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: Time Limit Exceeded)

def main():
  _map = map
  _range = range
  _len = len
  _max = max
  _input = input
  _int = int
  n, m = _map(_int, _input().split())
  d1 = [None] * (m + 1)
  for _ in _range(n):
    a, b = _map(_int, _input().split())
    if a > m:
      continue
    if d1[a] is None:
      d1[a] = [b]
    else:
      d1[a].append(b)
  result = 0
  d2 = {}
  maxb = -1
  for i in _range(1, m + 1):
    if d1[i] is None:
      if _len(d2) == 0:
        continue
    else:
      for j in d1[i]:
        if j not in d2:
          d2[j] = 1
        else:
          d2[j] += 1
        if j > maxb:
          maxb = j
    result += maxb
    d2[maxb] -= 1
    if d2[maxb] == 0:
      del d2[maxb]
      if _len(d2) == 0:
        maxb = -1
      else:
        maxb = _max(d2.keys())
  print(result)
main()