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 =manda1 ≤a2 ≤...≤an. Your task is to find a partition of a num- ber 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 fol- lows. 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. Input The first line of input contains a number c giving the number of cases that follow. Each of the subsequent clinescontainsthreenumbers: 1≤m≤220,1≤n≤10and1≤kwhichisnotbiggerthanthe number of partitions of m into n elements. Output 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. Sample Input 2 943 10 10 1 Sample Output 1 1 3 4 1 1 1 1 1 1 1 1

2/2 1 1