結果
| 問題 | No.2130 分配方法の数え上げ mod 998244353 |
| ユーザー |
 cubinglover
|
| 提出日時 | 2022-11-25 21:35:57 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
RE
|
| 実行時間 | - |
| コード長 | 13,274 bytes |
| コンパイル時間 | 2,050 ms |
| コンパイル使用メモリ | 202,324 KB |
| 実行使用メモリ | 6,820 KB |
| 最終ジャッジ日時 | 2024-10-02 04:10:14 |
| 合計ジャッジ時間 | 5,724 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge2 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 8 ms
6,816 KB |
| testcase_01 | AC | 9 ms
6,820 KB |
| testcase_02 | AC | 9 ms
6,816 KB |
| testcase_03 | AC | 9 ms
6,816 KB |
| testcase_04 | AC | 8 ms
6,816 KB |
| testcase_05 | AC | 9 ms
6,816 KB |
| testcase_06 | AC | 8 ms
6,820 KB |
| testcase_07 | AC | 10 ms
6,816 KB |
| testcase_08 | AC | 9 ms
6,820 KB |
| testcase_09 | AC | 9 ms
6,820 KB |
| testcase_10 | AC | 9 ms
6,816 KB |
| testcase_11 | AC | 9 ms
6,816 KB |
| testcase_12 | AC | 9 ms
6,820 KB |
| testcase_13 | AC | 9 ms
6,816 KB |
| testcase_14 | AC | 10 ms
6,816 KB |
| testcase_15 | AC | 8 ms
6,816 KB |
| testcase_16 | AC | 9 ms
6,816 KB |
| testcase_17 | AC | 9 ms
6,816 KB |
| testcase_18 | AC | 9 ms
6,816 KB |
| testcase_19 | AC | 8 ms
6,816 KB |
| testcase_20 | RE | - |
| testcase_21 | RE | - |
| testcase_22 | RE | - |
| testcase_23 | WA | - |
| testcase_24 | RE | - |
| testcase_25 | WA | - |
| testcase_26 | RE | - |
| testcase_27 | RE | - |
| testcase_28 | WA | - |
| testcase_29 | WA | - |
| testcase_30 | RE | - |
| testcase_31 | RE | - |
| testcase_32 | RE | - |
| testcase_33 | RE | - |
| testcase_34 | RE | - |
| testcase_35 | RE | - |
| testcase_36 | RE | - |
| testcase_37 | RE | - |
ソースコード
#include <bits/stdc++.h>
using namespace std;
#define repl(i, l, r) for (int i = (l); i < (int)(r); ++i)
#define rep(i, n) repl(i, 0, n)
#define CST(x) cout << fixed << setprecision(x)
#define all(x) (x).begin(), (x).end()
#define sz(x) (int)(x).size()
using ll = long long;
constexpr ll MOD = 998244353;
constexpr int inf = 1e9 + 10;
constexpr ll INF = (ll)4e18 + 10;
constexpr int dx[9] = {1, 0, -1, 0, 1, -1, -1, 1, 0};
constexpr int dy[9] = {0, 1, 0, -1, 1, 1, -1, -1, 0};
const double PI = acos(-1);
template <typename T>
using MaxHeap = priority_queue<T>;
template <typename T>
using MinHeap = priority_queue<T, vector<T>, greater<T>>;
template <typename T>
inline bool chmax(T& a, T b) {
return ((a < b) ? (a = b, true) : (false));
}
template <typename T>
inline bool chmin(T& a, T b) {
return ((a > b) ? (a = b, true) : (false));
}
template <typename T>
inline void yn(const T& a) {
((a) ? (cout << "Yes" << endl) : (cout << "No" << endl));
}
template <typename T>
inline void YN(const T& a) {
((a) ? (cout << "YES" << endl) : (cout << "NO" << endl));
}
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<(internal::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
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
struct barrett {
unsigned int _m;
unsigned long long im;
barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
unsigned int umod() const { return _m; }
unsigned int mul(unsigned int a, unsigned int b) const {
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;
}
};
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;
}
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);
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};
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;
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
if (m0 < 0) m0 += b / s;
return {s, m0};
}
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>;
template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : 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 = 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 = is_prime<m>;
};
template <int id>
struct dynamic_modint : modint_base {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = 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 = 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 barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id>
barrett dynamic_modint<id>::bt = 998244353;
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
template <class T>
using is_static_modint = std::is_base_of<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>;
using mint = modint998244353;
constexpr ll MAX = 210000;
mint fac[MAX], finv[MAX], inv[MAX];
void COMinit() {
fac[0] = fac[1] = 1;
finv[0] = finv[1] = 1;
inv[1] = 1;
repl(i, 2, MAX) {
fac[i] = fac[i - 1] * i;
inv[i] = MOD - inv[MOD % i] * (MOD / i);
finv[i] = finv[i - 1] * inv[i];
}
}
mint COM(int n, int k) {
if (n < k) return 0;
if (n < 0 or k < 0) return 0;
return fac[n] * finv[k] * finv[n - k];
}
int main() {
cin.tie(nullptr);
cout.tie(nullptr);
ios::sync_with_stdio(false);
COMinit();
mint n, m;
ll N, M;
cin >> N >> M;
n = N, m = M;
mint ans = 2;
ans = ans.pow(N);
rep(i, M) ans -= COM(N, i);
cout << ans.val() << endl;
return 0;
}