# Light OJ 1045 – Digits of Factorial

```
/*
*/

#include &lt;bits/stdc++.h&gt;

#define pii pair &lt;int,int&gt;
#define sc scanf
#define pf printf
#define Pi 2*acos(0.0)
#define ms(a,b) memset(a, b, sizeof(a))
#define pb(a) push_back(a)
#define MP make_pair
#define oo 1&lt;&lt;29
#define dd double
#define ll long long
#define EPS 10E-10
#define ff first
#define ss second
#define MAX 10000
#define SZ(a) (int)a.size()
#define getint(a) scanf(&quot;%d&quot;,&amp;a)
#define loop(i,n) for(int i=0;i&lt;n;i++)
#define all(a) a.begin(),a.end()
#define intlim 2147483648
#define inf 1000000
#define rtintlim 46340
#define llim 9223372036854775808
#define rtllim 3037000499
#define ull unsigned long long
#define I int

using namespace std;

double ara[1000010];

int main()
{
///freopen(&quot;in.txt&quot;,&quot;r&quot;,stdin);
///freopen(&quot;out.txt&quot;,&quot;w&quot;,stdout);
int t,cases=0;
getint(t);
for(int i=1;i&lt;=1000005;i++)
ara[i]=log((double)i)+ara[i-1];
while(t--)
{
ll num, base;
sc(&quot;%lld %lld&quot;,&amp;num,&amp;base);
double ans=0;
ans=ara[num];
ans/=log((double)base);
ans=floor(ans);
ans+=1;
ll x=ans;
pf(&quot;Case %d: %lld\n&quot;,++cases,x);
}
return 0;
}

```