B. Friends and Cookies
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Abood's birthday has come, and his n friends are aligned in a single line from 1 to n, waiting for their cookies, Abood has x cookies to give to his friends.

Here is an example to understand how Abood gives away the cookies. Suppose Abood has 4 friends and x cookies, then Abood will do the following:

  1. Give a cookie to the 1st friend.
  2. Give a cookie to the 2nd friend.
  3. Give a cookie to the 3rd friend.
  4. Give a cookie to the 4th friend.
  5. Give a cookie to the 3rd friend.
  6. Give a cookie to the 2nd friend.
  7. Give a cookie to the 1st friend.
  8. Give a cookie to the 2nd friend.
  9. And so on until all the x cookies are given away.

Your task is to find how many cookies each friend will get. Can you?

Input

The first line contains an integer T (1 ≤ T ≤ 100) specifying the number of test cases.

Each test case consists of a single line containing two integers x and n (1 ≤ x ≤ 1018, 1 ≤ n ≤ 1000), in which x is the number of cookies Abood has, and n is the number of his friends.

Output

For each test case, print a single line containing n space-separated integers a1, ..., an, in which ai represents how many cookies the ith friend got.

Example
Input
1
5 3
Output
2 2 1