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:
// package round_global_010;

import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class B {
	final static PrintWriter out = new PrintWriter(System.out);

	public static void solve() {
		In in = new In();
		int tests = in.ni();
		while (tests-- > 0) {
			int n = in.ni();
			long k = in.nl();
			long[] nums = in.nla(n);

			long max = Arrays.stream(nums).parallel().max().getAsLong();
			long[] first = Arrays.copyOf(nums, n);
			for(int i = 0; i < n; i++) first[i] = max - first[i];
			max = Arrays.stream(first).parallel().max().getAsLong();
			long[] second = Arrays.copyOf(first, n);
			for(int i = 0; i < n; i++) second[i] = max - second[i];
			if ((k & 1L) == 0) {
				for (long x : second)
					System.out.print(x + " ");
			} else {
				for (long x : first)
					System.out.print(x + " ");
			}
			System.out.println();
		}
	}


	public static void main(String[] args) throws IOException {
		// long start = System.nanoTime();
		solve();
		out.flush();
		// System.out.println("Elapsed: " + (System.nanoTime() - start) / 1000000 +
		// "ns");
	}

	@SuppressWarnings("unused")
	private static class In {
		final private static int BUFFER_SIZE = 1024;
		private byte[] buf;
		private InputStream is;
		private int buflen;
		private int bufptr;

		public In() {
			is = System.in;
			buf = new byte[BUFFER_SIZE];
			buflen = bufptr = 0;
		}

		public In(String input) {
			is = new ByteArrayInputStream(input.getBytes());
			buf = new byte[BUFFER_SIZE];
			buflen = bufptr = 0;
		}

		public int readByte() {
			if (bufptr >= buflen) {
				try {
					buflen = is.read(buf);
				} catch (IOException ioe) {
					throw new InputMismatchException();
				}
				bufptr = 0;
			}
			if (buflen <= 0)
				return -1;
			return buf[bufptr++];
		}

		public boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}

		public int skip() {
			int b;
			while ((b = readByte()) != -1 && isSpaceChar(b))
				;
			return b;
		}

		/* Next character */
		public char nc() {
			return (char) skip();
		}

		/* Next double */
		public double nd() {
			return Double.parseDouble(ns());
		}

		/* Next string */
		public String ns() {
			final StringBuilder sb = new StringBuilder();
			int b = skip();
			while (!isSpaceChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}

		/* Next integer */
		public int ni() {
			boolean minus = false;
			int num = 0;
			int b;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') {
				minus = true;
				b = readByte();
			}
			while (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
				b = readByte();
			}
			return minus ? -num : num;
		}

		/* Next long */
		public long nl() {
			boolean minus = false;
			long num = 0;
			int b;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') {
				minus = true;
				b = readByte();
			}
			while (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
				b = readByte();
			}
			return minus ? -num : num;
		}

		/* Next integer 1D array */
		public int[] nia(int n) {
			final int[] arr = new int[n];
			for (int i = 0; i < n; i++)
				arr[i] = ni();
			return arr;
		}

		/* Next long 1D array */
		public long[] nla(int n) {
			final long[] arr = new long[n];
			for (int i = 0; i < n; i++)
				arr[i] = nl();
			return arr;
		}

		/* Next string 1D array */
		public String[] nsa(int n) {
			final String[] arr = new String[n];
			for (int i = 0; i < n; i++)
				arr[i] = ns();
			return arr;
		}

		/* Next char 1D array */
		public char[] nca(int n) {
			final char[] arr = new char[n];
			for (int i = 0; i < n; i++)
				arr[i] = nc();
			return arr;
		}

		/* Next double 1D array */
		public double[] nda(int n) {
			final double[] arr = new double[n];
			for (int i = 0; i < n; i++)
				arr[i] = nc();
			return arr;
		}

		/* Next integer matrix */
		public int[][] nim(int n, int m) {
			final int[][] arr = new int[n][m];
			for (int i = 0; i < n; i++)
				for (int j = 0; j < m; j++)
					arr[i][j] = ni();
			return arr;
		}

		/* Next long matrix */
		public long[][] nlm(int n, int m) {
			final long[][] arr = new long[n][m];
			for (int i = 0; i < n; i++)
				for (int j = 0; j < m; j++)
					arr[i][j] = nl();
			return arr;
		}

		/* Next string matrix */
		public String[][] nsm(int n, int m) {
			final String[][] arr = new String[n][m];
			for (int i = 0; i < n; i++)
				for (int j = 0; j < m; j++)
					arr[i][j] = ns();
			return arr;
		}

		/* Next char matrix */
		public char[][] ncm(int n, int m) {
			final char[][] arr = new char[n][m];
			for (int i = 0; i < n; i++)
				for (int j = 0; j < m; j++)
					arr[i][j] = nc();
			return arr;
		}

		/* Next double matrix */
		public double[][] ndm(int n, int m) {
			final double[][] arr = new double[n][m];
			for (int i = 0; i < n; i++)
				for (int j = 0; j < m; j++)
					arr[i][j] = nd();
			return arr;
		}

		public static void log(Object... o) {
			System.out.println(Arrays.deepToString(o));
		}
	}

}