human
PYTHON3 solution for "An identity permutation of length n is an array [1, 2, 3, ..., 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 ≤ k ≤ 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.

Input

The first line contains one integer t (1 ≤ t ≤ 10^5) — the number of test cases.

Each test case consists of two lines. The first line contains two integers n and m (3 ≤ n ≤ 3 ⋅ 10^5.
0 ≤ m ≤ n/3).

The second line contains n integers p_1, p_2, ..., p_n (1 ≤ p_i ≤ 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 ⋅ 10^5.

Output

For each test case, print the answer in the following way:

  * firstly, print one integer r (0 ≤ r ≤ n) — the number of possible values of k for the cyclic shift operation.

  * secondly, print r integers k_1, k_2, ..., k_r (0 ≤ k_i ≤ n - 1) — all possible values of k in increasing order. 

Example

Input

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

Note

Consider 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...":



Write me a Python code to find all possible values of k in the cyclic shift operation?
assistant
#Here is Python code to find all possible values of k in the cyclic shift operation.
 def solve(n,m,perm):
    cyc_right = [0]*n
    for i,p in enumerate(perm):
        k = (n+i+1-p)%n
        cyc_right[k] += 1
    check_these= []
    for i,right in enumerate(cyc_right):
        if right >= n -2*m:
            check_these.append(i)

    check_these.sort()
    check_copy = check_these[:]
    for k in check_copy:
        swaps = 0
        tmp_perm = perm[:]
        for i,p in enumerate(tmp_perm):
            if k != (n+i+1-p)%n:
                tmp = tmp_perm[i]
                while k != (n+i+1-tmp)%n:
                    swap_index = (k+tmp) % n - 1
                    # assert k == (n + swap_index+1 - tmp)%n
                    tmp_perm[i] = tmp_perm[swap_index]
                    tmp_perm[swap_index] = tmp
                    tmp = tmp_perm[i]
                    swaps+=1
                if swaps > m:
                    check_these.remove(k)
                    break
    return check_these

import os
import io
# import time
# a=time.time()
if __name__ == "__main__":
    input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline

    T = int(input().decode().strip())
    for t in range(T):
        n,m=[int(x) for x in input().decode().strip().split(" ")]
        perm=[int(x) for x in input().decode().strip().split(" ")]
        res1 = solve(n,m,perm)
        if len(res1) ==0:
            print("0")
        else:
            res = str(len(res1))+" "+" ".join([str(x) for x in res1])
            print(res)