25061번 - Antennas 다국어

문제

There are $n$ equidistant antennas on a line, numbered from 1ドル$ to $n$. Each antenna has a power rating, the power of the $i$-th antenna is $p_i$.

The $i$-th and the $j$-th antenna can communicate directly if and only if their distance is at most the minimum of their powers, i.e., $|i - j| ≤ \min{(p_i, p_j)}$. Sending a message directly between two such antennas takes 1ドル$ second.

What is the minimum amount of time necessary to send a message from antenna $a$ to antenna $b,ドル possibly using other antennas as relays?

입력

Each test contains multiple test cases. The first line contains an integer $t$ (1ドル ≤ t ≤ 100,000円$) — the number of test cases. The descriptions of the $t$ test cases follow.

The first line of each test case contains three integers $n,ドル $a,ドル $b$ (1ドル ≤ a, b ≤ n ≤ 200,000円$) — the number of antennas, and the origin and target antenna.

The second line contains $n$ integers $p_1,ドル $p_2,ドル $\dots,ドル $p_n$ (1ドル ≤ p_i ≤ n$) — the powers of the antennas. The sum of the values of $n$ over all test cases does not exceed 200ドル,000円$.

출력

For each test case, print the number of seconds needed to trasmit a message from $a$ to $b$. It can be shown that under the problem constraints, it is always possible to send such a message.

제한

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