K-Periodic Array

1000ms

262144K

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 $\text{[math]}$ 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.

Input:

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, ..., a_n (1 ≤ a_i ≤ 2), a_i is the i-th element of the array.

Output:

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.

Sample Input:

6 2
2 1 2 2 2 1

Sample Output:

Sample Input:

8 4
1 1 2 1 1 1 2 1

Sample Output:

Sample Input:

9 3
2 1 1 1 2 1 1 1 2

Sample Output:

Note:

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.

Informação

Provedor Codeforces

Código CF371A