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.io.*;

public class Main {
    InputStream is;
    PrintWriter out;
    String INPUT = "";
    
    int MAX = (int) 1e5, MOD = (int)1e9+7;
    
    void solve(int TC) {
        int n = ni();
        long k = ni();
        long[] a = new long[n];
        long mx = Integer.MIN_VALUE;
        long mn = Integer.MAX_VALUE;
        for(int i=0;i<n;i++) {
            a[i] = nl();
            mx = Math.max(mx, a[i]);
        }
        for(int i=0;i<n;i++) a[i] = mx - a[i];
        --k;
        if(k==0) {
            for(long i: a) p(i+" ");pn("");
            return;
        }
        mx = Integer.MIN_VALUE;
        for(long i: a) mx = Math.max(mx, i);
        for(int i=0;i<n;i++) a[i] = mx - a[i];
        --k;
        if(k%2==0) {
            for(long i: a) p(i+" ");pn("");
            return;
        }
        mx = Integer.MIN_VALUE;
        for(long i: a) mx = Math.max(mx, i);
        for(int i=0;i<n;i++) a[i] = mx - a[i];
        for(long i: a) p(i+" ");pn("");
    }
    
    boolean TestCases = true;
    public static void main(String[] args) throws Exception { new Main().run(); }
    
    long pow(long a, long b) { // return pow(a,b) % MOD
        if(b==0 || a==1) return 1;
        long o = 1;
        for(long p = b; p > 0; p>>=1) {
            if((p&1)==1) o = (o*a) % MOD;
            a = (a*a) % MOD;
        } return o;
    }
    
    void sort(int[] a) {
        int n = a.length;
        ArrayList<Integer> s = new ArrayList<>();
        for(int i: a) s.add(i);
        Collections.sort(s);
        for(int i=0;i<n;i++) a[i] = s.get(i);
    }
    void sort(long[] a) {
        int n = a.length;
        ArrayList<Long> s = new ArrayList<>();
        for(long i: a) s.add(i);
        Collections.sort(s);
        for(int i=0;i<n;i++) a[i] = s.get(i);
    }
    
    long inv(long x) { // return Modular Inverse of x
        long o = 1;
        for(long p = MOD-2; p > 0; p>>=1) {
            if((p&1)==1)o = (o*x)%MOD;
            x = (x*x)%MOD;
        } return o;
    }
    long gcd(long a, long b) { return (b==0) ? a : gcd(b,a%b); }
    int gcd(int a, int b) { return (b==0) ? a : gcd(b,a%b); }
    
    void run() throws Exception {
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);
        long s = System.currentTimeMillis();
        int T = TestCases ? ni() : 1;
        for(int t=1;t<=T;t++) solve(t);
        out.flush();
        if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
    }
    
    void p(Object o) { out.print(o); }
    void pn(Object o) { out.println(o); }
    void pni(Object o) { out.println(o);out.flush(); }
    double PI = 3.141592653589793238462643383279502884197169399;
    
    int ni() {
        int num = 0, b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-') {
            minus = true;
            b = readByte();
        }
        while(true) {
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    long nl() {
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-') {
            minus = true;
            b = readByte();
        }
        while(true) {
            if(b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    double nd() { return Double.parseDouble(ns()); }
    char nc() { return (char)skip(); }
    
    int BUF_SIZE = 1024 * 8; // 1 MB is 1024*1024
    byte[] inbuf = new byte[BUF_SIZE];
    int lenbuf = 0, ptrbuf = 0;
    
    int readByte() {
        if(lenbuf == -1)throw new InputMismatchException();
        if(ptrbuf >= lenbuf){
            ptrbuf = 0;
            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        } return inbuf[ptrbuf++];
    }
    
    boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
    int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
    
    String ns() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!(isSpaceChar(b))) { // when nextLine, (b != '\n')
            sb.appendCodePoint(b); b = readByte();
        } return sb.toString();
    }
    
    char[] ns(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while(p < n && !(isSpaceChar(b))){
            buf[p++] = (char)b;
            b = readByte();
        } return n == p ? buf : Arrays.copyOf(buf, p);
    }
    
    void tr(Object... o) { if(INPUT.length() > 0)System.out.println(Arrays.deepToString(o)); }
}