Josh is playing with number pyramids! A number pyramid consists of ~N~ rows, labelled from ~1~ to ~N~ from top to bottom. The ~i~-th row contains ~i~ cells, each containing a single integer between ~0~ and ~K-1~ (inclusive).

A number pyramid has a special property; each cell (apart from those on the ~N~-th row) contains an integer equal to the sum of the two integers in the cells directly below it, modulo ~K~. Formally, if ~v_{i, j}~ is the integer written in the ~j~-th cell (from the left) of the ~i~-th row, then ~v_{i, j} = (v_{i+1, j} + v_{i+1, j+1})~ mod ~K~. A number pyramid with ~N = 6~ and ~K = 5~ is shown below for clarity.

Josh would like to construct a number pyramid such that the integer written in the topmost cell is ~X~ (i.e. ~v_{1, 1} = X~). He wonders the following question: what is the lexicographically largest sequence of integers written in the bottom row of any such number pyramid? Formally, what is the lexicographically largest possible sequence ~v_{N, 1}, v_{N, 2}, \dots, v_{N, N}~? Note that Josh cannot choose the values of ~N~ and ~K~, and that all integers in the pyramid must be between ~0~ and ~K-1~ (inclusive).

Sequence ~a_1, a_2, a_3, \dots, a_N~ is lexicographically larger than sequence ~b_1, b_2, b_3, \dots, b_N~ if, for the smallest ~i~ such that ~a_i \neq b_i~, ~a_i > b_i~.

Constraints

~2 \le N \le 10^6~

~1 \le K \le 10^9~

~0 \le X < K~

Subtask 1 [10%]

~N = 2~

Subtask 2 [20%]

~2 \le N \le 200~

~1 \le K \le 200~

Subtask 3 [30%]

~2 \le N \le 2000~

Subtask 4 [40%]

No additional constraints.

Input Specification

The only line contains three space-separated integers, ~N~, ~K~, and ~X~ respectively.

Output Specification

On a single line, output ~N~ space-separated integers, representing the lexicographically largest possible sequence of integers written on row ~N~.

Sample Input

3 2 1

Sample Output

1 1 0

Explanation

The optimal number pyramid is shown below.