This is the extreme version of the problem. In this version, the output of each query is different from the easy and hard versions. It is also guaranteed that $$$r \geq l+k-1$$$ for all queries.

For an arbitrary array $$$b$$$, Yunli can perform the following operation any number of times:

Select an index $$$i$$$. Set $$$b_i = x$$$ where $$$x$$$ is any integer she desires ($$$x$$$ is not limited to the interval $$$[1,n]$$$).

Denote $$$f(b)$$$ as the minimum number of operations she needs to perform until there exists a consecutive subarray$$$^{\text{∗}}$$$ of length at least $$$k$$$ in $$$b$$$.

Yunli is given an array $$$a$$$ of size $$$n$$$ and asks you $$$q$$$ queries. In each query, you must output $$$\sum_{i=l}^{r-k+1} \sum_{j=i+k-1}^{r} f([a_i, a_{i+1}, \ldots, a_j])$$$.

$$$^{\text{∗}}$$$If there exists a consecutive subarray of length $$$k$$$ that starts at index $$$i$$$ ($$$1 \leq i \leq |b|-k+1$$$), then $$$b_j = b_{j-1} + 1$$$ for all $$$i \lt j \leq i+k-1$$$.

Input

The first line contains $$$t$$$ ($$$1 \leq t \leq 10^4$$$) — the number of test cases.

The first line of each test case contains three integers $$$n$$$, $$$k$$$, and $$$q$$$ ($$$1 \leq k \leq n \leq 2 \cdot 10^5$$$, $$$1 \leq q \leq 2 \cdot 10^5$$$) — the length of the array, the length of the consecutive subarray, and the number of queries.

The following line contains $$$n$$$ integers $$$a_1, a_2, ..., a_n$$$ ($$$1 \leq a_i \leq n$$$).

The following $$$q$$$ lines contain two integers $$$l$$$ and $$$r$$$ ($$$1 \leq l \leq r \leq n$$$, $$$r \geq l+k-1$$$) — the bounds of the query.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$ and the sum of $$$q$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

Output $$$\sum_{i=l}^{r-k+1} \sum_{j=i+k-1}^{r} f([a_i, a_{i+1}, \ldots, a_j])$$$ for each query on a new line.

Note

In the first query of the first testcase, we can calculate the answer for the query through the following:

$$$i = 4$$$ and $$$j = 5$$$: $$$f([2, 1])=1$$$ because Yunli can set $$$b_2=3$$$, making a consecutive subarray of size $$$2$$$ in $$$1$$$ move.
$$$i = 4$$$ and $$$j = 6$$$: $$$f([2, 1, 2])=0$$$ because there is already a consecutive array of size $$$2$$$.
$$$i = 5$$$ and $$$j = 6$$$: $$$f([1, 2])=0$$$ because there is already a consecutive array of size $$$2$$$.

The answer to this query is $$$1+0+0=1$$$.

Yunli's Subarray Queries (extreme version)

Examples