C2. k-LCM (hard version)
constructive algorithms; math
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: \(a_1 + a_2 + \ldots + a_k = n\) \(LCM(a_1, a_2, \ldots, a_k) \le \frac{n}{2}\) 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.