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: Runtime Error)

#!/usr/bin/env python3

def total_money(bs, m, m_max):
    m = min(m, m_max)
    if m == 1:
        mx = 0
        for i in reversed(range(m)):
            if len(bs[i]) > 0:
                if bs[i][0] > mx:
                    mx = bs[i][0]
        return mx

    mx = 0
    max_tmp  = 0
    for i in reversed(range(m)):
        if len(bs[i]) > 0:
            tmp = bs[i][0]
            if tmp > max_tmp:
                max_tmp = tmp
                bs[i] = bs[i][1:]
                subtotal = total_money(bs, m-1, i+1)
                if tmp+subtotal > mx:
                    mx = tmp+subtotal
            bs[i].insert(0, tmp)
    return mx


def solve(N, M, A, B):
    # 下準備
    bs = [[]] * M
    for a,b in zip(A, B):
        if a <= M:
            bs[a-1] = sorted(bs[a-1] + [b], reverse=True)

    return total_money(bs, M, M)


if __name__ == '__main__':
    N, M = map(int, input().split())
    A = [0] * N
    B = [0] * N
    for idx in range(N):
        A[idx], B[idx] = map(int, input().split())

    ans = solve(N, M, A, B)

    print(ans)