Statement

There are several programs in high school, and since students have many interests and would like to enroll in more than one program but places are limited, the school has set up entrance exams. There are M high school programs and each program has capacity of c_i students. For each student you know the list of distinct programs they applied to (in strictly decreasing order of preference) and the corresponding final score for each program in the list. Each high school program must be assigned an integer cutoff score t_i and once the cutoff are assigned, the admission process is defined as follows: (1) A student j qualifies for program i if his/her score is at least t_i. (2) Each student is assigned to the first program in their preference list for which they qualify. (3) If a student does not qualify for any program in their list, they remain unassigned. A cutoff assignment is called feasible if for every program, the number of students assigned to it does not exceed its capacity c_i...