Problem: On a strip of land of length n there are k air conditioners: the i-th air conditioner is placed in cell a_i (1 ≤ a_i ≤ n). Two or more air conditioners cannot be placed in the same cell (i.e. all a_i are distinct).

Each air conditioner is characterized by one parameter: temperature. The i-th air conditioner is set to the temperature t_i.

<image> Example of strip of length n=6, where k=2, a=[2,5] and t=[14,16].

For each cell i (1 ≤ i ≤ n) find it's temperature, that can be calculated by the formula $$$min_{1 ≤ j ≤ k}(t_j + |a_j - i|),$$$

where |a_j - i| denotes absolute value of the difference a_j - i.

In other words, the temperature in cell i is equal to the minimum among the temperatures of air conditioners, increased by the distance from it to the cell i.

Let's look at an example. Consider that n=6, k=2, the first air conditioner is placed in cell a_1=2 and is set to the temperature t_1=14 and the second air conditioner is placed in cell a_2=5 and is set to the temperature t_2=16. In that case temperatures in cells are:

  1. temperature in cell 1 is: min(14 + |2 - 1|, 16 + |5 - 1|)=min(14 + 1, 16 + 4)=min(15, 20)=15; 
  2. temperature in cell 2 is: min(14 + |2 - 2|, 16 + |5 - 2|)=min(14 + 0, 16 + 3)=min(14, 19)=14; 
  3. temperature in cell 3 is: min(14 + |2 - 3|, 16 + |5 - 3|)=min(14 + 1, 16 + 2)=min(15, 18)=15; 
  4. temperature in cell 4 is: min(14 + |2 - 4|, 16 + |5 - 4|)=min(14 + 2, 16 + 1)=min(16, 17)=16; 
  5. temperature in cell 5 is: min(14 + |2 - 5|, 16 + |5 - 5|)=min(14 + 3, 16 + 0)=min(17, 16)=16; 
  6. temperature in cell 6 is: min(14 + |2 - 6|, 16 + |5 - 6|)=min(14 + 4, 16 + 1)=min(18, 17)=17. 



For each cell from 1 to n find the temperature in it.

Input

The first line contains one integer q (1 ≤ q ≤ 10^4) — the number of test cases in the input. Then test cases follow. Before each test case, there is an empty line.

Each test case contains three lines. The first line contains two integers n (1 ≤ n ≤ 3 ⋅ 10^5) and k (1 ≤ k ≤ n) — the length of the strip of land and the number of air conditioners respectively.

The second line contains k integers a_1, a_2, …, a_k (1 ≤ a_i ≤ n) — positions of air conditioners on the strip of land.

The third line contains k integers t_1, t_2, …, t_k (1 ≤ t_i ≤ 10^9) — temperatures of air conditioners.

It is guaranteed that the sum of n over all test cases does not exceed 3 ⋅ 10^5.

Output

For each test case output n integers separated by space: temperatures of air in cells.

Example

Input


5

6 2
2 5
14 16

10 1
7
30

5 5
3 1 4 2 5
3 1 4 2 5

7 1
1
1000000000

6 3
6 1 3
5 5 5


Output


15 14 15 16 16 17 
36 35 34 33 32 31 30 31 32 33 
1 2 3 4 5 
1000000000 1000000001 1000000002 1000000003 1000000004 1000000005 1000000006 
5 6 5 6 6 5 

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.Arrays;
import java.util.Hashtable;

public class AirConditionersUpsolve{
    static class InputReader {
        private static final int DEFAULT_BUFFER_SIZE = 1 << 16; // Change this to increase your input size //
        private static final InputStream DEFAULT_STREAM = System.in;private static final int MAX_DECIMAL_PRECISION = 21;private int c;private byte[] buf;private int bufferSize, bufIndex, numBytesRead;private InputStream stream;private static final byte EOF = -1;private static final byte NEW_LINE = 10;private static final byte CARRIAGE_RETURN = 13;private static final byte SPACE = 32;private static final byte DASH = 45;private static final byte DOT = 46;private char[] charBuffer;private static byte[] bytes = new byte[58];private static int[] ints = new int[58];private static char[] chars = new char[128];static { char ch = ' ';int value = 0;byte _byte = 0;for (int i = 48; i < 58; i++) bytes[i] = _byte++;for (int i = 48; i < 58; i++) ints[i] = value++;for (int i = 32; i < 128; i++) chars[i] = ch++; }private static final double[][] doubles = {{0.0d, 0.00d, 0.000d, 0.0000d, 0.00000d, 0.000000d, 0.0000000d, 0.00000000d, 0.000000000d, 0.0000000000d, 0.00000000000d, 0.000000000000d, 0.0000000000000d, 0.00000000000000d, 0.000000000000000d, 0.0000000000000000d, 0.00000000000000000d, 0.000000000000000000d, 0.0000000000000000000d, 0.00000000000000000000d, 0.000000000000000000000d}, {0.1d, 0.01d, 0.001d, 0.0001d, 0.00001d, 0.000001d, 0.0000001d, 0.00000001d, 0.000000001d, 0.0000000001d, 0.00000000001d, 0.000000000001d, 0.0000000000001d, 0.00000000000001d, 0.000000000000001d, 0.0000000000000001d, 0.00000000000000001d, 0.000000000000000001d, 0.0000000000000000001d, 0.00000000000000000001d, 0.000000000000000000001d}, {0.2d, 0.02d, 0.002d, 0.0002d, 0.00002d, 0.000002d, 0.0000002d, 0.00000002d, 0.000000002d, 0.0000000002d, 0.00000000002d, 0.000000000002d, 0.0000000000002d, 0.00000000000002d, 0.000000000000002d, 0.0000000000000002d, 0.00000000000000002d, 0.000000000000000002d, 0.0000000000000000002d, 0.00000000000000000002d, 0.000000000000000000002d}, {0.3d, 0.03d, 0.003d, 0.0003d, 0.00003d, 0.000003d, 0.0000003d, 0.00000003d, 0.000000003d, 0.0000000003d, 0.00000000003d, 0.000000000003d, 0.0000000000003d, 0.00000000000003d, 0.000000000000003d, 0.0000000000000003d, 0.00000000000000003d, 0.000000000000000003d, 0.0000000000000000003d, 0.00000000000000000003d, 0.000000000000000000003d}, {0.4d, 0.04d, 0.004d, 0.0004d, 0.00004d, 0.000004d, 0.0000004d, 0.00000004d, 0.000000004d, 0.0000000004d, 0.00000000004d, 0.000000000004d, 0.0000000000004d, 0.00000000000004d, 0.000000000000004d, 0.0000000000000004d, 0.00000000000000004d, 0.000000000000000004d, 0.0000000000000000004d, 0.00000000000000000004d, 0.000000000000000000004d}, {0.5d, 0.05d, 0.005d, 0.0005d, 0.00005d, 0.000005d, 0.0000005d, 0.00000005d, 0.000000005d, 0.0000000005d, 0.00000000005d, 0.000000000005d, 0.0000000000005d, 0.00000000000005d, 0.000000000000005d, 0.0000000000000005d, 0.00000000000000005d, 0.000000000000000005d, 0.0000000000000000005d, 0.00000000000000000005d, 0.000000000000000000005d}, {0.6d, 0.06d, 0.006d, 0.0006d, 0.00006d, 0.000006d, 0.0000006d, 0.00000006d, 0.000000006d, 0.0000000006d, 0.00000000006d, 0.000000000006d, 0.0000000000006d, 0.00000000000006d, 0.000000000000006d, 0.0000000000000006d, 0.00000000000000006d, 0.000000000000000006d, 0.0000000000000000006d, 0.00000000000000000006d, 0.000000000000000000006d}, {0.7d, 0.07d, 0.007d, 0.0007d, 0.00007d, 0.000007d, 0.0000007d, 0.00000007d, 0.000000007d, 0.0000000007d, 0.00000000007d, 0.000000000007d, 0.0000000000007d, 0.00000000000007d, 0.000000000000007d, 0.0000000000000007d, 0.00000000000000007d, 0.000000000000000007d, 0.0000000000000000007d, 0.00000000000000000007d, 0.000000000000000000007d}, {0.8d, 0.08d, 0.008d, 0.0008d, 0.00008d, 0.000008d, 0.0000008d, 0.00000008d, 0.000000008d, 0.0000000008d, 0.00000000008d, 0.000000000008d, 0.0000000000008d, 0.00000000000008d, 0.000000000000008d, 0.0000000000000008d, 0.00000000000000008d, 0.000000000000000008d, 0.0000000000000000008d, 0.00000000000000000008d, 0.000000000000000000008d}, {0.9d, 0.09d, 0.009d, 0.0009d, 0.00009d, 0.000009d, 0.0000009d, 0.00000009d, 0.000000009d, 0.0000000009d, 0.00000000009d, 0.000000000009d, 0.0000000000009d, 0.00000000000009d, 0.000000000000009d, 0.0000000000000009d, 0.00000000000000009d, 0.000000000000000009d, 0.0000000000000000009d, 0.00000000000000000009d, 0.000000000000000000009d}};
        public InputReader() { this(DEFAULT_STREAM, DEFAULT_BUFFER_SIZE); }
        public InputReader(int bufferSize) { this(DEFAULT_STREAM, bufferSize); }
        public InputReader(InputStream stream) { this(stream, DEFAULT_BUFFER_SIZE); }
        public InputReader(InputStream stream, int bufferSize) { if (stream == null || bufferSize <= 0) throw new IllegalArgumentException();buf = new byte[bufferSize];charBuffer = new char[128];this.bufferSize = bufferSize;this.stream = stream; }
        private byte read() throws IOException { if (numBytesRead == EOF) throw new IOException();if (bufIndex >= numBytesRead) { bufIndex = 0;numBytesRead = stream.read(buf);if (numBytesRead == EOF) return EOF; }return buf[bufIndex++]; }
        private int readJunk(int token) throws IOException { if (numBytesRead == EOF) return EOF;
            do { while (bufIndex < numBytesRead) { if (buf[bufIndex] > token) return 0;bufIndex++; }
                numBytesRead = stream.read(buf);if (numBytesRead == EOF) return EOF;bufIndex = 0; } while (true); }
        public byte nextByte() throws IOException {return (byte) nextInt(); }
        public int nextInt() throws IOException { if (readJunk(DASH - 1) == EOF) throw new IOException();int sgn = 1, res = 0;c = buf[bufIndex];if (c == DASH) { sgn = -1;bufIndex++; } do { while (bufIndex < numBytesRead) { if (buf[bufIndex] > SPACE) { res = (res << 3) + (res << 1);res += ints[buf[bufIndex++]]; } else { bufIndex++;return res * sgn; } }numBytesRead = stream.read(buf);if (numBytesRead == EOF) return res * sgn;bufIndex = 0; } while (true); }
        public long nextLong() throws IOException { if (readJunk(DASH - 1) == EOF) throw new IOException();int sgn = 1;long res = 0L;c = buf[bufIndex];if (c == DASH) { sgn = -1;bufIndex++; } do { while (bufIndex < numBytesRead) { if (buf[bufIndex] > SPACE) { res = (res << 3) + (res << 1);res += ints[buf[bufIndex++]]; } else { bufIndex++;return res * sgn; } }numBytesRead = stream.read(buf);if (numBytesRead == EOF) return res * sgn;bufIndex = 0; } while (true); }
        private void doubleCharBufferSize() { char[] newBuffer = new char[charBuffer.length << 1];for (int i = 0; i < charBuffer.length; i++) newBuffer[i] = charBuffer[i];charBuffer = newBuffer; }
        public String nextLine() throws IOException { try { c = read(); } catch (IOException e) { return null; }if (c == NEW_LINE) return "";if (c == EOF) return null;int i = 0;charBuffer[i++] = (char) c;do { while (bufIndex < numBytesRead) { if (buf[bufIndex] != NEW_LINE && buf[bufIndex] != CARRIAGE_RETURN) { if (i == charBuffer.length) doubleCharBufferSize();charBuffer[i++] = (char) buf[bufIndex++]; } else { if(buf[bufIndex] == CARRIAGE_RETURN) bufIndex++;bufIndex++;return new String(charBuffer, 0, i); } }numBytesRead = stream.read(buf);if (numBytesRead == EOF) return new String(charBuffer, 0, i);bufIndex = 0; } while (true); }
        public String nextString() throws IOException { if (numBytesRead == EOF) return null;if (readJunk(SPACE) == EOF) return null;for (int i = 0; ; ) { while (bufIndex < numBytesRead) { if (buf[bufIndex] > SPACE) { if (i == charBuffer.length) doubleCharBufferSize();charBuffer[i++] = (char) buf[bufIndex++]; } else {bufIndex++;return new String(charBuffer, 0, i); } }numBytesRead = stream.read(buf);if (numBytesRead == EOF) return new String(charBuffer, 0, i);bufIndex = 0; } }
        public double nextDoubleFast() throws IOException {c = read();int sgn = 1;while (c <= SPACE) c = read();if (c == DASH) { sgn = -1;c = read(); }double res = 0.0;while (c > DOT) { res *= 10.0;res += ints[c];c = read(); }if (c == DOT) { int i = 0;c = read();while (c > SPACE && i < MAX_DECIMAL_PRECISION) { res += doubles[ints[c]][i++];c = read(); } }return res * sgn; }
        public void close() throws IOException {stream.close(); }
    }

    // region variables
    static InputReader sc = new InputReader();
    static OutputStream outputStream = System.out;
    static PrintWriter w = new PrintWriter(outputStream);
    // endregion

    private static void initiateIO()
            throws IOException {if (System.getProperty("ONLINE_JUDGE") == null) { try { w = new PrintWriter("output.txt");sc = new InputReader(new FileInputStream("input.txt")); } catch (Exception e) { throw new IOException(); }} }

    public static void main(String[] args)
            throws IOException {

        initiateIO();

        int t = sc.nextInt();
        while(t-- > 0) {
            solve();
        }

        w.close();

    }

    static void solve() throws IOException {
        int n = sc.nextInt();
        int k = sc.nextInt();
        int[] ac = new int[n+1];
        Arrays.fill(ac, Integer.MAX_VALUE);
        int[] pos = new int[k+1];
        for(int i = 1; i <= k; i++) {
            pos[i] = sc.nextInt();
        }
        for(int i = 1; i <= k; i++) {
            int posi = pos[i];
            int temp = sc.nextInt();
            ac[posi] = temp;
        }

        long[] prev = new long[n+1];

        long temp = Integer.MAX_VALUE;
        for(int i = 1; i <= n; i++) {
            temp = Math.min(temp+1, ac[i]);
            prev[i] = temp;
        }

        long[] next = new long[n+1];

        temp = Integer.MAX_VALUE;
        for(int i = n; i > 0; i--) {
            temp = Math.min(temp+1, ac[i]);
            next[i] = temp;
        }

        for(int i = 1; i <= n; i++) {
            w.print(Math.min(prev[i], next[i])+" ");
        }
        w.println();
    }
}