結果
| 問題 | No.2896 Monotonic Prime Factors |
| ユーザー |
 Aging1986
|
| 提出日時 | 2024-09-22 12:11:08 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 194 ms / 2,000 ms |
| コード長 | 22,116 bytes |
| コンパイル時間 | 2,605 ms |
| コンパイル使用メモリ | 221,176 KB |
| 実行使用メモリ | 82,220 KB |
| 最終ジャッジ日時 | 2024-09-22 12:11:17 |
| 合計ジャッジ時間 | 8,702 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
（要ログイン）
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 | 123 ms
82,048 KB |
| testcase_01 | AC | 115 ms
82,116 KB |
| testcase_02 | AC | 116 ms
82,092 KB |
| testcase_03 | AC | 115 ms
81,988 KB |
| testcase_04 | AC | 144 ms
82,076 KB |
| testcase_05 | AC | 194 ms
82,012 KB |
| testcase_06 | AC | 157 ms
82,220 KB |
| testcase_07 | AC | 145 ms
82,000 KB |
| testcase_08 | AC | 144 ms
81,988 KB |
| testcase_09 | AC | 173 ms
82,116 KB |
| testcase_10 | AC | 135 ms
82,060 KB |
| testcase_11 | AC | 120 ms
81,988 KB |
| testcase_12 | AC | 134 ms
82,040 KB |
| testcase_13 | AC | 136 ms
82,004 KB |
| testcase_14 | AC | 145 ms
81,940 KB |
| testcase_15 | AC | 117 ms
82,168 KB |
| testcase_16 | AC | 124 ms
82,136 KB |
| testcase_17 | AC | 118 ms
82,064 KB |
| testcase_18 | AC | 152 ms
81,988 KB |
| testcase_19 | AC | 120 ms
82,048 KB |
ソースコード
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll, ll> pll;
typedef pair<int, int> pii;
typedef pair<double, double> pdd;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<double> vd;
typedef vector<string> vs;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<vll> vvll;
typedef vector<vvll> vvvll;
typedef vector<pii> vpii;
typedef vector<vpii> vvpii;
typedef vector<pll> vpll;
typedef vector<vpll> vvpll;
typedef vector<pdd> vpdd;
typedef vector<vd> vvd;
#define yn(ans) printf("%s\n", (ans)?"Yes":"No");
#define YN(ans) printf("%s\n", (ans)?"YES":"NO");
template<class T> bool chmax(T &a, T b) {
if (a >= b) return false;
a = b; return true;
}
template<class T> bool chmin(T &a, T b) {
if (a <= b) return false;
a = b; return true;
}
#define FOR(i, s, e, t) for ((i) = (s); (i) < (e); (i) += (t))
#define REP(i, e) for (int i = 0; i < (e); ++i)
#define REP1(i, s, e) for (int i = (s); i < (e); ++i)
#define RREP(i, e) for (int i = (e); i >= 0; --i)
#define RREP1(i, e, s) for (int i = (e); i >= (s); --i)
#define all(v) v.begin(), v.end()
#define pb push_back
#define qb pop_back
#define pf push_front
#define qf pop_front
#define maxe max_element
#define mine min_element
ll inf = 1e18;
#define DEBUG printf("%d\n", __LINE__); fflush(stdout);
template<class T> void print(vector<T> &v, bool withSize = false) {
if (withSize) cout << v.size() << endl;
REP(i, v.size()) cout << v[i] << " ";
cout << endl;
}
mt19937_64 rng((unsigned int) chrono::steady_clock::now().time_since_epoch().count());
int __FAST_IO__ = []() {
std::ios::sync_with_stdio(0);
std::cin.tie(0);
std::cout.tie(0);
return 0;
}();
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
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`
explicit 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 long long y = x * _m;
return (unsigned int)(z - y + (z < y ? _m : 0));
}
};
// @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);
// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
unsigned long long floor_sum_unsigned(unsigned long long n,
unsigned long long m,
unsigned long long a,
unsigned long long b) {
unsigned long long ans = 0;
while (true) {
if (a >= m) {
ans += n * (n - 1) / 2 * (a / m);
a %= m;
}
if (b >= m) {
ans += n * (b / m);
b %= m;
}
unsigned long long y_max = a * n + b;
if (y_max < m) break;
// y_max < m * (n + 1)
// floor(y_max / m) <= n
n = (unsigned long long)(y_max / m);
b = (unsigned long long)(y_max % m);
std::swap(m, a);
}
return ans;
}
} // namespace internal
} // namespace atcoder
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
using Mint = atcoder::modint998244353;
using Mint2 = atcoder::modint1000000007;
typedef vector<Mint> vm;
typedef vector<vm> vvm;
typedef vector<vvm> vvvm;
