human
Consider a sequence of integers a_1, a_2, …, a_n. In one move, you can select any element of the sequence and delete it. After an element is deleted, all elements to the right are shifted to the left by 1 position, so there are no empty spaces in the sequence. So after you make a move, the sequence's length decreases by 1. The indices of the elements after the move are recalculated.

E. g. let the sequence be a=[3, 2, 2, 1, 5]. Let's select the element a_3=2 in a move. Then after the move the sequence will be equal to a=[3, 2, 1, 5], so the 3-rd element of the new sequence will be a_3=1 and the 4-th element will be a_4=5.

You are given a sequence a_1, a_2, …, a_n and a number k. You need to find the minimum number of moves you have to make so that in the resulting sequence there will be at least k elements that are equal to their indices, i. e. the resulting sequence b_1, b_2, …, b_m will contain at least k indices i such that b_i = i.

Input

The first line contains one integer t (1 ≤ t ≤ 100) — the number of test cases. Then t test cases follow.

Each test case consists of two consecutive lines. The first line contains two integers n and k (1 ≤ k ≤ n ≤ 2000). The second line contains a sequence of integers a_1, a_2, …, a_n (1 ≤ a_i ≤ n). The numbers in the sequence are not necessarily different.

It is guaranteed that the sum of n over all test cases doesn't exceed 2000.

Output

For each test case output in a single line:

  * -1 if there's no desired move sequence.

  * otherwise, the integer x (0 ≤ x ≤ n) — the minimum number of the moves to be made so that the resulting sequence will contain at least k elements that are equal to their indices. 

Example

Input

4
7 6
1 1 2 3 4 5 6
5 2
5 1 3 2 3
5 2
5 5 5 5 4
8 4
1 2 3 3 2 2 5 5

Output

1
2
-1
2

Note

In the first test case the sequence doesn't satisfy the desired condition, but it can be provided by deleting the first element, hence the sequence will be [1, 2, 3, 4, 5, 6] and 6 elements will be equal to their indices.

In the second test case...
Solve the task in PYTHON3.

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Write me a Python code to find the minimum number of moves you have to make so that in the resulting sequence there will be at least k elements that are equal to their indices, i?
assistant
#Here is Python code to find the minimum number of moves you have to make so that in the resulting sequence there will be at least k elements that are equal to their indices, i.

import sys
input=sys.stdin.readline #文字列入力はするな！！

al3=list("abcdefghijklmnopqrstuvwx")

al2=["y","z"]


t=int(input())
for iii in range(t):
    n,k=map(int,input().split())
    a=[0]+list(map(int,input().split()))
    dp=[-10**18]*(n+3)*(n+3)
    def _(i,j):
        return i*(n+1)+j
    dp[_(0,0)]=0
    for i in range(1,n+1):
        for j in range(i+1):
            dp[_(i,j)]=dp[_(i-1,j)]
            if a[i]==(i-j):
                dp[_(i,j)]=max(dp[_(i,j)],dp[_(i-1,j)]+1)
            if j>=1:
                dp[_(i,j)]=max(dp[_(i,j)],dp[_(i-1,j-1)])
    ans=10**18
    for i in range(n+1):
        if dp[_(n,i)]>=k:
            ans=min(ans,i)
    print(ans if ans<10**18 else -1)