Time Limit: 1000 mSec Memory Limit : 32768 KB

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.

Process to the end of file.

For each case, output a line containing the k-th sequence.

9 4 3

1 1 3 4