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 Python (3.4.3) (judge verdict: Wrong Answer)

N,M = list(map(int,input().split()))

AB_list = []
for i in range(N):
    AB_list.append(list(map(int,input().split())))

AB_list = sorted(AB_list)

schedule = [0]*(M+1)
day = 0
hold_joblist = [0]

#どう考えてもTLE
for i in range(N):
    if day < AB_list[i][0]:
        day = AB_list[i][0]
        if M < day:
            break
    if schedule[day] == 0:
        if hold_joblist[0] < AB_list[i][1]:
            schedule[day] = AB_list[i][1]
        else:
            schedule[day] = hold_joblist.pop(0)
            if hold_joblist[0] < AB_list[i][1]:
                hold_joblist.insert(0,AB_list[i][1])
            else:
                hold_joblist.append(AB_list[i][1])
                list.sort(hold_joblist, reverse=True)
    elif schedule[day] < AB_list[i][1]:
        if hold_joblist[0] < schedule[day]:
            hold_joblist.insert(0,schedule[day])
        else:
            hold_joblist.append(schedule[day])
            list.sort(hold_joblist, reverse=True)
        schedule[day] = AB_list[i][1]
    else:
        if hold_joblist[0] < AB_list[i][1]:
                hold_joblist.insert(0,AB_list[i][1])
        else:
            hold_joblist.append(AB_list[i][1])
            list.sort(hold_joblist, reverse=True)

for i in range(day+1,M+1):
    if hold_joblist:
        schedule[i] = hold_joblist.pop(0)
    else:
        break

print(sum(schedule))