// ret = (a^b)%n
bint mod_exp(bint a,bint p,bint m) {
bint exp=a%m, res=1;
while(p>1) {
if(p&1)
res=muti_mod(res,exp,m);
exp = muti_mod(exp,exp,m);
p>>=1;
}
return muti_mod(res,exp,m);
}
LL pow_mod(LL x, LL n, LL mod) //返回x^n mod c ,非递归版
{
if (n == 1) return x % mod;
int bit[90], k = 0;
while (n)
{
bit[k++] = n & 1;
n >>= 1;
}
LL ret = 1;
for (k = k - 1; k >= 0; k--)
{
ret = muti_mod(ret, ret, mod);
if (bit[k] == 1) ret = muti_mod(ret, x, mod);
}
return ret;
}
bool witness(LL a, LL n, LL x, LL t) //以a为基，n-1=x*2^t，检验n是不是合数
{
LL ret = pow_mod(a, x, n);
LL last = ret;
for (int i = 1; i <= t; i++)
{
ret = muti_mod(ret, ret, n);
if (ret == 1 && last != 1 && last != n - 1)
return 1;
last = ret;
}
if (ret != 1) return 1;
return 0;
}
bint pollard_rho(bint n,int c) {
bint x,y,d,i = 1,k = 2;
srand(time(0));
x = rand()%(n-1)+1;
y = x;
while(true) {
i++;
x = (muti_mod(x,x,n) + c) % n;
d = gcd(y-x, n);
if (1 < d && d < n) return d;
if( y == x) return n;
if(i == k) {
y = x;
k <<= 1;
}
}
}
//miller-rabin
bool miller_rabin(bint n, int times) {
if(n==2)return 1;
if(n<2||!(n&1))return 0;
bint a, u=n-1, x, y;
int t=0;
while(u%2==0) {
t++;
u/=2;
}
srand(time(0));
for(int i=0; i<times; i++) {
a = rand() % (n-1) + 1;
x = mod_exp(a, u, n);
for(int j=0; j<t; j++) {
y = muti_mod(x, x, n);
if ( y == 1 && x != 1 && x != n-1 )
return false; //must not
x = y;
}
if( y!=1) return false;
}
return true;
}
LL Pollard_rho(LL x, LL c)
{
LL i = 1, x0 = rand() % x, y = x0, k = 2,d;
while (1)
{
i++;
x0 = (muti_mod(x0, x0, x) + c) % x;
if (y == x0)
return x;
if(y>x0)
d = gcd(y - x0, x);
else
d = gcd(x0 - y, x);
if (d != 1 && d != x)
return d;
if (i == k)
{
y = x0;
k += k;
}
}
}
