Sangheon's Course Registration Challenge

At KSA, students must pick the courses they want and register for them. Sangheon worries that if his total credits go over $M$, he cannot keep his GPA up, so he wants to register for courses whose total credits are at most $M$. There are $N$ courses available, numbered 1 through $N$. Sangheon's preference for course $i$ is $P_i$, and its credit count is $C_i$. Write a program that finds a way to register so that the total credits are at most $M$ and the total preference is maximized. Each course can be chosen at most once, and he must register for at least one course.

The first line contains two integers $N$ ($1 \le N \le 5000$) and $M$ ($1 \le M \le 5000$). Each of the next $N$ lines contains two integers $P_i$ ($1 \le P_i \le 10^5$) and $C_i$ ($1 \le C_i \le 5000$).

On the first line, print the number of courses to register for if a valid way exists, or -1 otherwise. If a way exists, print the course numbers in ascending order on the second line. If several answers exist, any of them is accepted.