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...
The above is tricky. Write me a correct solution in PYTHON3.
 Write me a Python program 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 program 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.

def naiveSolve():
    
    
    
    return


def main():
    
    t=int(input())
    allans=[]
    for _ in range(t):
        n,k=readIntArr()
        a=readIntArr()
        
        dp=[[-inf for __ in range(n+1)] for ___ in range(n)]
        # dp[idx][delete cnts] = max matches
        for i in range(n):
            for j in range(i+2): # j is the delete cnts
                if a[i]==i-j+1: add=1
                else: add=0
                if i-1>=0: dp[i][j]=max(dp[i][j],dp[i-1][j]+add)
                else: dp[i][j]=max(dp[i][j],add)
                
                if j>=1:
                    if i==0:
                        assert j==1
                        dp[i][j]=0
                    else:
                        dp[i][j]=max(dp[i][j],dp[i-1][j-1]) # delete this item
        ans=-1
        for delCnts in range(n+1):
            if dp[n-1][delCnts]>=k:
                ans=delCnts
                break
        allans.append(ans)
        
        # for row in dp:
        #     print(row)
        # for i in range(n):
        #     for j in range(n+1):
        #         print('i:{} j:{} dp:{}'.format(i,j,dp[i][j]))
        
    multiLineArrayPrint(allans)
    
    return

import sys
# input=sys.stdin.buffer.readlin,e #FOR READING PURE INTEGER INPUTS (space separation ok)
input=lambda: sys.stdin.readline().rstrip("\r\n") #FOR READING STRING/TEXT INPUTS.

def oneLineArrayPrint(arr):
    print(' '.join([str(x) for x in arr]))
def multiLineArrayPrint(arr):
    print('\n'.join([str(x) for x in arr]))
def multiLineArrayOfArraysPrint(arr):
    print('\n'.join([' '.join([str(x) for x in y]) for y in arr]))
 
def readIntArr():
    return [int(x) for x in input().split()]
# def readFloatArr():
#     return [float(x) for x in input().split()]
 
def makeArr(defaultValFactory,dimensionArr): # eg. makeArr(lambda:0,[n,m])
    dv=defaultValFactory;da=dimensionArr
    if len(da)==1:return [dv() for _ in range(da[0])]
    else:return [makeArr(dv,da[1:]) for _ in range(da[0])]
 
def queryInteractive(l,r):
   ...