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 (3.8.2) (judge verdict: Accepted)

N,M = map(int,input().split())
AB = [list(map(int,input().split())) for _ in range(N)]

AB.sort(key= lambda x:(-x[1],-x[0]))#報酬が高く、かつ、振り込みの日数が長いものからやるためのソート
memo = [0]*(10**5+1)#請け負うと決めた仕事の日のメモ。1がついている日は仕事がすでにある
work = [float('inf')]*(10**5+1)#振り込みまでに必要な日数のうち、前回請け負いを決めた日
noMore = float('inf') #これ以上の日数が振り込みにかかる仕事は受けれない
ans = 0
for a,b in AB:
    if a< noMore:#期日までに報酬が受け取れる仕事であること
        flag = 1
        for idx in range(min(M-a,work[a]),-1,-1):#この検索範囲の絞り込みがTLE解消の決め手。前回検索時に請け負った日またはM-a日以前の日
            if memo[idx] == 0:#仕事が請けられる
                ans += b#報酬を足す
                memo[idx]=1#仕事を受けたことの記録。この日はもう受けられない
                flag = 0#noMoreの更新分岐のため
                work[a] = idx#次回検索時のメモ
                break
        if flag ==1:#請けれる日が見つからなければ、今後この日数以上の日は受けれないので調べない
            noMore = a
    
print(ans)