An RGB Masterpiece

Task

Ovidiu is a fan of pixel art and is particularly interested in RGB grids.
An RGB grid consists of a rectangular grid where every cell is coloured either red, green, or blue.
He also figured out that, in order to create a masterpiece, the following rules have to be followed:

• The grid has $N$ rows and $M$ columns.
• There are exactly $R$ red cells, $G$ green cells and $B$ blue cells.
• There are no cells that share a side and have the same colour.

However, Ovidiu isn't able to create one himself, and he asked for your help.
Can you tell if a masterpiece exists and, if so, produce one?

Input data

The input file consists of a single line containing integers $N$, $M$, $R$, $G$, $B$.

Output data

If a masterpiece exists, the output file must contain $N+1$ lines, the first line must consist of the string YES and the following $N$ lines must contain a string of length $M$, consisting of characters R, G and B, representing a masterpiece.

If there are more than one possible masterpiecee, you may print any of them.

If no masterpiece exists, the output file must consist of a single line containing only the string NO.

Constraints and clarifications

• $1 \le N,M \le 10^5$.
• $1 \le N \cdot M \le 10^5$.
• $0 \le R,G,B \le 10^5$.
• $R + G + B = M \cdot N$.

Example 1

stdin

2 3 2 2 2

stdout

YES
RBG
BGR

Explanation

In the first sample case, one possible masterpiece is depicted below.
Note that there are $2$ red cells, $2$ green cells and $2$ blue cells. Also, no two adjacent cells have the same colors.

Example 2

stdin

3 3 1 6 2

stdout

NO

Explanation

In the second sample case, there are no masterpieces satisfying the requirements.