CF2063B Subsequence Update

After Little John borrowed expansion screws from auntie a few hundred times, eventually she decided to come and take back the unused ones.But as they are a crucial part of home design, Little John decides to hide some in the most unreachable places — under the eco-friendly wood veneers. You are given an integer sequence $ a_1, a_2, \ldots, a_n $ , and a segment $ [l,r] $ ( $ 1 \le l \le r \le n $ ). You must perform the following operation on the sequence exactly once. - Choose any subsequence $ ^{\text{∗}} $ of the sequence $ a $ , and reverse it. Note that the subsequence does not have to be contiguous. Formally, choose any number of indices $ i_1,i_2,\ldots,i_k $ such that $ 1 \le i_1 < i_2 < \ldots < i_k \le n $ . Then, change the $ i_x $ -th element to the original value of the $ i_{k-x+1} $ -th element simultaneously for all $ 1 \le x \le k $ . Find the minimum value of $ a_l+a_{l+1}+\ldots+a_{r-1}+a_r $ after performing the operation. $ ^{\text{∗}} $ A sequence $ b $ is a subsequence of a sequence $ a $ if $ b $ can be obtained from $ a $ by the deletion of several (possibly, zero or all) element from arbitrary positions.

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10^4 $ ). The description of the test cases follows. The first line of each test case contains three integers $ n $ , $ l $ , $ r $ ( $ 1 \le l \le r \le n \le 10^5 $ ) — the length of $ a $ , and the segment $ [l,r] $ . The second line of each test case contains $ n $ integers $ a_1,a_2,\ldots,a_n $ ( $ 1 \le a_{i} \le 10^9 $ ). It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 10^5 $ .

For each test case, output the minimum value of $ a_l+a_{l+1}+\ldots+a_{r-1}+a_r $ on a separate line.

On the second test case, the array is $ a=[1,2,3] $ and the segment is $ [2,3] $ . After choosing the subsequence $ a_1,a_3 $ and reversing it, the sequence becomes $ [3,2,1] $ . Then, the sum $ a_2+a_3 $ becomes $ 3 $ . It can be shown that the minimum possible value of the sum is $ 3 $ .