//Pollard_rho 随机算法，找到一个n的较小的约数
ll Pollard_rho(ll n, int c) {
ll i = 1, k = 2, x = rand()%n, y = x, d;
while (1) {
i++;
x = (mul_mod(x, x, n)+c) % n;
d = GCD(y-x, n); //y-x可能小于0，GCD需要改动
if (d!=1 && d!=n) return d;
if (y == x) return n;
if (i == k) { y = x; k <<= 1; }
}
}
static bool rabin(const large_digit &ld)
{
int k;
int i, r;
bool result = false;
large_digit m, a, u;
r = 0;
m = ld - 1;
while (m.bit(r++));
m >>= (--r);
for (k = 0; k < 5; k++) {
rand_product(a);
a %= (ld - 2);
a += 2;
u = expr_mod(a, m, ld);
if (u == 1)
continue;
for (i = 0; i < r; i++) {
if (u + 1 == ld)
break;
u = mul_mod (u, u, ld);
}
if (i == r) {
goto failure;
}
}
#if 1
for (i = 0; i < 200; i++) {
if (ld <= aprime[i]) {
break;
}
if (ld % aprime[i] == 0) {
goto failure;
}
}
#endif
result = true;
failure:
return result;
}
bool Wintess(int64 aa, int64 n, int64 mod) /*是以aa为底的伪质数返回0,是合数返回1*/
{
int t = 0;
while ((n & 1) == 0){ /*n = d * 2^t; n = d;*/
n >>= 1;
++ t;
}
int64 x = pow_mod(aa, n, mod), y;
while (t --){
y = mul_mod (x, x, mod);
if (y == 1 && x != 1 && x != mod-1) return 1;
x = y;
}
return (y != 1);
}
// 用miller rabin素数测试判断n是否为质数
bool is_prime(LL n) {
if (n <= 1) return false;
if (n <= 3) return true;
if (~n & 1) return false;
const int u[] = {2,3,5,7,325,9375,28178,450775,9780504,1795265022,0};
LL e = n - 1, a, c = 0; // 原理：http://miller-rabin.appspot.com/
while (~e & 1) e >>= 1, ++c;
for (int i = 0; u[i]; ++i) {
if (n <= u[i]) return true;
a = pow_mod_LL(u[i], e, n);
if (a == 1) continue;
for (int j = 1; a != n - 1; ++j) {
if (j == c) return false;
a = mul_mod(a, a, n);
}
}
return true;
}
// Rabin-Miller primality testing algorithm
bool isPrime(llui n){
llui d = n-1;
llui s = 0;
if(n <=3 || n == 5) return true;
if(!(n&1)) return false;
while(!(d&1)){ s++; d>>=1; }
for(llui i = 0;i<32;i++){
llui a = rand();
a <<=32;
a+=rand();
a%=(n-3); a+=2;
llui x = pot(a,d,n);
if(x == 1 || x == n-1) continue;
for(llui j = 1;j<= s-1;j++){
x = mul_mod(x,x,n);
if(x == 1) return false;
if(x == n-1)break;
}
if(x != n-1) return false;
}
return true;
}
// 与えられた数が素数かどうかをO(log^3 n)で確率的に判定する
// 以下の関数はn < 341,550,071,728,321について正しい
bool miller_rabin(LL n){
if(n == 2) return true;
if(n % 2 == 0 || n <= 1) return false;
vector<LL> a = {2, 3, 5, 7, 11, 13, 17};
LL d = n - 1, s = 0;
while((d & 1) == 0){
d >>= 1;
s++;
}
for(int i = 0; i < a.size() && a[i] < n; i++){
LL x = pow_mod(a[i], d, n);
if(x == 1) continue;
for(int r = 0; r < s; r++){
if(x == n - 1) break;
if(r + 1 == s) return false;
x = mul_mod(x, x, n);
}
}
return true;
}
int is_probably_prime(llu n) {
if (n <= 1) return 0;
if (n <= 3) return 1;
llu s = 0, d = n - 1;
while (d % 2 == 0) {
d/= 2; s++;
}
for (int k = 0; k < 64; k++) {
llu a = (llrand() % (n - 3)) + 2;
llu x = exp_mod(a, d, n);
if (x != 1 && x != n-1) {
for (int r = 1; r < s; r++) {
x = mul_mod(x, x, n);
if (x == 1)
return 0;
if (x == n-1)
break;
}
if (x != n-1)
return 0;
}
}
return 1;
}
llui f(llui a, llui b){
llui tmp;
tmp = mul_mod(a,a,b);
tmp+=C; tmp%=b;
return tmp;
}
