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: Wrong Answer)

use std::collections::HashMap;

fn main(){
    let mut reward:HashMap<usize, Vec<usize>>  = HashMap::new();
    let inp: Vec<usize> = read_vec();
    // 面倒になった...
    for e in 0..inp[1] {
        reward.insert(e, Vec::new());
    }
    for i in 0..inp[0] {
        let edge: Vec<usize> = read_vec();
        let a = edge[0]-1;
        let b = edge[1];
        let num = reward.entry(a).or_insert(Vec::new());
        num.push(b);
    };


    let mut heap = Heap{
        tree: Vec::new(),
        n: 0
    };

    let mut ans = 0;
    for i in 0..inp[1] {
        if let Some(x_ls) = reward.get(&i) {
            for fee in x_ls {
                heap.insert(*fee);
            };
        }
        if heap.n > 0 {
            let val = heap.take();
            ans += val;
        }
    };

    println!("{}", ans);


}

struct Heap {
    tree: Vec<usize>,
    n: usize,
}

impl Heap {
    fn insert(&mut self, m: usize){
        self.n += 1;
        self.tree.push(m);
        let mut index = self.n-1;
        let mut done = false;
        if index == 0 {
            done = true;
        }
        while !done {
            let next_index = (index-1) / 2;
            if self.tree[next_index as usize] > self.tree[index as usize]{
                done = true;
            } else {
                let next_val = self.tree[next_index as usize];
                self.tree[next_index as usize] = self.tree[index as usize];
                self.tree[index as usize] = next_val;
                index = next_index;
                if index == 0 {
                    done = true;
                }
            }
        }
    }


    fn take(&mut self) -> usize {
        let res = self.tree[0];
        self.tree[0] = self.tree[self.n-1];
        self.tree.pop();
        self.n -= 1;
        let mut index = 0;
        let mut done = false;
        while !done {
            if self.n < 2 * index + 2 {
                done = true;
            } else if self.n == 2 * index + 2{
                done = true;
                if self.tree[2*index+1] > self.tree[index] {
                    let next_val = self.tree[2*index+1];
                    self.tree[2*index+1] = self.tree[index];
                    self.tree[index] = next_val;
                }
            } else {
                let next_index = if self.tree[2*index + 1] > self.tree[2*index+2] {2 * index + 1} else {2* index + 2};
                let next_val = self.tree[next_index];
                self.tree[next_index] = self.tree[index];
                self.tree[index] = next_val;
                index = next_index;
            } 
        };
        res
    }

}


fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().split_whitespace().map(|e| e.parse().ok().unwrap()).collect()
}