C2. k-LCM (hard version)time limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputIt 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.InputThe 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.OutputFor each test case print k positive integers a_1, a_2, \ldots, a_k, for which all conditions are satisfied.ExampleInput
2
6 4
9 5
Output
1 2 2 1 
1 3 3 1 1 

2
6 4
9 5

1 2 2 1  1 3 3 1 1  
['constructive algorithms', 'math', '*1600']