# Combinatorics + function = lot of fun

Let $$A = \{a_1, a_2, \ldots, a_{100}\}$$ and $$B = \{b_1, b_2, \ldots, b_{50}\}$$ be two sets of real numbers.

How many non-decreasing function from $$A$$ to $$B$$ are there such that every element of $$B$$ has an inverse image?

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