Jethalal and Babita

Jethalal's favourite numbers are $n$ and 1, and Babita's favourite numbers are $m$ and −1. One day Jethalal and Babita met and wrote down every possible array of length $n+m$ such that some $n$ of its elements are equal to 1 and another $m$ elements are equal to −1. For each such array they counted its maximal prefix sum, probably an empty one which is equal to 0 (in another words, if every nonemp