vector<Mint> fac, ifac;
void initFac(int N) {
fac.resize(N + 1);
ifac.resize(N + 1);
fac[0] = ifac[0] = 1;
REP1(i, 1, N + 1) {
fac[i] = fac[i - 1] * i;
}
ifac[N] = 1 / fac[N];
RREP1(i, N - 1, 1) {
ifac[i] = (i + 1) * ifac[i + 1];
}
}
Mint C(int m, int n) {
if (m < n || n < 0) return 0;
return fac[m] * ifac[n] * ifac[m - n];
}
Mint P(int m, int n) {
if (m < n || n < 0) return 0;
return fac[m] * ifac[m - n];
}
vector<vector<Mint>> fastmulti(vector<vector<Mint>> &a, vector<vector<Mint>> &b) {
vector<vector<Mint>> ans(a.size(), vector<Mint>(b[0].size(), Mint(0)));
REP(i, a.size()) {
REP(j, a[0].size()) {
REP(k, b[0].size()) {
ans[i][k] += a[i][j] * b[j][k];
}
}
}
return ans;
}
vector<vector<Mint>> pow(vector<vector<Mint>> &a, ll k) {
vector<vector<Mint>> res(a.size(), vector<Mint>(a.size(), 0)), y = a;
REP(i, a.size()) res[i][i] = 1;
while (k) {
if (k & 1) res = fastmulti(y, res);
y = fastmulti(y, y);
k >>= 1;
}
return res;
}
template< typename Mint >
struct NumberTheoreticTransformFriendlyModInt {
vector< Mint > dw, idw;
int max_base;
Mint root;
NumberTheoreticTransformFriendlyModInt() {
const unsigned mod = Mint::mod();
assert(mod >= 3 && mod % 2 == 1);
auto tmp = mod - 1;
max_base = 0;
while(tmp % 2 == 0) tmp >>= 1, max_base++;
root = 2;
while(root.pow((mod - 1) >> 1) == 1) root += 1;
assert(root.pow(mod - 1) == 1);
dw.resize(max_base);
idw.resize(max_base);
for(int i = 0; i < max_base; i++) {
dw[i] = -root.pow((mod - 1) >> (i + 2));
idw[i] = Mint(1) / dw[i];
}
}
void ntt(vector< Mint > &a) {
const int n = (int) a.size();
assert((n & (n - 1)) == 0);
assert(__builtin_ctz(n) <= max_base);
for(int m = n; m >>= 1;) {
Mint w = 1;
for(int s = 0, k = 0; s < n; s += 2 * m) {
for(int i = s, j = s + m; i < s + m; ++i, ++j) {
auto x = a[i], y = a[j] * w;
a[i] = x + y, a[j] = x - y;
}
w *= dw[__builtin_ctz(++k)];
}
}
}
void intt(vector< Mint > &a, bool f = true) {
const int n = (int) a.size();
assert((n & (n - 1)) == 0);
assert(__builtin_ctz(n) <= max_base);
for(int m = 1; m < n; m *= 2) {
Mint w = 1;
for(int s = 0, k = 0; s < n; s += 2 * m) {
for(int i = s, j = s + m; i < s + m; ++i, ++j) {
auto x = a[i], y = a[j];
a[i] = x + y, a[j] = (x - y) * w;
}
w *= idw[__builtin_ctz(++k)];
}
}
if(f) {
Mint inv_sz = Mint(1) / n;
for(int i = 0; i < n; i++) a[i] *= inv_sz;
}
}
vector< Mint > multiply(vector< Mint > a, vector< Mint > b) {
int need = a.size() + b.size() - 1;
int nbase = 1;
while((1 << nbase) < need) nbase++;
int sz = 1 << nbase;
a.resize(sz, 0);
b.resize(sz, 0);
ntt(a);
ntt(b);
Mint inv_sz = Mint(1) / sz;
for(int i = 0; i < sz; i++) a[i] *= b[i] * inv_sz;
intt(a, false);
a.resize(need);
return a;
}
void sq(vector<Mint> &a, vector<Mint> &b, bool mult) {
int need = a.size() + b.size() - 1;
int nbase = 1;
while((1 << nbase) < need) nbase++;
int sz = 1 << nbase;
b.resize(sz, 0);
ntt(b);
Mint inv_sz = Mint(1) / sz;
if (mult) {
a.resize(sz, 0);
ntt(a);
for(int i = 0; i < sz; i++) a[i] *= b[i] * inv_sz;
intt(a, false);
a.resize(need);
}
for (int i = 0; i < sz; i++) b[i] *= b[i] * inv_sz;
intt(b, false);
b.resize(need);
}
void pow(vector<Mint> &a, vector<Mint> &b, int p) {
int len = a.size();
while (p) {
sq(a, b, p & 1);
a.resize(len);
b.resize(len);
p >>= 1;
}
}
};
NumberTheoreticTransformFriendlyModInt<Mint> ntt;
// O(nloglogn) prime generation, f: sum of gcd(i, j) for all 1 <= j <= i
vector<bool> is_prime;
vector<int> prime, sub;
void init_prime(int n) {
is_prime.resize(n + 1, true);
sub.resize(n + 1, 1);
for (int i = 2; i <= n; ++i) {
if (is_prime[i]) {
prime.push_back(i);
sub[i] = i;
}
for (int j = 0; prime[j] * i <= n && prime[j] <= sub[i] && j < prime.size(); ++j) {
is_prime[prime[j] * i] = false;
sub[prime[j] * i] = prime[j];
if (i % prime[j] == 0) break;
}
}
}
#define TESTS int t; cin >> t; while (t--)
#define TEST
int main() {
init_prime(1e5);
initFac(1e7);
int len = 0;
TESTS {
int A, B;
cin >> A >> B;
while (A > 1) {
int y = sub[A];
len++, A /= y;
}
printf("%d\n", C(len - 1, B - 1).val());
}
return 0;
}