Note: The time limit for this problem is 3s, 1.5x the default. The memory limit for this problem is 512MB, twice the default. Bessie is taking an $N$-question true or false test ($1\le N\le 2\cdot 10^5$). For the $i$-th question, she will gain $a_i$ points if she gets it correct, lose $b_i$ points if she gets it incorrect, or remain even if she does not answer it ($0 < a_i,b_i\le 10^9$). Bessie knows all the answers because she is a smart cow, but worries that Elsie (who is administering the test) will retroactively change up to $k$ of the questions after the test such that Bessie does not get those questions correct. Given $Q$ ($1\le Q\le N+1$) candidate values of $k$ ($0\le k\le N$), determine the number of points Bessie can guarantee for each $k$, given that she must answer at least $k$ questions.

Input Format

The next $N$ lines each contain $a_i$ and $b_i$. The next $Q$ lines each contain a value of $k$. No value of $k$ appears more than once.

The next $Q$ lines each contain a value of $k$. No value of $k$ appears more than once.

Output Format

The answer for each $k$ on a separate line.

Sample Data

Sample Input

2 3
3 1
4 2
2
1
0

Sample Output

-3
1
7

Sample Explanation

For each value of $k$, it is optimal for Bessie to answer all of the questions.

Constraints

• Inputs 2-4: $N\le 100$
• Inputs 5-7: $Q\le 10$, $N\le 2\cdot 10^5$
• Inputs 7-20: No additional constraints.