Retrograde problem 1

Logic Level 2

In the following position, the color of each piece is unknown (each piece could either be white or black), but it is known that the position arose from a series of legal moves, starting at the usual starting position.

Before the last move was made, Black had \(a\) pieces worth \(b\) points (on the scale Queen = 9, Rook = 5, Bishop = Knight = 3, Pawn = 1, King = 0). What is the product of \(a\) and \(b\)?

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