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bool isPrime(ll n) { // Miller Rabin Primzahltest. O(log n)
if(n == 2) return true;
if(n < 2 || n % 2 == 0) return false;
ll d = n - 1, j = 0;
while(d % 2 == 0) d >>= 1, j++;
for(int a = 2; a <= min((ll)37, n - 1); a++) {
ll v = powMod(a, d, n); // Implementierung von oben.
if(v == 1 || v == n - 1) continue;
for(int i = 1; i <= j; i++) {
v = multMod(v, v, n); // Implementierung von oben.
if(v == n - 1 || v <= 1) break;
}
if(v != n - 1) return false;
}
return true;
}
ll rho(ll n) { // Findet Faktor < n, nicht unbedingt prim.
if (~n & 1) return 2;
ll c = rand() % n, x = rand() % n, y = x, d = 1;
while (d == 1) {
x = (multMod(x, x, n) + c) % n;
y = (multMod(y, y, n) + c) % n;
y = (multMod(y, y, n) + c) % n;
d = __gcd(abs(x - y), n);
}
return d == n ? rho(n) : d;
}
void factor(ll n, map<ll, int> &facts) {
if (n == 1) return;
if (isPrime(n)) {
facts[n]++;
return;
}
ll f = rho(n);
factor(n/f, facts);
factor(f, facts);
}
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