Little Sasha likes to swap elements in his array. Initially, he has an array of numbers in ascending order. Then, he swaps some elements in it times. He really likes this sequence of swaps and repeats it times. However, Sasha forgot his favorite swap sequence the next day.
Given the resulting permutation, find the swap sequence used by Sasha or say that there is no such sequence.
Input Format
The first line of input contains three integers , , and , respectively.
The second line contains a permutation of numbers .
Constraints
Output Format
Print lines. The line contains two distinct integers , which means that the swap will be of and numbers. If there are multiple possible answers, print any of them.
Otherwise, if there is no such sequence of swaps, print "no solution" without quotes.
Sample Input
5 3 2
4 3 2 1 5
Sample Output
1 2
2 4
3 4
Explanation
Let's look at the sequence after each swap:
The first series of swaps:
The second series of swaps: