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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