human
What is a Python code to find all possible values of k in the cyclic shift operation given the following:
PYTHON 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...":
assistant
#Here is Python code to find all possible values of k in the cyclic shift operation.
 from __future__ import division,print_function
from heapq import*
import sys
le = sys.__stdin__.read().split("\n")[::-1]
af=[]
def m_s(l1,l2):
    n=max(l2)
    index_in_l1=[0]*(n+1)
    for k in range(n):
        index_in_l1[l1[k]]=k
    #print(index_in_l1,l1)
    s=0
    for k in range(n):
        u=l2[k]
        if l1[k]!=u:
            s+=1
            i=index_in_l1[u]
            l1[k],l1[i]=l1[i],l1[k]
            index_in_l1[u]=k
            index_in_l1[l1[i]]=i
    #print(l1)
    return s

for zorg in range(int(le.pop())):
    n,m=list(map(int,le.pop().split()))
    l= list(map(int,le.pop().split()))
    diff=[(k+1-l[k])%n for k in range(n)]
    nbd=[0]*n
    for k in diff:
        nbd[k]+=1
    def possible(x,m):#x==1 is impossible anyway
        return x<=2*m and (x,m)!=(1,1)
    """for k in range(n):
        if nbd[k]<=2*m:
            print(m_s(list(range(n-k+1,n+1)+range(1,n-k+1)),l))
            print(list(range(n-k+1,n+1)+range(1,n-k+1)),l)"""
    r=[k for k in range(n) if n-nbd[k]<=2*m and m_s(list(range(n-k+1,n+1)+range(1,n-k+1)),l)<=m]
    af.append(str(len(r))+" "+" ".join(map(str,r)))
print("\n".join(map(str,af)))