E. Wolftime limit per test4 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputWolf has found $$$n$$$ sheep with tastiness values $$$p_1, p_2, ..., p_n$$$ where $$$p$$$ is a permutation$$$^{\text{∗}}$$$. Wolf wants to perform binary search on $$$p$$$ to find the sheep with tastiness of $$$k$$$, but $$$p$$$ may not necessarily be sorted. The success of binary search on the range $$$[l, r]$$$ for $$$k$$$ is represented as $$$f(l, r, k)$$$, which is defined as follows:If $$$l > r$$$, then $$$f(l, r, k)$$$ fails. Otherwise, let $$$m = \lfloor\frac{l + r}{2}\rfloor$$$, and: If $$$p_m = k$$$, then $$$f(l, r, k)$$$ is successful, If $$$p_m < k$$$, then $$$f(l, r, k) = f(m+1, r, k)$$$, If $$$p_m > k$$$, then $$$f(l, r, k) = f(l, m-1, k)$$$. Cow the Nerd decides to help Wolf out. Cow the Nerd is given $$$q$$$ queries, each consisting of three integers $$$l$$$, $$$r$$$, and $$$k$$$. Before the search begins, Cow the Nerd may choose a non-negative integer $$$d$$$, and $$$d$$$ indices $$$1 \le i_1 < i_2 < \ldots < i_d \le n$$$ where $$$p_{i_j} \neq k$$$ over all $$$1 \leq j \leq d$$$. Then, he may re-order the elements $$$p_{i_1}, p_{i_2}, ..., p_{i_d}$$$ however he likes.For each query, output the minimum integer $$$d$$$ that Cow the Nerd must choose so that $$$f(l, r, k)$$$ can be successful, or report that it is impossible. Note that the queries are independent and the reordering is not actually performed.$$$^{\text{∗}}$$$A permutation of length $$$n$$$ is an array that contains every integer from $$$1$$$ to $$$n$$$ exactly once.InputThe first line of the input contains a single integer $$$t$$$ $$$(1 \le t \le 10^4)$$$ — the number of test cases.The first line of each test contains two integers $$$n$$$ and $$$q$$$ $$$(1 \le n, q \le 2 \cdot 10^5)$$$ — the length of $$$p$$$ and the number of queries respectively.The second line contains $$$n$$$ integers $$$p_1, p_2, ..., p_n$$$ — the tastiness of the $$$i$$$-th sheep. It is guaranteed that every integer from $$$1$$$ to $$$n$$$ appears exactly once in $$$p$$$.The following $$$q$$$ lines contain three integers $$$l$$$, $$$r$$$, and $$$k$$$ $$$(1 \le l \le r \le n, 1 \le k \le n)$$$ — the range that the binary search will be performed on and the integer being searched for each query.It is guaranteed that the sum of $$$n$$$ and the sum of $$$q$$$ over all cases do not exceed $$$2 \cdot 10^5$$$.OutputFor each query, output the minimum integer $$$d$$$ that Cow the Nerd must choose so that $$$f(l, r, k)$$$ is successful on a new line. If it is impossible, output $$$-1$$$.ExampleInput85 31 2 3 4 51 5 41 3 43 4 47 43 1 5 2 7 6 43 4 22 3 51 5 61 7 32 12 11 2 11 111 1 17 13 4 2 5 7 1 61 7 116 116 10 12 6 13 9 14 3 8 11 15 2 7 1 5 41 16 416 114 1 3 15 4 5 6 16 7 8 9 10 11 12 13 21 16 1413 112 13 10 9 8 4 11 5 7 6 2 1 31 13 2Output0 -1 0
2 0 -1 4
-1
0
-1
-1
-1
-1
NoteIn the first example, second query: Since $$$4$$$ does not exist in the first three elements, it is impossible to find it when searching for it in that range.In the second example, on the first query, you may choose the indices $$$2$$$, $$$3$$$, and swap them so $$$p = [3, 5, 1, 2, 7, 6, 4]$$$. Then, $$$f(3, 4, 2)$$$ will work as follows: Let $$$m = \lfloor \frac{3 + 4}{2} \rfloor = 3$$$. Because $$$p_3 = 1 < 2$$$, then $$$f(3, 4, 2) = f(4, 4, 2)$$$. Let $$$m = \lfloor \frac{4 + 4}{2} \rfloor = 4$$$. Because $$$p_4 = 2 = k$$$, then $$$f(4, 4, 2)$$$ is successful. Therefore, $$$f(3, 4, 2)$$$ is also successful. The total indices chosen were $$$2$$$, so the final cost is $$$2$$$, which can be shown that is minimum. Note that for this query we can't choose index $$$4$$$, since $$$p_4 = k = 2$$$.In the last query of the second example, we can choose indices $$$2, 3, 4, 5$$$ and re-arrange them so $$$p = [3, 5, 2, 7, 1, 6, 4]$$$. Then, $$$f(1, 7, 3)$$$ is successful.