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D - Summer Vacation

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.

3 4
4 3
4 1
2 2

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.

5 3
1 2
1 3
1 4
2 1
2 3

10

1 1
2 1

0