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| #include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#define LL long long
#define rep(i, x, y) for (int i = x; i <= y; i++)
const int prime_list[12] = { 2, 3, 5, 7, 11, 13, (LL) 1e9 + 7 };
const int small_prime[6] = { 2, 3, 5, 7, 11 };
const int luck_prime = 19260817;
template <typename T>
inline void read(T &x) {
x = 0;
LL f = 1;
char c = getchar();
for (; !isdigit(c); c = getchar()) {
if (c == '-')
f = -f;
}
for (; isdigit(c); c = getchar()) {
x = x * 10 + c - 48;
}
x *= f;
}
LL ksc(LL a, LL b, LL m) {
LL d = ((long double)a / m * b + 1e-8);
LL r = a * b - d * m;
return r < 0 ? r + m : r;
}
LL ksm(LL a, LL b, LL p) {
LL sum = 1;
for (; b >= 1; b >>= 1, a = ksc(a, a, p)) {
if (b & 1)
sum = ksc(sum, a, p);
}
return sum;
}
LL gcd(LL a, LL b) {
if (!a) return b;
if (!b) return a;
#define ctz __builtin_ctzll
int t = ctz(a | b);
a >>= ctz(a);
do {
b >>= ctz(b);
if (a > b) {
LL t = b;
b = a;
a = t;
}
b -= a;
} while (b != 0);
return a << t;
}
bool miller_rabin(LL x) {
if (x < 2)
return false;
if (x == 2 || x == 3 || x == 5 || x == 7)
return true;
if (x % 2 == 0 || x % 3 == 0 || x % 5 == 0 || x % 7 == 0)
return false;
LL cnt = 0, rem = x - 1;
while (!(rem & 1)) {
cnt++;
rem >>= 1;
}
rep(i, 0, 6) {
if(x == prime_list[i]) return true;
if(x % prime_list[i] == 0) return false;
LL rt = ksm(prime_list[i], rem, x);
LL y = rt;
rep(i, 1, cnt) {
rt = ksc(rt, rt, x);
if (rt == 1 && y != 1 && y != x - 1) {
return false;
}
y = rt;
}
if (rt != 1)
return false;
}
return true;
}
int M = (1 << 7) - 1;
LL f(LL x, LL p, LL c) {
LL ans = ksc(x, x, p) + c;
return ans < p ? ans : ans - p;
}
LL abs(LL x) {
return x < 0? -x : x;
}
LL pollards_rho(LL x) {
if (x % 2 == 0)
return 2;
if (x % 3 == 0)
return 3;
if (x % 5 == 0)
return 5;
if (x % 7 == 0)
return 7;
LL base = 1ll * rand() % (x - 1) + 1;
LL sp = 0, tp = 0;
int i = 1, j = 0;
LL val = 1;
LL d;
for(i = 1; ; i <<= 1, sp = tp, val = 1) {
for(j = 1; j <= i; ++j) {
tp = f(tp, x, base);
val = ksc(val, abs(tp - sp) , x);
if(!(j & M)) {
d = gcd(val, x);
if(d > 1) return d;
}
}
d = gcd(val, x);
if(d > 1) return d;
}
}
LL factor[5], m = 0;
void work(LL x) {
if(x <= 1) return;
if(miller_rabin(x)) {
factor[++m] = x;
return;
}
LL num = x;
while(num >= x) {
num = pollards_rho(x);
}
while(x % num == 0) {x /= num;}
if(x >= 2) work(x);
if(num >= 2) work(num);
}
LL exgcd(LL a, LL b, LL &x, LL &y) {
if(b == 0) {x = 1; y = 0; return a;}
LL d = exgcd(b, a%b, x, y);
LL z = x;
x = y;
y = z - y * (a / b);
return d;
}
LL inv(LL a, LL p) {
LL x, y;
LL d = exgcd(a, p, x, y);
return d == 1? (x + p) % p : -1;
}
int main() {
srand((unsigned)time(0));
LL e, N, c;
read(e); read(N); read(c);
work(N);
std::sort(factor + 1, factor + m + 1);
LL r = (factor[1] - 1) * (factor[2] - 1);
LL d = inv(e, r);
printf("%lld %lld\n", d, ksm(c, d, N));
return 0;
}
|