2009 Gauss 8 Problem 13

In how many ways can 101 be expressed as the sum of two integers, both greater than zero, with the second integer greater than the first?

\textbf{(A)}\ 50\quad \textbf{(B)}\ 51\quad \textbf{(C)}\ 101\quad \textbf{(D)}\ 102\quad \textbf{(E)}\ 25

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Gauss contests here.