USACO 2024 December Contest, Platinum
Problem 2. It's Mooin' Time
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**Note: The time limit for this problem is 3s, 1.5x the default.**
Bessie has a string of length $N$ ($1\le N\le 3\cdot 10^5$) consisting solely of the characters M and O. For each position $i$ of the string, there is a cost $c_i$ to change the character at that position to the other character ($1\le c_i\le 10^8$).
Bessie thinks the string will look better if it contains more moos of length $L$ ($1\le L\le \min(N, 3)$). A moo of length $L$ is an M followed by $L-1$ Os.
For each positive integer $k$ from $1$ to $\lfloor N/L\rfloor$ inclusive, compute the minimum cost to change the string to contain at least $k$ substrings equal to a moo of length $L$.
INPUT FORMAT (input arrives from the terminal / stdin):
The first line contains $L$ and $N$.The next line contains Bessie's length-$N$ string, consisting solely of Ms and Os.
The next line contains space-separated integers $c_1\dots c_N$.
OUTPUT FORMAT (print output to the terminal / stdout):
Output $\lfloor N/L\rfloor$ lines, the answer for each $k$ in increasing order.SAMPLE INPUT:
1 4 MOOO 10 20 30 40
SAMPLE OUTPUT:
0 20 50 90
SAMPLE INPUT:
3 4 OOOO 50 40 30 20
SAMPLE OUTPUT:
40
SAMPLE INPUT:
2 20 OOOMOMOOOMOOOMMMOMOO 44743602 39649528 94028117 50811780 97338107 30426846 94909807 22669835 78498782 18004278 16633124 24711234 90542888 88490759 12851185 74589289 54413775 21184626 97688928 10497142
SAMPLE OUTPUT:
0 0 0 0 0 12851185 35521020 60232254 99881782 952304708
SAMPLE INPUT:
3 20 OOOMOMOOOMOOOMMMOMOO 44743602 39649528 94028117 50811780 97338107 30426846 94909807 22669835 78498782 18004278 16633124 24711234 90542888 88490759 12851185 74589289 54413775 21184626 97688928 10497142
SAMPLE OUTPUT:
0 0 0 44743602 119332891 207066974
SCORING:
- Input 5: $L=3, N\le 5000$
- Input 6: $L=1$
- Inputs 7-10: $L=2$
- Inputs 11-18: $L=3$
Problem credits: Benjamin Qi