Period

Description
For each prefix of a given string S with N characters (each character has an
ASCII code between 97 and 126, inclusive), we want to know whether the prefix
is a periodic string. That is, for each i (2 ≤ i ≤ N) we want to know the largest K > 1 (if there is one) such that the prefix of S with length i can be written as AK ,
that is A concatenated K times, for some string A. Of course, we also want to
know the period K.

Input
The input file consists of several test cases. Each test case consists of two
lines. The first one contains N (2 <= N <= 1 000 000) – the size of the string S.
The second line contains the string S. The input file ends with a line, having the
number zero on it.

Output
For each test case, output “Test case #” and the consecutive test case
number on a single line; then, for each prefix with length i that has a period K >
1, output the prefix size i and the period K separated by a single space; the
prefix sizes must be in increasing order. Print a blank line after each test case.

Sample
Input

3

aaa

12

aabaabaabaab

0

Output

Test case #1

2 2

3 3

Test case #2

2 2

6 2

9 3

12 4

Hint

#include<bits/stdc++.h>

using namespace std;

char s[1000010];
int Next[1000010];

void get_next()
{
   memset(Next, 0, sizeof(Next));
   int i = 0;
   int j = -1;
   Next[0] = -1;
   int len = strlen(s);
   while(i < len)
   {
       if(j == -1 || s[i] == s[j])
       {
           Next[++i] = ++j;
           if((i % (i - Next[i]) == 0) && (i / (i - Next[i]) > 1))
               printf("%d %d\n", i, i / (i - Next[i]));
       }
       else
           j = Next[j];
   }
}
int main()
{
   int n;
   int cnt = 0;
   while(~scanf("%d", &n) && n != 0)
   {
       cnt++;
       scanf("%s", s);
       printf("Test case #%d\n", cnt);
       get_next();
       printf("\n");
   }
   return 0;
}