1045 - Digits of Factorial

/***

            Bismillahir Rahmanir Rahim
            Read the name of Allah, who created you!!!
            Author : Shah Newaj Rabbi Shishir
            Department of CSE, City University, Bangladesh.
***/

#include <bits/stdc++.h>
using namespace std;

#define sf scanf
#define pf printf
#define scase sf ("%d",&tc)
#define sn sf ("%d",&n)
#define whilecase while (tc--)
#define eof while (cin >> n)
#define forloop for (pos=1; pos<=tc; pos++)
#define arrayloop (i=0; i<n; i++)
#define cinstr cin >> str
#define getstr getline (cin,str)
#define pcase pf ("Case %d: ",pos)
#define pb push_back
#define in insert
#define llu unsigned long long
#define lld long long
#define U unsigned int

const int MAX = 1000001;
double fact_digits[MAX];

int main (void)
{
    /*freopen ("input.txt","r",stdin);
    freopen ("output.txt","w",stdout);*/
    int tc,pos,n,b,i;
    double res;

    for (i=1; i<1000001; i++)
        fact_digits[i] = log(i) + fact_digits[i-1];

    sf ("%d",&tc);

    for (pos=1; pos<=tc; pos++)
    {
        sf ("%d %d",&n,&b);
        res = floor(fact_digits[n]/log(b))+1;
        pf ("Case %d: %0.lf\n",pos,res);
    }

    return 0;
}