3243: K-Periodic Array
Description
This task will exclusively concentrate only on the arrays where all elements equal 1 and/or 2.
Array a is k-period if its length is divisible by k and there is such array b of length k, that a is represented by array b written exactly times consecutively. In other words, array a is k-periodic, if it has period of length k.
For example, any array is n-periodic, where n is the array length. Array [2,1,2,1,2,1] is at the same time 2-periodic and 6-periodic and array [1,2,1,1,2,1,1,2,1] is at the same time 3-periodic and 9-periodic.
For the given array a, consisting only of numbers one and two, find the minimum number of elements to change to make the array k-periodic. If the array already is k-periodic, then the required value equals 0.
The first line of the input contains a pair of integers n, k (1≤k≤n≤100), where n is the length of the array and the value n is divisible by k. The second line contains the sequence of elements of the given array a1,a2,...,an (1≤ai≤2), ai is the i-th element of the array.
Print the minimum number of array elements we need to change to make the array k-periodic. If the array already is k-periodic, then print 0.
6 2
2 1 2 2 2 1
1
8 4
1 1 2 1 1 1 2 1
0
9 3
2 1 1 1 2 1 1 1 2
3
In the first sample it is enough to change the fourth element from 2 to 1, then the array changes to [2,1,2,1,2,1].
In the second sample, the given array already is 4-periodic.
In the third sample it is enough to replace each occurrence of number two by number one. In this case the array will look as [1,1,1,1,1,1,1,1,1] − this array is simultaneously 1-, 3- and 9-periodic.