P10059 Choose

[Enhanced version](https://www.luogu.com.cn/problem/U397746). For a sequence $a$ of length $n$, define the range of $a$ as the difference between the maximum value and the minimum value in $a$. Define $C(a,l,r)$ as the **contiguous** subsequence $[a_l,a_{l+1},\dots,a_r]$, where $1\le l\le r\le n$.

Given a sequence $a$ of length $n$. You need to select $k$ different **contiguous** subsequences of $a$, all with length $L$ $(1\le L\le n-k+1)$: $C(a,l_1,l_1+L-1),C(a,l_2,l_2+L-1),\dots,C(a,l_k,l_k+L-1)$, where $1\le l_1

**This problem contains multiple test cases.** The first line contains an integer $T$, the number of test cases. For each test case: - The first line contains two integers $n,k$. - The second line contains $n$ integers $a_1,a_2,\dots,a_n$.

For each test case: - Output one line with two integers $X,L$, representing the required range and the subsequence length.

**[Sample 1 Explanation]** - When $k=1$, the maximum possible range is at most $4$. One shortest valid choice is $[1,2,3,4,5]$. - When $k=2$, the maximum possible range is at most $3$. One shortest valid choice is $[1,2,3,4]$ and $[2,3,4,5]$. - When $k=3$, the maximum possible range is at most $2$. One shortest valid choice is $[1,2,3]$, $[2,3,4]$, and $[3,4,5]$. **[Constraints and Notes]** **This problem uses bundled testdata.** | Subtask | Score | $n\le$ | $k\le$ | Special Property | | :----------: | :----------: | :----------: | :----------: | :----------: | | $1$ | $5$ | $10^5$ | $n$ | All $a_i$ are equal | | $2$ | $5$ | $10^5$ | $1$ | Testdata is randomly generated | | $3$ | $10$ | $100$ | $n$ | The required $X$ is at most $10^3$ | | $4$ | $20$ | $100$ | $n$ | None | | $5$ | $20$ | $10^4$ | $n$ | None | | $6$ | $40$ | $10^5$ | $n$ | None | For $100\%$ of the testdata, $1\le T\le 10$, $1\le n\le 10^5$, $1\le k\le n$, $-10^9\le a_i\le 10^9$. Translated by ChatGPT 5