E. Permutation Shifttime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputAn identity permutation of length n is an array [1, 2, 3, \dots, n].We performed the following operations to an identity permutation of length n:  firstly, we cyclically shifted it to the right by k positions, where k is unknown to you (the only thing you know is that 0 \le k \le n - 1). When an array is cyclically shifted to the right by k positions, the resulting array is formed by taking k last elements of the original array (without changing their relative order), and then appending n - k first elements to the right of them (without changing relative order of the first n - k elements as well). For example, if we cyclically shift the identity permutation of length 6 by 2 positions, we get the array [5, 6, 1, 2, 3, 4];  secondly, we performed the following operation at most m times: pick any two elements of the array and swap them. You are given the values of n and m, and the resulting array. Your task is to find all possible values of k in the cyclic shift operation.InputThe first line contains one integer t (1 \le t \le 10^5) — the number of test cases.Each test case consists of two lines. The first line contains two integers n and m (3 \le n \le 3 \cdot 10^5; 0 \le m \le \frac{n}{3}).The second line contains n integers p_1, p_2, \dots, p_n (1 \le p_i \le n, each integer from 1 to n appears in this sequence exactly once) — the resulting array.The sum of n over all test cases does not exceed 3 \cdot 10^5.OutputFor each test case, print the answer in the following way:  firstly, print one integer r (0 \le r \le n) — the number of possible values of k for the cyclic shift operation;  secondly, print r integers k_1, k_2, \dots, k_r (0 \le k_i \le n - 1) — all possible values of k in increasing order. ExampleInput
4
4 1
2 3 1 4
3 1
1 2 3
3 1
3 2 1
6 0
1 2 3 4 6 5
Output
1 3
1 0
3 0 1 2
0
NoteConsider the example:   in the first test case, the only possible value for the cyclic shift is 3. If we shift [1, 2, 3, 4] by 3 positions, we get [2, 3, 4, 1]. Then we can swap the 3-rd and the 4-th elements to get the array [2, 3, 1, 4];  in the second test case, the only possible value for the cyclic shift is 0. If we shift [1, 2, 3] by 0 positions, we get [1, 2, 3]. Then we don't change the array at all (we stated that we made at most 1 swap), so the resulting array stays [1, 2, 3];  in the third test case, all values from 0 to 2 are possible for the cyclic shift:   if we shift [1, 2, 3] by 0 positions, we get [1, 2, 3]. Then we can swap the 1-st and the 3-rd elements to get [3, 2, 1];  if we shift [1, 2, 3] by 1 position, we get [3, 1, 2]. Then we can swap the 2-nd and the 3-rd elements to get [3, 2, 1];  if we shift [1, 2, 3] by 2 positions, we get [2, 3, 1]. Then we can swap the 1-st and the 2-nd elements to get [3, 2, 1];   in the fourth test case, we stated that we didn't do any swaps after the cyclic shift, but no value of cyclic shift could produce the array [1, 2, 3, 4, 6, 5]. 
4
4 1
2 3 1 4
3 1
1 2 3
3 1
3 2 1
6 0
1 2 3 4 6 5

1 3 1 0 3 0 1 2 0 
['brute force', 'combinatorics', 'constructive algorithms', 'dfs and similar', 'dsu', 'graphs', 'math', '*2100']