D. Elephant grassland
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

To restore the elephant population in an African country, it was proposed that a specialized farm be created. A $$$n\times m$$$ kilometers section of savannah was allocated for the farm. The number of an elephant herd is such that in a day it eats vegetation on 1 square kilometer area, after which it should be moved to another place.

To optimize the process, the entire farm was divided into square plots with a side of 1 km, fenced. It was decided that the relocation of the herd would be carried out only once a day and only to the neighboring plot, which has a common side with the current one.

It was found that to maintain the most natural feeding process, elephants should eat the same grass for $$$ k $$$ days in a row. Each plot of the future grassland will be sown with one type of grass, and a total of $$$ p $$$ of grass varieties will be used.

To restore vegetation between herd visits as much as possible, it was proposed to create a cyclic route in such a way that it:

  • was as long as possible;
  • crossed only the vertical or horizontal boundaries of the plots;
  • did not contain self-intersections;
  • consisted of $$$ p $$$ segments sown with the same grass, with $$$ k $$$ plots in each.

Write a program that, using the given numbers $$$ n $$$, $$$ m $$$, $$$ k $$$ and $$$ p $$$, creates a route of the elephant herd, or report that there is no such solution.

Input

Input contains of four integers: $$$n ~ (1 \leq n\leq 100)$$$, $$$m ~ (1 \leq m\leq 100)$$$, $$$k$$$ and $$$ p $$$ $$$( k, p \gt 0,~ 2 \lt k\times p \leq n \times m )$$$ separated by spaces.

Output

The first line of the output should contain the word "YES" (without quotes) if a solution exists, and the word "NO" otherwise.

If a solution exists, then output a block of $$$n$$$ lines.

The block describes the route of the herd. Each line consists of $$$m$$$ different characters:

  • "."(dot) if this section is not visited;
  • "-"(minus) if the herd route crosses the left and right boundaries of the site;
  • "|"(vertical line) if the herd route crosses the upper and lower boundaries of the site;
  • "L"(capital Latin L) if the herd route crosses the upper and right boundaries of the site;
  • "r"(lowercase Latin r) if the herd route crosses the lower and right boundaries of the site;
  • "J"(Latin capital J) if the herd route crosses the left and upper boundaries of the site;
  • "7"(number 7) if the herd route crosses the left and lower boundaries of the site.

If there are multiple solutions, output any of them.

Examples
Input
3 3 2 4
Output
YES
r-7
|rJ
LJ.
Input
3 3 3 3
Output
NO