Fortune Telling 2

Professor K is the president of the Japanese committee for the International Olympiad in Informatics. He likes fortune telling and always has several kinds of it going. Today he decided to tell the fortune of this year's Japanese delegation with cards.

An integer is written on each side of every card. The two integers on one card are not necessarily different. Once a card lies on the table, only the integer on the upper side is visible and the integer on the other side is hidden.

The fortune telling goes as follows.

• Professor K puts $N$ cards on the table. The cards are numbered from 1 to $N$. The integer $A_i$ is written on one side of card $i$ and the integer $B_i$ is written on its other side. For every $i$ he puts card $i$ down so that $A_i$ is visible.
• For $j = 1, 2, \dots, K$ in this order he performs the following operation. He turns over every card whose visible integer is less than or equal to $T_j$.
• The result of the fortune telling is the sum of the integers visible on the cards after all $K$ operations are finished.

Deciding which cards to turn over is a boring job, so Professor K gave up telling fortunes with cards. He only wants the sum of the integers visible on the table after all $K$ operations are finished.

Given the integers written on the cards and the description of the operations, write a program that computes the sum of the integers visible on the cards after every operation is finished.

Read the following data from standard input.

• The first line contains two integers $N$ and $K$ separated by a space. There are $N$ cards and $K$ operations.
• The $i$-th of the next $N$ lines ($1 \le i \le N$) contains two integers $A_i$ and $B_i$ separated by a space. The integers written on card $i$ are $A_i$ and $B_i$.
• The $j$-th of the next $K$ lines ($1 \le j \le K$) contains an integer $T_j$. In the $j$-th operation every card whose visible integer is less than or equal to $T_j$ is turned over.

All input data satisfy the following conditions.

• $1 \le N \le 200000$
• $1 \le K \le 200000$
• $1 \le A_i \le 1000000000$ ($1 \le i \le N$)
• $1 \le B_i \le 1000000000$ ($1 \le i \le N$)
• $1 \le T_j \le 1000000000$ ($1 \le j \le K$)

Print to standard output, on one line, the sum of the integers visible on the cards after the $K$ operations are finished.

In the first example the integers visible at the start are 4, 9, 8, 4, 3 in this order. The operations run as follows.

• Every card whose visible integer is at most 8 is turned over. After the operation the visible integers are 6, 9, 8, 2, 7.
• Every card whose visible integer is at most 2 is turned over. After the operation the visible integers are 6, 9, 8, 4, 7.
• Every card whose visible integer is at most 9 is turned over. After the operation the visible integers are 4, 1, 8, 2, 3.

After all operations the sum of the visible integers is $4+1+8+2+3 = 18$.