Cleaning Drive

There is a hallway of length $N-1$ and you have $M$ workers to clean the floor. Each worker is responsible for segment $[L_i, R_i]$, i.e., the segment starting at $L_i$ and ending at $R_i$. The segments might overlap. Every unit of length of the floor should be cleaned by at least one worker. A worker can clean $1$ unit of length of the floor in $1$ unit of time and can start from any position