Alice Potter And Dumbledore Army

Dumbledore's Army consists of $N$ members. Alice Potter is planning to hold $M$ Dumbledore's Army sessions, where the members will perform training tasks to improve their skills in Defense Against the Dark Arts. Initially, each member of the Army has no tasks. Before the $i$-th training session, Alice gives the $P_i$-th participant a task that he can complete in $T_i$ seconds. And each subsequent