Search Target <= in Col. "B" to return Date in Col. "A"

[u473]

1. An inputbox for a Target amount (Integer)
2. Search that Target in Col. "B" for <= amount, same worksheet.
3. Return a Date in Col. "A" same row.
..
I cannot use VLookup because I understand the searched value has to be
in the leftmost column. What solutions do I have ?
Help appreciated,
J.P.