USACO 2025 February Contest, Platinum
Problem 3. True or False Test
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**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 (input arrives from the terminal / stdin):
The first line contains $N$ and $Q$.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.
OUTPUT FORMAT (print output to the terminal / stdout):
The answer for each $k$ on a separate line.SAMPLE INPUT:
2 3 3 1 4 2 2 1 0
SAMPLE OUTPUT:
-3 1 7
For each value of $k$, it is optimal for Bessie to answer all of the questions.
SCORING:
- Inputs 2-4: $N\le 100$
- Inputs 5-7: $Q\le 10$, $N\le 2\cdot 10^5$
- Inputs 7-20: No additional constraints.
Problem credits: Benjamin Qi