Submitted a solution but that doesn’t seem to work for precision loss.

Went through the tutorial, but not able to understand a specific observation which is stated as

" This algorithm works because if Liss divides an interval into two intervals *A* and *B* and she enters *A*, she will never enter *B* ."

Tutorial link: Codeforces Round #162 Tutorial - Codeforces

Can someone please explain to me what is the signification of the above line.