202. 最幸运的数字 - AcWing题库

 

#include<bits/stdc++.h>
#define IOS ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define endl '\n'
 
using namespace std;
 
typedef pair<int, int> PII;
typedef long long ll;
typedef long double ld;

ll qmi(ll a, ll k, ll mod)
{
	ll res = 1;
	while(k)
	{
		if(k & 1)res = (__int128)res * a % mod;
		a = (__int128)a * a % mod;
		k >>= 1;
	}
	return res;
}

ll get_euler(ll x)
{
	ll res = x;
	for(int i = 2; i <= x / i; i ++)
	{
		if(x % i == 0)
		{
			res = res / i * (i - 1);
			while(x % i == 0)x /= i;
		}
	}
	if(x > 1)res = res / x * (x - 1);
	return res;
}

int main()
{
	IOS
	int cnt = 0;
	ll L;
	while(cin >> L, L)
	{
		L *= 9;
		int d = 1;
		while(L % (d * 2) == 0 && d * 2 <= 8)d *= 2;
		ll C = L / d;
		
		ll phi = get_euler(C), res = 2e18;
		if(__gcd(10ll, C) != 1)res = 0;
		
		for(ll i = 1; i * i <= phi; i ++)
		{
			if(phi % i == 0)
			{
				if(qmi(10, i, C) == 1)
				{
					res = min(res, i);
					break;
				}
				if(qmi(10, phi / i, C) == 1)
				{
					res = min(res, phi / i);
				}
			}
		}
		
		cout << "Case " << ++ cnt << ": " << res << endl;
	}
	
	return 0;
}