Problem Description

Nadan is a successful businessman who frequently invests in software developers.

This year, he has decided to allocate \( K \) kuna (Croatian currency) to \( N \) projects, ensuring that each project receives at least 1 kuna, and the amounts allocated to each project are distinct positive integers. It is guaranteed that such an allocation is always possible.

Input Format

The first line contains a positive integer \( K \).

The second line contains a positive integer \( N \).

Output Format

Output \( N \) lines, where the \( i \)-th line indicates the amount allocated to the \( i \)-th project.

Sample Input and Output

Sample Input #1

100
5

Sample Output #1

10
30
20
5
35

Sample Input #2

200
1

Sample Output #2

200

Sample Input #3

100
4

Sample Output #3

21
36
12
31

Notes

Data Size and Constraints

For 50% of the test cases, \( N = 5 \).

For 100% of the test cases, \( 100 \leq K \leq 10^6 \) and \( 1 \leq N \leq 100 \).

Scoring Method

If a set of data contains identical allocation amounts but the total sum is correct, you can earn 3 out of the 5 points for that data set.

This problem uses a custom Special Judge, which can also be obtained from the attachments. Due to the Special Judge, please add a newline character after the last number in your output. Feel free to hack (privately message or post directly).

Note

This problem's score is set according to the original COCI contest, with a maximum of 50 points.

The problem is translated from COCI2018-2019 CONTEST #1 T1 Nadan.

见题面 Input 部分

见题面 Output 部分