A. Assemble the Tower
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You need to build a tower with a height of $$$H$$$ layers. The tower is constructed from blocks stacked from the bottom up. Each block, except for the topmost one, consists of $$$K$$$ layers. The top block can contain at most $$$K$$$ layers. Each layer in a block consists of exactly $$$P$$$ bricks. All bricks in a block are of the same color. There are $$$C$$$ different colors of bricks available.

The bottom block is made of bricks of color $$$1$$$, the next block of color $$$2$$$, and so on, such that the $$$C$$$-th block is of color $$$C$$$. The block after that (the $$$(C + 1)$$$-th block) is of color $$$1$$$, the $$$(C + 2)$$$-th block is of color $$$2$$$, etc.

Currently, only the bottom part of the tower has been built, consuming $$$N$$$ bricks. Your task is to calculate how many bricks of each color will be needed to complete the tower to the full height of $$$H$$$ layers.

Input

The input file contains a single line with five integers $$$H$$$, $$$P$$$, $$$C$$$, $$$K$$$, and $$$N$$$ ($$$2 \leq H \leq 100,000$$$, $$$3 \leq P \leq 10,000$$$, $$$1 \leq C \leq H$$$, $$$1 \leq K \leq H$$$, and $$$1 \leq N \leq H \cdot P - 1$$$), which correspond to the tower's height, the number of bricks in one layer, the number of different colors, the number of layers in a block, and the number of bricks used in the constructed part, respectively.

Output

Output $$$C$$$ integers in a single line, where the $$$i$$$-th integer represents the required number of bricks of color $$$i$$$.

Examples
Input
5 4 2 2 7
Output
5 8
Input
10 5 10 10 1
Output
49 0 0 0 0 0 0 0 0 0