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 Ruby (2.3.3) (judge verdict: Wrong Answer)

#!/usr/bin/ruby

n, m = gets.split.map { |s| s.to_i }
ab = []
(0...n).each { |i|
  ab[i] = gets.split.map { |s| s.to_i }
}
ab.sort! { |ab1, ab2|
  a1, b1 = ab1
  a2, b2 = ab2
  if b1 != b2
    b2 <=> b1
  else
    a1 <=> a2
  end
}
max = 0
ab.combination([n, m].min) { |abm|
  occupied = (0...m).to_a.map { false }
  sum = 0
  (0...abm.length).each { |i|
    a, b = abm[i]
    while a <= m && occupied[a]
      a += 1
    end
    break if a > m
    occupied[a] = true
    sum += b
  }
  max = sum if max < sum
}
puts max