K. To-do list
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Igor wants to improve self-organization, so he decided to make a huge to-do list and a plan that he will stick to for $$$k$$$ days.

There were $$$n$$$ tasks in the list. Igor considered it necessary to repeat the task number $$$i$$$ from this list after $$$a_i$$$ days to develop a habit. Having decided on the list and the frequency of repetition of tasks, Igor immediately completed all tasks from the list, only to repeat them in the future. Therefore, he was very tired and completely forgot to make a plan for the next $$$k$$$ days.

Help Igor make a plan by specifying for each of the following days the number of tasks that Igor needs to complete.

Input

The first line contains two integers $$$n$$$, $$$k$$$ $$$(1\leq n,k\leq 10^5)$$$ — the number of tasks in Igor list and the number of days during which Igor wants to stick to the plan.

The second line contains $$$n$$$ integers $$$a_i$$$ $$$(0\leq a_i\leq 10^5,1\leq i\leq n)$$$ — the number of days after which it is necessary to repeat the $$$i$$$ th task.

Output

In a single line print $$$k$$$ numbers $$$m_j$$$ separated by a space. $$$m_j$$$ — the number of tasks planned by Igor for $$$j$$$ th $$$(1\leq j\leq k)$$$ day.

Examples
Input
2 10
1 2
Output
0 1 1 1 0 2 0 1 1 1
Input
2 6
0 1
Output
1 2 1 2 1 2
Input
3 15
1 2 3
Output
0 1 1 2 0 2 0 2 1 1 0 3 0 1 1