Paint the Canvas

You are given a canvas of n rows and m columns, and k colors numbered from 1 to k. The task is to fill the canvas with colors such that the following constraints are satisfied for every cell:

• No cell in the p cells directly above (if any) has the same color.
• No cell in the q cells immediately to the left (if any) has the same color.
• No cell in the r cells diagonally top-left (if any) has the same color.

Determine whether there exists a valid way to paint the entire canvas following these rules. If such a valid coloring exists, output YES followed by the canvas configuration. Otherwise, output NO.

Note: If there are multiple valid solutions, outputting any one of them is acceptable. All formulas in this statement are provided in LaTeX format. For example, the constraints are as follows:

\( \text{Above constraint: For cell } (i,j), \; \forall t \in \{1,2,\ldots,p\}, \; \text{if } i-t \ge 0 \text{ then } canvas[i-t][j] \neq canvas[i][j] \).

\( \text{Left constraint: For cell } (i,j), \; \forall t \in \{1,2,\ldots,q\}, \; \text{if } j-t \ge 0 \text{ then } canvas[i][j-t] \neq canvas[i][j] \).

\( \text{Diagonal constraint: For cell } (i,j), \; \forall t \in \{1,2,\ldots,r\}, \; \text{if } i-t \ge 0 \text{ and } j-t \ge 0 \text{ then } canvas[i-t][j-t] \neq canvas[i][j] \).

inputFormat

The input consists of a single line containing six space-separated integers: n, m, k, p, q, and r.

• n: Number of rows of the canvas.
• m: Number of columns of the canvas.
• k: Total number of colors available (colors are labeled 1 through k).
• p: The number of cells above to check for color conflicts.
• q: The number of cells to the left to check for color conflicts.
• r: The number of cells in the top-left diagonal to check for color conflicts.

outputFormat

If a valid painting exists, output should consist of:

• A first line with the string "YES".
• n subsequent lines where each line contains m space-separated integers representing the colors of the canvas row.

If no valid coloring exists, output should be a single line containing "NO".## sample

3 3 3 2 2 1

YES
1 2 3
2 3 1
3 1 2

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