You are given a permutation $P$ of number $1, \cdots , n$ (I.E. each number occurs exactly once). Now you want to introduce some chaos to this permutation. To introduce chaos, you can perform at most $k$ swaps between adjacent positions. The chaosness of the final permutation is calculated as the count of the mismatches I.E. the number of indices $i$ such that $P[i] \neq i$ (the indices are 1-indexed). Output the maximum number of mismatch you can make and also output such a sequence of swaps.
Input
There will be $T$ testcases.
Each testcase begins with a line containing space separated numbers $n$, $k$. Next line contains $n$ space separated numbers representing the initial permutation.
$1 \leq T \leq 10^5$$3 \leq n \leq 10^5$$0 \leq k \leq n$
sum of $n$ over all testcases $ \leq 10^5 $
Output
For each testcase first output one number $s$ in a line, $s$ is the number of swaps you will perform. In the next $s$ lines, output the swaps to be performed. To swap positions $x$ and $y$ output the numbers $x$ and $y$. Note that the swaps you perform should be between adjacent positions.
In case of multiple answer, you can output any.
Sample
| Input | Output |
|---|---|
2 4 2 1 4 2 3 10 2 1 2 3 4 5 6 7 8 9 10 | 1 1 2 2 1 2 9 10 |
