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

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastReader in = new FastReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        BOmkarAndInfinityClock solver = new BOmkarAndInfinityClock();
        solver.solve(1, in, out);
        out.close();
    }

    static class BOmkarAndInfinityClock {
        public void solve(int testNumber, FastReader s, PrintWriter out) {
            int t = s.nextInt();
            while (t-- > 0) {
                int n = s.nextInt();
                long k = s.nextLong();
                long[] arr = s.nextLongArray(n);
                long max = Integer.MIN_VALUE;
                for (int i = 0; i < n; i++) {
                    max = Math.max(max, arr[i]);
                }

                long[] ans = new long[n];

                for (int i = 0; i < n; i++) {
                    ans[i] = max - arr[i];
                }

                k--;
                if (k % 2L != 0L) {
                    max = Long.MIN_VALUE;
                    for (int i = 0; i < n; i++) {
                        max = Math.max(max, ans[i]);
                    }

                    for (int i = 0; i < n; i++) {
                        ans[i] = max - ans[i];
                    }
                }

                out.println(BOmkarAndInfinityClock.arrays.printArr(ans));

            }
        }

        private static class arrays {
            static String formatString(String str) {
                str = str.replace(",", "").replace("[", "").replace("]", "");
                return str;
            }

            static StringBuilder printArr(Object arr) {
                String str = null;
                if (arr instanceof int[]) {
                    str = Arrays.toString((int[]) arr);
                }

                if (arr instanceof long[]) {
                    str = Arrays.toString((long[]) arr);
                }

                if (arr instanceof char[]) {
                    str = Arrays.toString((char[]) arr);
                }

                if (arr instanceof boolean[]) {
                    str = Arrays.toString((boolean[]) arr);
                }

                if (arr instanceof byte[]) {
                    str = Arrays.toString((byte[]) arr);
                }

                if (arr instanceof double[]) {
                    str = Arrays.toString((double[]) arr);
                }

                if (arr instanceof float[]) {
                    str = Arrays.toString((float[]) arr);
                }

                if (arr instanceof short[]) {
                    str = Arrays.toString((short[]) arr);
                }

                if (str != null) {
                    return new StringBuilder(formatString(str));
                }

                return null;

            }

        }

    }

    static class FastReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private FastReader.SpaceCharFilter filter;

        public FastReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public long[] nextLongArray(int n) {
            long[] array = new long[n];
            for (int i = 0; i < n; ++i) array[i] = nextLong();
            return array;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}