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 $a_i\ne b_i$, $a_i>b_i$.

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.