Problem:
Score : 400 points

Problem Statement

There are N one-off jobs available. If you take the i-th job and complete it, you will earn the reward of B_i after A_i days from the day you do it.

You can take and complete at most one of these jobs in a day.

However, you cannot retake a job that you have already done.

Find the maximum total reward that you can earn no later than M days from today.

You can already start working today.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq A_i \leq 10^5

1 \leq B_i \leq 10^4

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
A_2 B_2
\vdots
A_N B_N

Output

Print the maximum total reward that you can earn no later than M days from today.

Sample Input 1

3 4
4 3
4 1
2 2

Sample Output 1

5

You can earn the total reward of 5 by taking the jobs as follows:

Take and complete the first job today. You will earn the reward of 3 after four days from today.

Take and complete the third job tomorrow. You will earn the reward of 2 after two days from tomorrow, that is, after three days from today.

Sample Input 2

5 3
1 2
1 3
1 4
2 1
2 3

Sample Output 2

10

Sample Input 3

1 1
2 1

Sample Output 3

0

Solution in Rust (1.15.1) (judge verdict: Accepted)

fn read_stdin() -> String {
    use std::io::Read;
    let mut input = String::new();
    std::io::stdin().read_to_string(&mut input).unwrap();
    input
}

fn scan<'a, I: Iterator<Item = &'a str>, T: std::str::FromStr>(tokens: &mut I) -> T {
    tokens.next().unwrap().parse().ok().unwrap()
}

fn vec<T, F: FnMut(usize) -> T>(n: usize, mut f: F) -> Vec<T> {
    (0..n).map(|i| f(i)).collect()
}

fn main() {
    use std::collections::{BinaryHeap, VecDeque};
    let input = read_stdin();
    let tokens = &mut input.split_whitespace();
    let n: usize = scan(tokens);
    let m: usize = scan(tokens);
    let mut ab: Vec<(usize, usize)> = vec(n, |_| {
        let a: usize = scan(tokens);
        let b: usize = scan(tokens);
        (a, b)
    });
    ab.sort();
    let mut ab = VecDeque::from(ab);
    let mut heap = BinaryHeap::new();
    let mut ans = 0;
    for i in 0..m + 1 {
        while ab.front().map_or(false, |&(a, _)| a <= i) {
            let (_, b) = ab.pop_front().unwrap();
            heap.push(b);
        }
        if let Some(b) = heap.pop() {
            ans += b;
        }
    }
    println!("{}", ans);
}