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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.

Input format:
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 $$$10^5$$$.
Output format:
For each test case, output the minimum value of $$$a_l+a_{l+1}+\ldots+a_{r-1}+a_r$$$ on a separate line.
Example Input 0:
6
2 1 1
2 1
3 2 3
1 2 3
3 1 3
3 1 2
4 2 3
1 2 2 2
5 2 5
3 3 2 3 5
6 1 3
3 6 6 4 3 2

Example Output 0:
1
3
6
3
11
8

Notes:
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 $$$3$$$.

Example input:
6
2 1 1
2 1
3 2 3
1 2 3
3 1 3
3 1 2
4 2 3
1 2 2 2
5 2 5
3 3 2 3 5
6 1 3
3 6 6 4 3 2


Example output:
1
3
6
3
11
8