Firdavs is living on planet F. There are $N$ cities (numbered $1$ through $N$) on this planet; let's denote the value of city $i$ by $v_i$. Firdavs can travel directly from each city to any other city. When he travels directly from city $x$ to city $y$, he needs to pay $f(x, y) = |v_y-v_x|+y-x$ coins (this number can be negative, in which case he receives $-f(x, y)$ coins).
Let's define a simple path from city $x$ to city $y$ with length $k \ge 1$ as a sequence of cities $a_1, a_2, \ldots, a_k$ such that all cities in this sequence are different, $a_1 = x$ and $a_k = y$. The cost of such a path is $\sum_{i=1}^{k-1} f(a_i, a_{i+1})$.
You need to answer some queries for Firdavs. In each query, you are given two cities $x$ and $y$, and you need to find the minimum cost of a simple path from city $x$ to city $y$. Then, you need to find the length of the longest simple path from $x$ to $y$ with this cost.

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains two space-separated integers $N$ and $Q$.
- The second line contains $N$ space-separated integers $v_1, v_2, \ldots, v_N$.
- The following $Q$ lines describe queries. Each of these lines contains two space-separated integers $x$ and $y$.

-----Output-----
For each query, print a single line containing two space-separated integers ― the minimum cost and the maximum length.

-----Constraints-----
- $1 \le T \le 100$
- $1 \le N, Q \le 2 \cdot 10^5$
- $0 \le v_i \le 10^9$ for each valid $i$
- $1 \le x, y \le N$
- the sum of $N$ in all test cases does not exceed $5 \cdot 10^5$
- the sum of $Q$ in all test cases does not exceed $5 \cdot 10^5$

-----Subtasks-----
Subtask #1 (30 points):
- $1 \le N, Q \le 1,000$
- $v_1 < v_2 < \ldots < v_N$
- the sum of $N$ in all test cases does not exceed $5,000$
- the sum of $Q$ in all test cases does not exceed $5,000$
Subtask #2 (70 points): original constraints

-----Example Input-----
2
4 2
4 2 5 7
2 3
3 4
2 1
1 1
2 1

-----Example Output-----
4 3
3 2
-1 2

-----Explanation-----
Example case 1: For the first query, there are two paths with cost $4$ from city $2$ to city $3$:
- $2 \rightarrow 1 \rightarrow 3$: cost $(|4-2|+1-2)+(|5-4|+3-1) = 4$, length $3$
- $2 \rightarrow 3$: cost $|5-2|+3-2 = 4$, length $2$
All other paths have greater costs, so the minimum cost is $4$. Among these two paths, we want the one with greater length, which is $3$.

见题面

见题面