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.util.*;

import java.io.*;

public class cf {
  static Reader sc = new Reader();
  static PrintWriter out = new PrintWriter(System.out);
  static long mod = (long) 1e9 + 7;

  public static void main(String[] args) {
    int tc = sc.ni();
    while (tc-- > 0) {
      int n = sc.ni(), k = sc.ni();

      long[] arr = new long[n];
      Arrays.fill(arr, Integer.MAX_VALUE);
      int[][] ACs = new int[k][2];
      for (int i = 0; i < k; i++) {
        ACs[i][0] = sc.ni();
      }
      for (int i = 0; i < k; i++) {
        ACs[i][1] = sc.ni();
      }
      for (int i = 0; i < k; i++) {
        arr[ACs[i][0] - 1] = ACs[i][1];
      }

      long minVal = Integer.MAX_VALUE;
      for (int i = 0; i < n; i++) {
        arr[i] = min(arr[i], minVal + i);
        minVal = min(minVal, arr[i] - i);
      }
      minVal = Integer.MAX_VALUE;
      for (int i = n - 1; i >= 0; i--) {
        arr[i] = min(arr[i], minVal - i);
        minVal = min(minVal, arr[i] + i);
      }

      for (long e : arr)
        out.print(e + " ");

      out.println();

    }
    out.close();

  }

  public static long pow(long a, long b, long m) {
    if (b == 0) {
      return 1;
    }
    if (b % 2 == 0) {
      return pow((a * a) % m, b / 2, m) % m;
    } else {
      return (a * pow((a * a) % m, b / 2, m)) % m;
    }
  }

  // snippets

  static class Pair implements Comparable<Pair> {
    int x;
    int y;

    Pair(int x, int y) {
      this.x = x;
      this.y = y;

    }

    @Override
    public int compareTo(Pair o) {
      if (this.x > o.x)
        return 1;
      else if (this.x < o.x)
        return -1;
      else {
        if (this.y > o.y)
          return 1;
        else if (this.y < o.y)
          return -1;
        else
          return 0;
      }
    }

    public int hashCode() {
      int ans = 1;
      ans = x * 31 + y * 13;
      return ans;
    }

    @Override
    public boolean equals(Object o) {
      if (this == o) {
        return true;
      }
      if (o == null) {
        return false;
      }
      if (this.getClass() != o.getClass()) {
        return false;
      }
      Pair other = (Pair) o;
      if (this.x == other.x && this.y == other.y) {
        return true;
      }
      return false;
    }

  }

  static void add_map(HashMap<Integer, Integer> map, int v) {
    if (!map.containsKey(v)) {
      map.put(v, 1);
    } else {
      map.put(v, map.get(v) + 1);
    }
  }

  static void remove_map(HashMap<Integer, Integer> map, int v) {
    if (map.containsKey(v)) {
      map.put(v, map.get(v) - 1);
      if (map.get(v) == 0)
        map.remove(v);
    }
  }

  static int gcd(int a, int b) {
    if (b == 0)
      return a;
    return gcd(b, a % b);
  }

  static long gcd(long a, long b) {
    if (b == 0)
      return a;
    return gcd(b, a % b);
  }

  static void sort(int[] arr) {
    // shuffle
    Random rand = new Random();
    for (int i = 0; i < arr.length; i++) {
      int j = rand.nextInt(i + 1);
      int tmp = arr[i];
      arr[i] = arr[j];
      arr[j] = tmp;
    }
    Arrays.sort(arr);
  }

  static void sort(long[] arr) {
    // shuffle
    Random rand = new Random();
    for (int i = 0; i < arr.length; i++) {
      int j = rand.nextInt(i + 1);
      long tmp = arr[i];
      arr[i] = arr[j];
      arr[j] = tmp;
    }
    Arrays.sort(arr);
  }

  static boolean isPrime(int n) {
    if (n <= 1)
      return false;
    if (n <= 3)
      return true;
    if (n % 2 == 0 || n % 3 == 0)
      return false;
    double sq = Math.sqrt(n);

    for (int i = 5; i <= sq; i = i + 6)
      if (n % i == 0 || n % (i + 2) == 0)
        return false;
    return true;
  }

  static boolean isPrime(long n) {
    if (n <= 1)
      return false;
    if (n <= 3)
      return true;
    if (n % 2 == 0 || n % 3 == 0)
      return false;
    double sq = Math.sqrt(n);

