結果

問題 No.2896 Monotonic Prime Factors
ユーザー AerenAeren
提出日時 2024-09-20 21:40:55
言語 C++23
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 198 ms / 2,000 ms
コード長 14,044 bytes
コンパイル時間 2,836 ms
コンパイル使用メモリ 253,156 KB
実行使用メモリ 120,968 KB
最終ジャッジ日時 2024-09-20 21:41:03
合計ジャッジ時間 7,994 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge2
このコードへのチャレンジ
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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 163 ms
120,956 KB
testcase_01 AC 145 ms
120,888 KB
testcase_02 AC 146 ms
120,960 KB
testcase_03 AC 143 ms
120,928 KB
testcase_04 AC 171 ms
120,824 KB
testcase_05 AC 196 ms
120,948 KB
testcase_06 AC 185 ms
120,960 KB
testcase_07 AC 172 ms
120,900 KB
testcase_08 AC 171 ms
120,880 KB
testcase_09 AC 198 ms
120,968 KB
testcase_10 AC 163 ms
120,832 KB
testcase_11 AC 179 ms
120,832 KB
testcase_12 AC 146 ms
120,960 KB
testcase_13 AC 165 ms
120,952 KB
testcase_14 AC 170 ms
120,960 KB
testcase_15 AC 147 ms
120,940 KB
testcase_16 AC 152 ms
120,848 KB
testcase_17 AC 148 ms
120,900 KB
testcase_18 AC 175 ms
120,796 KB
testcase_19 AC 176 ms
120,796 KB
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ソースコード

diff # 

// #include <bits/allocator.h> // Temp fix for gcc13 global pragma
// #pragma GCC target("avx2,bmi2,popcnt,lzcnt")
// #pragma GCC optimize("O3,unroll-loops")
#include <bits/stdc++.h>
// #include <x86intrin.h>
using namespace std;
#if __cplusplus >= 202002L
using namespace numbers;
#endif
#ifdef LOCAL
	#include "Debug.h"
#else
	#define debug_endl() 42
	#define debug(...) 42
	#define debug2(...) 42
	#define debugbin(...) 42
#endif

struct number_theory{
	int SZ;
	vector<int> lpf, prime;
	number_theory(int SZ): SZ(SZ), lpf(SZ + 1){ // O(SZ)
		lpf[0] = lpf[1] = numeric_limits<int>::max() / 2;
		for(auto i = 2; i <= SZ; ++ i){
			if(!lpf[i]) lpf[i] = i, prime.push_back(i);
			for(auto j = 0; j < (int)prime.size() && prime[j] <= lpf[i] && prime[j] * i <= SZ; ++ j) lpf[prime[j] * i] = prime[j];
		}
	}
	vector<int> precalc_mobius() const{
		vector<int> mobius(SZ + 1, 1);
		for(auto i = 2; i <= SZ; ++ i){
			if(i / lpf[i] % lpf[i]) mobius[i] = -mobius[i / lpf[i]];
			else mobius[i] = 0;
		}
		return mobius;
	}
	vector<int> precalc_phi() const{
		vector<int> phi(SZ + 1, 1);
		for(auto i = 2; i <= SZ; ++ i){
			if(i / lpf[i] % lpf[i]) phi[i] = phi[i / lpf[i]] * (lpf[i] - 1);
			else phi[i] = phi[i / lpf[i]] * lpf[i];
		}
		return phi;
	}
	// Returns {gcd(0, n), ..., gcd(SZ, n)}
	vector<int> precalc_gcd(int n) const{
		vector<int> res(SZ + 1, 1);
		res[0] = n;
		for(auto x = 2; x <= SZ; ++ x) res[x] = n % (lpf[x] * res[x / lpf[x]]) ? res[x / lpf[x]] : lpf[x] * res[x / lpf[x]];
		return res;
	}
	bool is_prime(int x) const{
		assert(0 <= x && x <= SZ);
		return lpf[x] == x;
	}
	int mu_large(long long x) const{ // O(sqrt(x))
		int res = 1;
		for(auto i = 2LL; i * i <= x; ++ i) if(x % i == 0){
			if(x / i % i) return 0;
			x /= i, res = -res;
		}
		if(x > 1) res = -res;
		return res;
	}
	long long phi_large(long long x) const{ // O(sqrt(x))
		long long res = x;
		for(auto i = 2LL; i * i <= x; ++ i) if(x % i == 0){
			while(x % i == 0) x /= i;
			res -= res / i;
		}
		if(x > 1) res -= res / x;
		return res;
	}
	// returns an array is_prime of length high-low where is_prime[i] = [low+i is a prime]
	vector<int> sieve(long long low, long long high) const{
		assert(high - 1 <= 1LL * SZ * SZ);
		vector<int> is_prime(high - low, true);
		for(auto p: prime) for(auto x = max(1LL * p, (low + p - 1) / p) * p; x < high; x += p) is_prime[x - low] = false;
		for(auto x = 1; x >= low; -- x) is_prime[x - low] = false;
		return is_prime;
	}
};

