22005_Partitioningforfunandprofi

A partition of a positive integer number m into n elements (n ≤ m) is a sequence of positive numbers a₁, ...,a_n such that a₁+...+a_n = m and a₁ ≤ a₂ ≤ ... ≤ a_n. Your task is to find a partition of a number m which occupies the k-th position in the lexicographically ordered sequence of all partitions of m into n elements.

The lexicographic ordering among the partitions of a number is defined as follows. For two partitions a and b of m into n elements such that a = [a₁,...,a_n] and b = [b₁,...,b_n] we have a < b if and only if there exists an 1 ≤ i ≤ n such that for all j < i we have a_j = b_j and a_i < b_i. The sequence of all partitions is ordered in increasing lexicographic order and at the first we have the following sequence 1, 1, ... 1, m-n+1.

The first line of input contains a number c giving the number of cases that follow. Each of the subsequent c lines contains three numbers: 1 ≤ m ≤ 220, 1 ≤ n ≤ 10 and 1 ≤ k which is not bigger than the number of partitions of m into n elements.

For each input data set print the k-th partition of m into n elements. Each element of a partition is to be printed in a separate line.

2
9 4 3
10 10 1

1
1
3
4
1
1
1
1
1
1
1
1
1
1