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 (1.42.0) (judge verdict: Accepted)

#![allow(unused_imports)]
use std::cmp::*;
use std::collections::*;
use itertools::Itertools;
use num::clamp;
use proconio::{input, marker::*, fastout};
use superslice::*;

#[fastout()]
fn main() {
    input! {
        n: usize, m: usize,
        mut ab: [(isize, i64); n]
    }

    ab.sort_by_key(|&(a, b)| (Reverse(b), a));
    let mut booked = (0..m as isize).collect_vec();
    let mut ans = 0;
    for (days, money) in ab {
        let idx = m as isize - days;
        if idx < 0 {
            continue;
        }
        let mut idx2 = booked[idx as usize];
        while idx2 >= 0 && idx2 != booked[idx2 as usize]  {
            idx2 -= 1;
        }
        if idx2 >= 0 {
            ans += money;
            booked[idx2 as usize] = idx2 - 1;
        }
        booked[idx as usize] = idx2 - 1;
    }
    println!("{}", ans);
}