template<class data_t, data_t _mod>
struct modular_fixed_base{
#define IS_INTEGRAL(T) (is_integral_v<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
#define IS_UNSIGNED(T) (is_unsigned_v<T> || is_same_v<T, __uint128_t>)
	static_assert(IS_UNSIGNED(data_t));
	static_assert(_mod >= 1);
	static constexpr bool VARIATE_MOD_FLAG = false;
	static constexpr data_t mod(){
		return _mod;
	}
	template<class T>
	static vector<modular_fixed_base> precalc_power(T base, int SZ){
		vector<modular_fixed_base> res(SZ + 1, 1);
		for(auto i = 1; i <= SZ; ++ i) res[i] = res[i - 1] * base;
		return res;
	}
	template<class T>
	static vector<modular_fixed_base> precalc_geometric_sum(T base, int SZ){
		vector<modular_fixed_base> res(SZ + 1);
		for(auto i = 1; i <= SZ; ++ i) res[i] = res[i - 1] * base + base;
		return res;
	}
	static vector<modular_fixed_base> _INV;
	static void precalc_inverse(int SZ){
		if(_INV.empty()) _INV.assign(2, 1);
		for(auto x = _INV.size(); x <= SZ; ++ x) _INV.push_back(_mod / x * -_INV[_mod % x]);
	}
	// _mod must be a prime
	static modular_fixed_base _primitive_root;
	static modular_fixed_base primitive_root(){
		if(_primitive_root) return _primitive_root;
		if(_mod == 2) return _primitive_root = 1;
		if(_mod == 998244353) return _primitive_root = 3;
		data_t divs[20] = {};
		divs[0] = 2;
		int cnt = 1;
		data_t x = (_mod - 1) / 2;
		while(x % 2 == 0) x /= 2;
		for(auto i = 3; 1LL * 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(auto g = 2; ; ++ g){
			bool ok = true;
			for(auto i = 0; i < cnt; ++ i){
				if(modular_fixed_base(g).power((_mod - 1) / divs[i]) == 1){
					ok = false;
					break;
				}
			}
			if(ok) return _primitive_root = g;
		}
	}
	constexpr modular_fixed_base(){ }
	modular_fixed_base(const double &x){ data = _normalize(llround(x)); }
	modular_fixed_base(const long double &x){ data = _normalize(llround(x)); }
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> modular_fixed_base(const T &x){ data = _normalize(x); }
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> static data_t _normalize(const T &x){
		int sign = x >= 0 ? 1 : -1;
		data_t v =  _mod <= sign * x ? sign * x % _mod : sign * x;
		if(sign == -1 && v) v = _mod - v;
		return v;
	}
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> operator T() const{ return data; }
	modular_fixed_base &operator+=(const modular_fixed_base &otr){ if((data += otr.data) >= _mod) data -= _mod; return *this; }
	modular_fixed_base &operator-=(const modular_fixed_base &otr){ if((data += _mod - otr.data) >= _mod) data -= _mod; return *this; }
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> modular_fixed_base &operator+=(const T &otr){ return *this += modular_fixed_base(otr); }
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> modular_fixed_base &operator-=(const T &otr){ return *this -= modular_fixed_base(otr); }
	modular_fixed_base &operator++(){ return *this += 1; }
	modular_fixed_base &operator--(){ return *this += _mod - 1; }
	modular_fixed_base operator++(int){ modular_fixed_base result(*this); *this += 1; return result; }
	modular_fixed_base operator--(int){ modular_fixed_base result(*this); *this += _mod - 1; return result; }
	modular_fixed_base operator-() const{ return modular_fixed_base(_mod - data); }
	modular_fixed_base &operator*=(const modular_fixed_base &rhs){
		if constexpr(is_same_v<data_t, unsigned int>) data = (unsigned long long)data * rhs.data % _mod;
		else if constexpr(is_same_v<data_t, unsigned long long>){
			long long res = data * rhs.data - _mod * (unsigned long long)(1.L / _mod * data * rhs.data);
			data = res + _mod * (res < 0) - _mod * (res >= (long long)_mod);
		}
		else data = _normalize(data * rhs.data);
		return *this;
	}
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>
