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: Accepted)

n, m = gets.split.map(&:to_i)
ab = n.times.map {gets.split.map(&:to_i)}.sort_by{|e| e[0]}

@heap = Array.new(n+1, 0)
@l = 0

def enque(x)
    @l += 1
    @heap[@l] = x
    i = @l
    while i > 1 && @heap[i] > @heap[i/2]
        @heap[i], @heap[i/2] = @heap[i/2], @heap[i]
        i /= 2
    end
end

def deque
    if @l == 0
        0
    elsif @l == 1
        @l = 0
        x, @heap[1] = @heap[1], 0
        x
    else
        x, @heap[1], @heap[@l] = @heap[1], @heap[@l], 0
        @l -= 1
        i = 1
        while i*2 <= @l
            j = @heap[i*2] > @heap[i*2+1] ? i*2 : i*2+1
            break if @heap[i] >= @heap[j]
            @heap[i], @heap[j] = @heap[j], @heap[i]
            i = j
        end
        x
    end
end

ans = 0
0.upto(m) do |i|
    enque(ab.shift[1]) while !ab.empty? && ab[0][0] <= i
    ans += deque
end

puts ans