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coding company - cses

hi I stuck at this problem for quite a long time (coding company - cses), I really need to understand the newk. For example, the sample input /output in cses: 3 2/ 2 5 3. so from dp[0][0][0] there is a way to caculate dp[1][1][0], the newk is 0 which is easy to understand, but for example we consider a case that to i = 1, the numer of unfinished team: 1, and k = 0, the case is: {2) [ ')' mean haven't finished yet] so
from dp[1][1][0] simultaneously it leads to dp[2][2][1], this is where I stuck, i mean from the case that have 1 unfinished team and zero penalty how can it becomes 2 unfinished team and penalty = 1 because i think 2 unfinished team is {2), and {3) or i am misunderstanding and the team is {2,3) and (} which is a team that don't have anyone? which is the case, please help me.

Shortest Subsequence

for given testcase
Example
Input:
ACGTACGT

Output:
AAA

output getting is TTA ? But still solution is accepted

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