	modular_fixed_base &inplace_power(T e){
		if(e == 0) return *this = 1;
		if(data == 0) return *this = {};
		if(data == 1 || e == 1) return *this;
		if(data == mod() - 1) return e % 2 ? *this : *this = -*this;
		if(e < 0) *this = 1 / *this, e = -e;
		if(e == 1) return *this;
		modular_fixed_base res = 1;
		for(; e; *this *= *this, e >>= 1) if(e & 1) res *= *this;
		return *this = res;
	}
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>
	modular_fixed_base power(T e) const{
		return modular_fixed_base(*this).inplace_power(e);
	}
	// c + c * x + ... + c * x^{e-1}
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>
	modular_fixed_base &inplace_geometric_sum(T e, modular_fixed_base c = 1){
		if(e == 0) return *this = {};
		if(data == 0) return *this = {};
		if(data == 1) return *this = c * e;
		if(e == 1) return *this = c;
		if(data == mod() - 1) return *this = c * abs(e % 2);
		modular_fixed_base res = 0;
		if(e < 0) return *this = geometric_sum(-e + 1, -*this) - 1;
		if(e == 1) return *this = c * *this;
		for(; e; c *= 1 + *this, *this *= *this, e >>= 1) if(e & 1) res += c, c *= *this;
		return *this = res;
	}
	// c + c * x + ... + c * x^{e-1}
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>
	modular_fixed_base geometric_sum(T e, modular_fixed_base c = 1) const{
		return modular_fixed_base(*this).inplace_geometric_sum(e, c);
	}
	modular_fixed_base &operator/=(const modular_fixed_base &otr){
		make_signed_t<data_t> a = otr.data, m = _mod, u = 0, v = 1;
		if(a < _INV.size()) return *this *= _INV[a];
		while(a){
			make_signed_t<data_t> t = m / a;
			m -= t * a; swap(a, m);
			u -= t * v; swap(u, v);
		}
		assert(m == 1);
		return *this *= u;
	}
#define ARITHMETIC_OP(op, apply_op)\
modular_fixed_base operator op(const modular_fixed_base &x) const{ return modular_fixed_base(*this) apply_op x; }\
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>\
modular_fixed_base operator op(const T &x) const{ return modular_fixed_base(*this) apply_op modular_fixed_base(x); }\
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>\
friend modular_fixed_base operator op(const T &x, const modular_fixed_base &y){ return modular_fixed_base(x) apply_op y; }
	ARITHMETIC_OP(+, +=) ARITHMETIC_OP(-, -=) ARITHMETIC_OP(*, *=) ARITHMETIC_OP(/, /=)
#undef ARITHMETIC_OP
#define COMPARE_OP(op)\
bool operator op(const modular_fixed_base &x) const{ return data op x.data; }\
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>\
bool operator op(const T &x) const{ return data op modular_fixed_base(x).data; }\
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>\
friend bool operator op(const T &x, const modular_fixed_base &y){ return modular_fixed_base(x).data op y.data; }
	COMPARE_OP(==) COMPARE_OP(!=) COMPARE_OP(<) COMPARE_OP(<=) COMPARE_OP(>) COMPARE_OP(>=)
#undef COMPARE_OP
	friend istream &operator>>(istream &in, modular_fixed_base &number){
		long long x;
		in >> x;
		number.data = modular_fixed_base::_normalize(x);
		return in;
	}
//#define _SHOW_FRACTION
	friend ostream &operator<<(ostream &out, const modular_fixed_base &number){
		out << number.data;
	#if defined(LOCAL) && defined(_SHOW_FRACTION)
		cerr << "(";
		for(auto d = 1; ; ++ d){
			if((number * d).data <= 1000000){
				cerr << (number * d).data;
				if(d != 1) cerr << "/" << d;
				break;
			}
			else if((-number * d).data <= 1000000){
				cerr << "-" << (-number * d).data;
				if(d != 1) cerr << "/" << d;
				break;
			}
		}
		cerr << ")";
	#endif
		return out;
	}
	data_t data = 0;
#undef _SHOW_FRACTION
#undef IS_INTEGRAL
#undef IS_UNSIGNED
};
template<class data_t, data_t _mod> vector<modular_fixed_base<data_t, _mod>> modular_fixed_base<data_t, _mod>::_INV;
template<class data_t, data_t _mod> modular_fixed_base<data_t, _mod> modular_fixed_base<data_t, _mod>::_primitive_root;

