시간 제한메모리 제한제출정답맞힌 사람정답 비율
2 초 128 MB0000.000%

## 문제

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.

## 입력

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.

## 출력

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.

## 예제 입력 1

2
9 4 3
10 10 1


## 예제 출력 1

1
1
3
4
1
1
1
1
1
1
1
1
1
1