A partition of a positive integer m into n parts is defined to construct a sequence a1,..,an such that a1+...+an=m, and a1<=a2<=...<=an.
It is apparent that such partition is not unique. We arrange them in lexicographic order. Your task is to find the k-th sequence.
There are multiple test cases. Each case has only 1 line with 3 integers: m,n,k (1<=n<=10, 1<=m<=220). Please note that k can be very large but are always within the range.
Process to the end of file.
For each case, output a line containing the k-th sequence.
9 4 3
1 1 3 4