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Partitioning for fun and profit
A partition of a positive integer number m into n elements (n <= m) is a sequence of positive numbers a1,...,an such that a1+...+an = m and a1 <= a2 <= ... <= an. 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,...,an] and b = [b1,...,bn] we have a < b if and only if there exists an 1 <= i <= n such that for all j < i we have aj = bj and ai < bi. 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
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