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#include "math/factorize.hpp"
#pragma once
#include <cmath>
#include <numeric>
long long modmul(long long x, long long y, long long mod) {
using i128 = __int128_t;
return (long long)(i128(x) * i128(y) % i128(mod));
}
long long modpow(long long a, long long n, long long mod) {
long long ret = 1;
while (n > 0) {
if (n & 1) ret = modmul(ret, a, mod);
a = modmul(a, a, mod);
n >>= 1;
}
return ret;
}
long long rho(long long n) {
long long z = 0;
auto f = [&](long long x) -> long long {
long long ret = modmul(x, x, n) + z;
if (ret == n) return 0;
return ret;
};
while (true) {
long long x = ++z;
long long y = f(x);
while (true) {
long long d = std::gcd(std::abs(x - y), n);
if (d == n) break;
if (d > 1) return d;
x = f(x);
y = f(f(y));
}
}
}
#include <initializer_list>
bool miller_rabin(long long n) {
if (n == 1) return 0;
long long d = n - 1, s = 0;
while (~d & 1) d >>= 1, s++;
auto check = [&](long long a) -> bool {
long long x = modpow(a, d, n);
if (x == 1) return 1;
long long y = n - 1;
for (int i = 0; i < s; i++) {
if (x == y) return true;
x = modmul(x, x, n);
}
return false;
};
for (long long a : {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}) {
if (a >= n) break;
if (!check(a)) return false;
}
return true;
}
#include <map>
#include <queue>
std::map<long long, int> factorize(long long n) {
std::map<long long, int> ret;
while (~n & 1) n >>= 1, ret[2]++;
std::queue<long long> q;
q.push(n);
while (!q.empty()) {
long long p = q.front();
q.pop();
if (p == 1) continue;
if (miller_rabin(p)) {
ret[p]++;
continue;
}
long long d = rho(p);
q.push(d);
q.push(p / d);
}
return ret;
}
#line 2 "math/factorize.hpp"
#include <cmath>
#include <numeric>
long long modmul(long long x, long long y, long long mod) {
using i128 = __int128_t;
return (long long)(i128(x) * i128(y) % i128(mod));
}
long long modpow(long long a, long long n, long long mod) {
long long ret = 1;
while (n > 0) {
if (n & 1) ret = modmul(ret, a, mod);
a = modmul(a, a, mod);
n >>= 1;
}
return ret;
}
long long rho(long long n) {
long long z = 0;
auto f = [&](long long x) -> long long {
long long ret = modmul(x, x, n) + z;
if (ret == n) return 0;
return ret;
};
while (true) {
long long x = ++z;
long long y = f(x);
while (true) {
long long d = std::gcd(std::abs(x - y), n);
if (d == n) break;
if (d > 1) return d;
x = f(x);
y = f(f(y));
}
}
}
#include <initializer_list>
bool miller_rabin(long long n) {
if (n == 1) return 0;
long long d = n - 1, s = 0;
while (~d & 1) d >>= 1, s++;
auto check = [&](long long a) -> bool {
long long x = modpow(a, d, n);
if (x == 1) return 1;
long long y = n - 1;
for (int i = 0; i < s; i++) {
if (x == y) return true;
x = modmul(x, x, n);
}
return false;
};
for (long long a : {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}) {
if (a >= n) break;
if (!check(a)) return false;
}
return true;
}
#include <map>
#include <queue>
std::map<long long, int> factorize(long long n) {
std::map<long long, int> ret;
while (~n & 1) n >>= 1, ret[2]++;
std::queue<long long> q;
q.push(n);
while (!q.empty()) {
long long p = q.front();
q.pop();
if (p == 1) continue;
if (miller_rabin(p)) {
ret[p]++;
continue;
}
long long d = rho(p);
q.push(d);
q.push(p / d);
}
return ret;
}