PARTIT - Partition


A partition of positive integer m into n components is any sequence a1,...,an of positive integers such that a1+...+an=m and a1<=a2<=...<=an. Your task is to determine the partition, which occupies the k-th position in the lexicographic order of all partitions of m into n components.

The lexicographic order is defined as follows: sequence a1,...,an comes before b1,...,bn iff there exists such an integer i,1<=i<=n, that aj=bj for all j, 1<= j< i, and ai< bi.

Input

The input begins with the integer t, the number of test cases. Then t test cases follow.

For each test case the input consists of three lines, containing the positive integers m, n and k respectively (1<=n<= 10, 1<= m<=220, k is not larger than the number of partitions of m into n components).

Output

For each test case output the ordered elements of the sought partition, separated by spaces.

Example

Sample input:
1
9
4
3

Sample output:
1 1 3 4

hide comments
minhthai: 2016-03-21 15:48:19

didn't think it is DP at first sight. Thanks for the nice problem!
hint: use 64-bit int

kejriwal: 2015-09-18 00:15:28

nice dp :D

paras meena: 2014-12-31 17:41:04

silly mistake got 4+ WA :(

nikhil: 2014-01-17 11:50:22

more test cases plz...


Added by:adrian
Date:2004-07-19
Time limit:7s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All
Resource:VI Polish Collegiate Team Programming Contest (AMPPZ), 2001