Description:
You are given an integer array $$$a_1,\ldots, a_n$$$, where $$$1\le a_i \le n$$$ for all $$$i$$$.
There's a "replace" function $$$f$$$ which takes a pair of integers $$$(l, r)$$$, where $$$l \le r$$$, as input and outputs the pair $$$$$$f\big( (l, r) \big)=\left(\min\{a_l,a_{l+1},\ldots,a_r\},\, \max\{a_l,a_{l+1},\ldots,a_r\}\right).$$$$$$
Consider repeated calls of this function. That is, from a starting pair $$$(l, r)$$$ we get $$$f\big((l, r)\big)$$$, then $$$f\big(f\big((l, r)\big)\big)$$$, then $$$f\big(f\big(f\big((l, r)\big)\big)\big)$$$, and so on.
Now you need to answer $$$q$$$ queries. For the $$$i$$$-th query you have two integers $$$l_i$$$ and $$$r_i$$$ ($$$1\le l_i\le r_i\le n$$$). You must answer the minimum number of times you must apply the "replace" function to the pair $$$(l_i,r_i)$$$ to get $$$(1, n)$$$, or report that it is impossible.
Input Format:
The first line contains two positive integers $$$n$$$, $$$q$$$ ($$$1\le n,q\le 10^5$$$) — the length of the sequence $$$a$$$ and the number of the queries.
The second line contains $$$n$$$ positive integers $$$a_1,a_2,\ldots,a_n$$$ ($$$1\le a_i\le n$$$) — the sequence $$$a$$$.
Each line of the following $$$q$$$ lines contains two integers $$$l_i$$$, $$$r_i$$$ ($$$1\le l_i\le r_i\le n$$$) — the queries.
Output Format:
For each query, output the required number of times, or $$$-1$$$ if it is impossible.
Note:
In the first example, $$$n=5$$$ and $$$a=[2,5,4,1,3]$$$.
For the first query: $$$(4,4)\to(1,1)\to(2,2)\to(5,5)\to(3,3)\to(4,4)\to\ldots$$$, so it's impossible to get $$$(1,5)$$$.
For the second query, you already have $$$(1,5)$$$.
For the third query: $$$(1,4)\to(1,5)$$$.
For the fourth query: $$$(3,5)\to(1,4)\to(1,5)$$$.
For the fifth query: $$$(4,5)\to(1,3)\to(2,5)\to(1,5)$$$.
For the sixth query: $$$(2,3)\to(4,5)\to(1,3)\to(2,5)\to(1,5)$$$.