    for (int i = 5; i <= sq; i = i + 6)
      if (n % i == 0 || n % (i + 2) == 0)
        return false;
    return true;
  }

  static void print_arr(int A[]) {
    for (int i : A) {
      System.out.print(i + " ");
    }
    System.out.println();
  }

  static void print_arr(long A[]) {
    for (long i : A) {
      System.out.print(i + " ");
    }
    System.out.println();
  }

  static void print_arr(char A[]) {
    for (char i : A) {
      System.out.print(i + " ");
    }
    System.out.println();
  }

  static int min(int a, int b) {
    return Math.min(a, b);
  }

  static int min(int a, int b, int c) {
    return Math.min(a, Math.min(b, c));
  }

  static int min(int a, int b, int c, int d) {
    return Math.min(a, Math.min(b, Math.min(c, d)));
  }

  static int max(int a, int b) {
    return Math.max(a, b);
  }

  static int max(int a, int b, int c) {
    return Math.max(a, Math.max(b, c));
  }

  static int max(int a, int b, int c, int d) {
    return Math.max(a, Math.max(b, Math.max(c, d)));
  }

  static long min(long a, long b) {
    return Math.min(a, b);
  }

  static long min(long a, long b, long c) {
    return Math.min(a, Math.min(b, c));
  }

  static long min(long a, long b, long c, long d) {
    return Math.min(a, Math.min(b, Math.min(c, d)));
  }

  static long max(long a, long b) {
    return Math.max(a, b);
  }

  static long max(long a, long b, long c) {
    return Math.max(a, Math.max(b, c));
  }

  static long max(long a, long b, long c, long d) {
    return Math.max(a, Math.max(b, Math.max(c, d)));
  }

  static int max(int A[]) {
    int max = Integer.MIN_VALUE;
    for (int i = 0; i < A.length; i++) {
      max = Math.max(max, A[i]);
    }
    return max;
  }

  static int min(int A[]) {
    int min = Integer.MAX_VALUE;
    for (int i = 0; i < A.length; i++) {
      min = Math.min(min, A[i]);
    }
    return min;
  }

  static long max(long A[]) {
    long max = Long.MIN_VALUE;
    for (int i = 0; i < A.length; i++) {
      max = Math.max(max, A[i]);
    }
    return max;
  }

  static long min(long A[]) {
    long min = Long.MAX_VALUE;
    for (int i = 0; i < A.length; i++) {
      min = Math.min(min, A[i]);
    }
    return min;
  }

  static long sum(int A[]) {
    long sum = 0;
    for (int i : A) {
      sum += i;
    }
    return sum;
  }

  static long sum(long A[]) {
    long sum = 0;
    for (long i : A) {
      sum += i;
    }
    return sum;
  }

  static ArrayList<Integer> sieve(int n) {
    ArrayList<Integer> primes = new ArrayList<>();
    boolean[] isPrime = new boolean[n];
    Arrays.fill(isPrime, true);
    isPrime[0] = isPrime[1] = false;
    for (int i = 2; i * i <= n; i++) {
      if (isPrime[i]) {
        for (int j = i * i; j < n; j += i) {
          isPrime[j] = false;
        }
      }
    }
    for (int i = 2; i < n; i++) {
      if (isPrime[i])
        primes.add(i);
    }
    return primes;
  }

  static class Reader {
    BufferedReader br;
    StringTokenizer st;

    Reader() {
      br = new BufferedReader(new InputStreamReader(System.in));
      st = new StringTokenizer("");
    }

    Reader(File f) throws FileNotFoundException {
      br = new BufferedReader(new FileReader(f));
      st = new StringTokenizer("");
    }

    String next() {
      while (!st.hasMoreTokens())
        try {
          st = new StringTokenizer(br.readLine());
        } catch (IOException e) {
        }
      return st.nextToken();
    }

    int ni() {
      return Integer.parseInt(next());
    }

    long nl() {
      return Long.parseLong(next());
    }

    double nextDouble() {
      return Double.parseDouble(next());
    }

    int[] nai(int n) {
      int[] a = new int[n];
      for (int i = 0; i < n; i++)
        a[i] = ni();
      return a;
    }

    long[] nal(int n) {
      long[] a = new long[n];
      for (int i = 0; i < n; i++)
        a[i] = nl();
      return a;
    }
  }

}