subtask #7:
score: 15
Accepted
Test #31:
score: 15
Accepted
time: 62ms
memory: 8320kb
input:
96 96 2 453296971
output:
222864385
result:
ok single line: '222864385'
Test #32:
score: 0
Accepted
time: 65ms
memory: 8304kb
input:
85 96 2 859572601
output:
457416092
result:
ok single line: '457416092'
Test #33:
score: 0
Accepted
time: 60ms
memory: 8300kb
input:
89 94 2 753918677
output:
366789523
result:
ok single line: '366789523'
Test #34:
score: 0
Accepted
time: 56ms
memory: 8240kb
input:
91 92 2 202806031
output:
64270709
result:
ok single line: '64270709'
Test #35:
score: 0
Accepted
time: 73ms
memory: 8304kb
input:
100 100 1 493945957
output:
109570004
result:
ok single line: '109570004'