Of Sets and Sums

Consider the set \( \lbrace{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\rbrace}\).

For each of its subsets, let \( M \) be the greatest number. Find the last three digits of the sum of all the \( M \)'s.

Assume that \(0\) is the greatest number of the empty subset.

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