232. Infinite Fraction

time limit per test: 0.25 sec.
memory limit per test: 4096 KB
input: standard
output: standard



You are given integer numbers N and K and an array D[0..N-1] of decimal digits (0<=D[i]<=9, D[i] is an integer).
Consider an array A of real numbers, such that integer part of A[i] is equal to zero, and fractional part is an infinite decimal fraction with digits D[[(i + 0K) mod N], D[(i + 1K) mod N], D[(i + 2K) mod N] and so on.
For example, for N = 3, K = 2 and D = '194':

A[1] = 0.1491491491...
A[2] = 0.9149149149...
A[3] = 0.4914914914...

You are to find an element of array A with the greatest value and output first N digits of its fractional part.

Input
The first line contains integer numbers N and K (1<=N<=150000; 0<=K<=10^9). The second line contains an array of digits D, given without spaces.

Output
You are to output exactly N characters to the output file, according to the task.

Sample test(s)

Input
Test #1 
3 2 
194 
 
Test #2 
2 1 
57 
 
Test #3 
4 1 
0000 

Output
Test #1 
914 
 
Test #2 
75 
 
Test #3 
0000 
  
  
Author:Antony Popovich 
Resource:--- 
Date:October, 2003