Progressive Art

Carlo is a big fan of progressive music and he recently found out that progressive paintings exist too! Clearly, he wants to dive into it, therefore he hired you as his assistant. A progressive painting is made using Vim, and consists of a rectangle of $N \times M$ coloured square cells. Since Carlo wants to be even more progressive, he only uses the colors red, green, and blue.

Carlo has a weird way of judging the beauty of his works. He invented a measure called $L$-beauty. A square of size $L$ (that is, consisiting of $L\times L$ contiguous cells of the painting) is beautiful if it contains an equal number of red, green, and blue cells. The $L$-beauty of the painting is the number of beautiful squares of size $L$ in it.

Task

Carlo asked you a question to test your skill. Given $N$, $M$, $L$ and $K$, does a painting with $N$ rows, $M$ columns, and an $L$-beauty equal to $K$ exist? If so, could you paint one for him?

Input data

The input file consists of a single line, containing the integers $N$, $M$, $L$, and $K$.

Output data

If it is possible to produce a suitable painting, you have to output $N + 1$ lines:

• One line containing the string YES.
• $N$ lines, each containing a string of length $M$, consisting of R, G, and B only, representing red, green, and blue cells in the painting.

If it is not possible to do so, you have to output a single line containing the string NO.

Constraints and clarifications

• $1 \le N \le 1 \ 000$
• $1 \le M \le 1 \ 000$
• $1 \le L \le \min(N, M)$
• $0 \le K \le N\cdot M$

Example 1

stdin

4 3 2 4

stdout

NO

Explanation

It is not possible to make a painting satisfying the constraints.

Example 2

stdin

4 4 3 2

stdout

YES
RBRR
BGGB
GRBG
RBBG

Explanation

One possible painting, represented in the output, is the following:

It contains $4$ squares of size $3$, that are the following:

Only the first $2$ of them contain the same amount of red, green and blue cells. Hence, the painting satisfies Carlo's request.