Problem: Being stuck at home, Ray became extremely bored. To pass time, he asks Lord Omkar to use his time bending power: Infinity Clock! However, Lord Omkar will only listen to mortals who can solve the following problem:

You are given an array a of n integers. You are also given an integer k. Lord Omkar wants you to do k operations with this array.

Define one operation as the following: 

  1. Set d to be the maximum value of your array. 
  2. For every i from 1 to n, replace a_{i} with d-a_{i}. 



The goal is to predict the contents in the array after k operations. Please help Ray determine what the final sequence will look like!

Input

Each test contains multiple test cases. The first line contains the number of cases t (1 ≤ t ≤ 100). Description of the test cases follows.

The first line of each test case contains two integers n and k (1 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ k ≤ 10^{18}) – the length of your array and the number of operations to perform.

The second line of each test case contains n integers a_{1},a_{2},...,a_{n} (-10^9 ≤ a_{i} ≤ 10^9) – the initial contents of your array.

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.

Output

For each case, print the final version of array a after k operations described above.

Example

Input


3
2 1
-199 192
5 19
5 -1 4 2 0
1 2
69


Output


391 0
0 6 1 3 5
0

Note

In the first test case the array changes as follows:

  * Initially, the array is [-199, 192]. d = 192.

  * After the operation, the array becomes [d-(-199), d-192] = [391, 0].

Solution (in JAVA):

Solution:
import java.util.*;
import java.lang.*;
// StringBuilder uses java.lang
 
 
public class mC {
    
    
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        StringBuilder st = new StringBuilder();
        for (int test=0;test<t;test++) {
            int n = sc.nextInt();
            long k = sc.nextLong();
            long[] arr = new long[n];
            for (int i=0;i<n;i++) {
                arr[i]=sc.nextLong();
            }
            long minimum = 1000000002;
            int minAt = -1;
            long maximum = -1000000002;
            int maxAt = -1;
            for (int i=0;i<n;i++) {
                if (maximum<arr[i]) {
                    maximum = arr[i];
                    maxAt=i;
                }
                if (minimum>arr[i]) {
                    minimum = arr[i];
                    minAt=i;
                }
            }
            if (k%2==0) {
                for (int i=0;i<n;i++) {
                    st.append(arr[i]-minimum+" ");
                }
            } else {
                for (int i=0;i<n;i++) {
                    st.append(maximum-arr[i]+" ");
                }
            }
            st.append("\n");
        }
        System.out.print(st.toString());
        
    }
    
    public static int findNthInArray(int[] arr,int val,int start,int o) {
        if (o==0) {
            return start-1;
        } else if (arr[start] == val) {
            return findNthInArray(arr,val,start+1,o-1);
        } else {
            return findNthInArray(arr,val,start+1,o);
        }
    }
    public static ArrayList<Integer> dfs(int at,ArrayList<Integer> went,ArrayList<ArrayList<Integer>> connect) {
        for (int i=0;i<connect.get(at).size();i++) {
            if (!(went.contains(connect.get(at).get(i)))) {
                went.add(connect.get(at).get(i));
                went=dfs(connect.get(at).get(i),went,connect);
            }
        }
        return went;
    } public static int[] bfs (int at, int[] went, ArrayList<ArrayList<Integer>> queue, int numNodes, ArrayList<ArrayList<Integer>> connect) {
        if (went[at]==0) {
            went[at]=queue.get(numNodes).get(1);
            for (int i=0;i<connect.get(at).size();i++) {
                if (went[connect.get(at).get(i)]==0) {
                    ArrayList<Integer> temp = new ArrayList<>();
                    temp.add(connect.get(at).get(i));
                    temp.add(queue.get(numNodes).get(1)+1);
                    queue.add(temp);
                }
            }
            
        }
        if (queue.size()==numNodes+1) {
            return went;
        } else {
            return bfs(queue.get(numNodes+1).get(0),went, queue, numNodes+1, connect);
        }
    }
    public static long fastPow(int base,long exp,long mod) {
        if (exp==0) {
            return 1;
        } else {
            if (exp % 2 == 1) {
                long z = fastPow(base,(exp-1)/2,mod);
                return ((((z*base) % mod) * z) % mod);
            } else {
                long z = fastPow(base,exp/2,mod);
                return ((z*z) % mod);
            }
        }
    }
    public static long fastPow(int base,long exp) {
        if (exp==0) {
            return 1;
        } else {
            if (exp % 2 == 1) {
                long z = fastPow(base,(exp-1)/2);
                return ((((z*base)) * z));
            } else {
                long z = fastPow(base,exp/2);
                return ((z*z));
            }
        }
    }
    public static int firstLarger(int val,ArrayList<Integer> ok,int left,int right) {
        if (ok.get(right)<=val) {
            return -1;
        }
        if (left==right) {
            return left;
        } else if (left+1==right) {
            if (val<ok.get(left)) {
                return left;
            } else {
                return right;
            }
        } else {
            int mid = (left+right)/2;
            if (ok.get(mid)>val) {
                return firstLarger(val,ok,left,mid);
            } else {
                return firstLarger(val,ok,mid+1,right);
            }
        }
    }
}