Mabel has a line of ~N~ marbles, each of which is one of ~M~ colours.

She can swap the position of two adjacent marbles, with the goal of creating a "complete colour grouping". A complete colour grouping for a colour ~c~ occurs when all marbles of colour ~c~ are arranged contiguously in a block of consecutive marbles.

Help Mabel find the minimum number of swaps to reach a complete colour grouping for each colour.

Input Specification

The first line will contain two space-separated integers, ~N (1 \leq N \leq 10^5)~ and ~M (1 \leq M \leq N)~, the number of marbles and the number of colours.

The second line will contain ~N~ space-separated integers, ~a_i (1 \leq a_i \leq M)~, representing the colour of the ~i^{th}~ of marble.

Output Specification

Output one line containing ~M~ space-separated integers, representing the minimum number of swaps required to reach a complete colour grouping for each of the ~M~ colours.

Sample Input

8 3
3 1 3 2 2 1 3 2

Sample Output

3 2 4

Sample Explanation

For colour 1, a complete colour grouping can be achieved in the following state: 3 1 1 3 2 2 3 2. This takes 3 swaps to reach.

For colour 2, a complete colour grouping can be achieved in the following state: 3 1 3 2 2 2 1 3. This takes 2 swaps to reach.

For colour 3, a complete colour grouping can be achieved in the following state: 1 3 3 3 2 2 1 2. This takes 4 swaps to reach.