const unsigned int mod = (119 << 23) + 1; // 998244353
// const unsigned int mod = 1e9 + 7; // 1000000007
// const unsigned int mod = 1e9 + 9; // 1000000009
// const unsigned long long mod = (unsigned long long)1e18 + 9;
using modular = modular_fixed_base<decay_t<decltype(mod)>, mod>;
modular operator""_m(const char *x){ return stoll(x); }

template<class T>
struct combinatorics{
#ifdef LOCAL
	#define ASSERT(c) assert(c)
#else
	#define ASSERT(c) 42
#endif
	// O(n)
	static vector<T> precalc_fact(int n){
		vector<T> f(n + 1, 1);
		for(auto i = 1; i <= n; ++ i) f[i] = f[i - 1] * i;
		return f;
	}
	// O(n * m)
	static vector<vector<T>> precalc_C(int n, int m){
		vector<vector<T>> c(n + 1, vector<T>(m + 1));
		for(auto i = 0; i <= n; ++ i) for(auto j = 0; j <= min(i, m); ++ j) c[i][j] = i && j ? c[i - 1][j - 1] + c[i - 1][j] : T(1);
		return c;
	}
	int SZ = 0;
	vector<T> inv, fact, invfact;
	combinatorics(){ }
	// O(SZ)
	combinatorics(int SZ): SZ(SZ), inv(SZ + 1, 1), fact(SZ + 1, 1), invfact(SZ + 1, 1){
		for(auto i = 1; i <= SZ; ++ i) fact[i] = fact[i - 1] * i;
		invfact[SZ] = 1 / fact[SZ];
		for(auto i = SZ - 1; i >= 0; -- i){
			invfact[i] = invfact[i + 1] * (i + 1);
			inv[i + 1] = invfact[i + 1] * fact[i];
		}
	}
	// O(1)
	T C(int n, int k) const{
		ASSERT(0 <= min(n, k) && max(n, k) <= SZ);
		return n >= k ? fact[n] * invfact[k] * invfact[n - k] : T{0};
	}
	// O(1)
	T P(int n, int k) const{
		ASSERT(0 <= min(n, k) && max(n, k) <= SZ);
		return n >= k ? fact[n] * invfact[n - k] : T{0};
	}
	// O(1)
	T H(int n, int k) const{
		ASSERT(0 <= min(n, k));
		if(n == 0) return 0;
		return C(n + k - 1, k);
	}
	// Multinomial Coefficient
	T mC(int n, const vector<int> &a) const{
		ASSERT((int)a.size() >= 2 && accumulate(a.begin(), a.end(), 0) == n);
		ASSERT(0 <= min(n, *min_element(a.begin(), a.end())) && max(n, *max_element(a.begin(), a.end())) <= SZ);
		T res = fact[n];
		for(auto x: a) res *= invfact[x];
		return res;
	}
	// Multinomial Coefficient
	template<class... U, typename enable_if<(is_integral_v<U> && ...)>::type* = nullptr>
	T mC(int n, U... pack){
		ASSERT(sizeof...(pack) >= 2 && (... + pack) == n);
		return (fact[n] * ... * invfact[pack]);
	}
	// O(min(k, n - k))
	T naive_C(long long n, long long k) const{
		ASSERT(0 <= min(n, k));
		if(n < k) return 0;
		T res = 1;
		k = min(k, n - k);
		ASSERT(k <= SZ);
		for(auto i = n; i > n - k; -- i) res *= i;
		return res * invfact[k];
	}
	// O(k)
	T naive_P(long long n, int k) const{
		ASSERT(0 <= min<long long>(n, k));
		if(n < k) return 0;
		T res = 1;
		for(auto i = n; i > n - k; -- i) res *= i;
		return res;
	}
	// O(k)
	T naive_H(long long n, int k) const{
		ASSERT(0 <= min<long long>(n, k));
		return naive_C(n + k - 1, k);
	}
	// O(1)
	bool parity_C(long long n, long long k) const{
		ASSERT(0 <= min(n, k));
		return n >= k ? (n & k) == k : false;
	}
	// Number of ways to place n '('s and k ')'s starting with m copies of '(' such that in each prefix, number of '(' is equal or greater than ')'
	// Catalan(n, n, 0): n-th catalan number
	// Catalan(s, s+k-1, k-1): sum of products of k catalan numbers where the index of product sums up to s.
	// O(1)
	T Catalan(int n, int k, int m = 0) const{
		ASSERT(0 <= min({n, k, m}));
		return k <= m ? C(n + k, k) : k <= n + m ? C(n + k, k) - C(n + k, k - m - 1) : T();
	}
#undef ASSERT
};

int main(){
	cin.tie(0)->sync_with_stdio(0);
	cin.exceptions(ios::badbit | ios::failbit);
	number_theory nt(100'000);
	combinatorics<modular> C(1e7);
	int qn;
	cin >> qn;
	int cnt = 0;
	for(auto qi = 0; qi < qn; ++ qi){
		int a, b;
		cin >> a >> b;
		while(a >= 2){
			int p = nt.lpf[a];
			a /= p;
			++ cnt;
		}
		cout << C.C(cnt - 1, b - 1) << "\n";
	}
	return 0;
}

/*

*/
0