Copy data in table to column in worksheet

I would like to know if a macro, or a formula, can accomplish the following.
ON worksheet 1, I have data in table format. Within the range of data (every
other column), for each cell that has a value, I would like that value copied
to the first blank row, within column A, of worksheet 2. Column B of WS2
would then be populated with the row label for that piece of data; Column C
of WS 2 would be populated with the column label for that piece of data.

The data can be copied from WS1 in any order (top to bottom first, left to
right first), but it should only search for data in every other column (B & D
in the example below). If a cell is blank, nothing would be copied to WS2.
That cell would not remain blank, however. EAch searchd cell in WS1 (with
data) would be copied to the next blank cell in Col A in WS2

Worksheet 1:

A B C D E
1 Line # AM PM
2 L1 2199 Smith 2173 Jones
3 L2 2203 Johnson
4 L3 2200 Brown 2177 Edwards


Worksheet 2 results:

A B C
1 2199 L1 AM
2 2200 L3 AM
3 2173 L1 PM
4 2203 L2 PM
5 2177 L3 PM

Thank you all for your help