G. K-Regular Array
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

An array $$$a$$$ of size $$$n$$$ is considered $$$k$$$-regular if every subarray of $$$a$$$ of size $$$k$$$ contains all integers from $$$1$$$ to $$$k$$$, inclusive.

For example, $$$a = [2, 1, 3, 2]$$$ is $$$3$$$-regular, because its two subarrays of size $$$3$$$ are $$$[2, 1, 3]$$$ and $$$[1, 3, 2]$$$, each of which contains all integers from $$$1$$$ to $$$3$$$. On the other hand, $$$a = [1, 2, 3, 4]$$$ is not $$$3$$$-regular because the subarray $$$[2, 3, 4]$$$ of size $$$k=3$$$ does not contain $$$1$$$.

Your task is to find a $$$k$$$-regular array $$$a$$$ of size $$$n$$$ such that the sum of its elements is maximized.

Input

The first line of the input contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases. The description of the test cases follows.

Each test case consists of a single line containing two integers $$$n$$$ and $$$k$$$ ($$$1 \le k \le n \le 2\cdot 10^5$$$) — the desired size of the array $$$a$$$, and the parameter $$$k$$$ described above.

It is guaranteed that the sum of $$$n$$$ across all test cases is at most $$$2\cdot 10^5$$$.

Output

For each test case, output a single line containing $$$n$$$ integers $$$a_1, a_2, \cdots a_n$$$ — a $$$k$$$-regular array $$$a$$$ of size $$$n$$$ with maximal sum.

If there are multiple solutions, you may print any.

Example
Input
4
4 3
5 1
3 2
1 1
Output
3 1 2 3
1 1 1 1 1 
2 1 2 
1
Note

In the first sample case, the array $$$a = [3, 1, 2, 3]$$$ is $$$3$$$-regular because its two subarrays of size $$$3$$$ are $$$[3, 1, 2]$$$ and $$$[1, 2, 3]$$$, each of which contains all integers from $$$1$$$ to $$$3$$$. The sum of this array is $$$3 + 1 + 2 + 3 = 9$$$, which we can show is maximal for this $$$n$$$ and $$$k$$$.

In the second sample case, each subarray of size $$$1$$$ must contain $$$1$$$, and therefore, the array must consist only of ones.