2024 AMC 10B Problem 5

In the following expression, Melanie changed some of the plus signs to minus signs:

\[1 + 3 + 5 + 7 + \cdots + 97 + 99\]

When the new expression was evaluated, it was negative. What is the least number of plus signs that Melanie could have changed to minus signs?

\textbf{(A)} 14 \qquad \textbf{(B)} 15 \qquad \textbf{(C)} 16 \qquad \textbf{(D)} 17 \qquad \textbf{(E)} 18

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.