k-LCM (hard version)

1000ms

262144K

Description:

It is the hard version of the problem. The only difference is that in this version $$$3 \le k \le n$$$.

You are given a positive integer $$$n$$$. Find $$$k$$$ positive integers $$$a_1, a_2, \ldots, a_k$$$, such that:

Here $$$LCM$$$ is the least common multiple of numbers $$$a_1, a_2, \ldots, a_k$$$.

We can show that for given constraints the answer always exists.

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

The only line of each test case contains two integers $$$n$$$, $$$k$$$ ($$$3 \le n \le 10^9$$$, $$$3 \le k \le n$$$).

It is guaranteed that the sum of $$$k$$$ over all test cases does not exceed $$$10^5$$$.

For each test case print $$$k$$$ positive integers $$$a_1, a_2, \ldots, a_k$$$, for which all conditions are satisfied.

2
6 4
9 5

1 2 2 1 
1 3 3 1 1

Informação

Provedor Codeforces

Código CF1497C2