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Chef Anup is making dishes. Each dish consists of N ingredients, and quantity of each ingredient is an integer between 1 and K inclusive.
Relative quality of 2 dishes is determined by their lexicographic order. Dish A is of lower quality than dish B if there is a position i (1≤i≤N) such that A_{j} = B_{j} for all j < i and A_{i} < B_{i}.
E.g., if N = 2 and K = 2, then the possible dishes in lexicographic order are (1,1), (1,2), (2,1), (2,2).
Given an integer L, determine the L^{th} possible dish in increasing order of quality.

------ Input Format ------

The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.
Each test case description consists of a single line containing three integers N, K and L as described above.

------ Output Format ------

For each test case, print N space-separated integers in a single line describing the quantities of the ingredients for the Lth dish.

------ Constraints ------

$1 ≤ T ≤ 10$
$L will not exceed the total number of possible dishes.$

------ subtasks ------

$For 20 points : N = 3, 2 ≤ K ≤ 102, 1 ≤ L ≤ 106$
$For 30 points : 1 ≤ N ≤ 102, 2 ≤ K ≤ 102, 1 ≤ L ≤ 104$
$For 50 points : 1 ≤ N ≤ 103, 2 ≤ K ≤ 103, 1 ≤ L ≤ 1018$

----- Sample Input 1 ------
4
3 3 1
3 3 2
3 3 3
3 3 4
----- Sample Output 1 ------
1 1 1
1 1 2
1 1 3
1 2 1
----- explanation 1 ------

First 4 dishes in order have ingredients (1,1,1), (1,1,2), (1,1,3), and (1,2,1).

----- Sample Input 2 ------
4
4 3 1
4 3 2
4 3 3
4 3 4
----- Sample Output 2 ------
1 1 1 1
1 1 1 2
1 1 1 3
1 1 2 1
----- explanation 2 ------

First 4 dishes in order have ingredients (1,1,1,1), (1,1,1,2), (1,1,1,3), and (1,1,2,1).

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