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.lang.*;
import java.io.*;


public class cf {
    static PrintWriter out;
    static int MOD = 1000000007;
    static FastReader scan;

    /*-------- I/O using short named function ---------*/
    public static String ns() {
        return scan.next();
    }

    public static int ni() {
        return scan.nextInt();
    }

    public static long nl() {
        return scan.nextLong();
    }

    public static double nd() {
        return scan.nextDouble();
    }

    public static String nln() {
        return scan.nextLine();
    }

    public static void p(Object o) {
        out.print(o);
    }

    public static void ps(Object o) {
        out.print(o + " ");
    }

    public static void pn(Object o) {
        out.println(o);
    }

    /*-------- for output of an array ---------------------*/
    static void iPA(int arr[]) {
        StringBuilder output = new StringBuilder();
        for (int i = 0; i < arr.length; i++) output.append(arr[i] + " ");
        out.println(output);
    }

    static void lPA(long arr[]) {
        StringBuilder output = new StringBuilder();
        for (int i = 0; i < arr.length; i++) output.append(arr[i] + " ");
        out.println(output);
    }

    static void sPA(String arr[]) {
        StringBuilder output = new StringBuilder();
        for (int i = 0; i < arr.length; i++) output.append(arr[i] + " ");
        out.println(output);
    }

    static void dPA(double arr[]) {
        StringBuilder output = new StringBuilder();
        for (int i = 0; i < arr.length; i++) output.append(arr[i] + " ");
        out.println(output);
    }

    /*-------------- for input in an array ---------------------*/
    static void iIA(int arr[]) {
        for (int i = 0; i < arr.length; i++) arr[i] = ni();
    }

    static void lIA(long arr[]) {
        for (int i = 0; i < arr.length; i++) arr[i] = nl();
    }

    static void sIA(String arr[]) {
        for (int i = 0; i < arr.length; i++) arr[i] = ns();
    }

    static void dIA(double arr[]) {
        for (int i = 0; i < arr.length; i++) arr[i] = nd();
    }

    /*------------ for taking input faster ----------------*/
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

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

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

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

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    public static ArrayList<Integer> sieveOfEratosthenes(int n) {
        // Create a boolean array
        // "prime[0..n]" and
        // initialize all entries
        // it as true. A value in
        // prime[i] will finally be
        // false if i is Not a
        // prime, else true.
        boolean prime[] = new boolean[n + 1];
        for (int i = 0; i <= n; i++)
            prime[i] = true;

        for (int p = 2; p * p <= n; p++) {
            // If prime[p] is not changed, then it is a
            // prime
            if (prime[p] == true) {
                // Update all multiples of p
                for (int i = p * p; i <= n; i += p)
                    prime[i] = false;
            }
        }
        ArrayList<Integer> arr = new ArrayList<>();
        // Print all prime numbers
        for (int i = 2; i <= n; i++) {
            if (prime[i] == true)
                arr.add(i);
        }
        return arr;
    }

    // Method to check if x is power of 2
    static boolean isPowerOfTwo(int x) {
        return x != 0 && ((x & (x - 1)) == 0);
    }

    //Method to return lcm of two numbers
    static int gcd(int a, int b) {
        return a == 0 ? b : gcd(b % a, a);
    }

    //Method to count digit of a number
    static int countDigit(long n) {
        String sex = Long.toString(n);
        return sex.length();
    }

    static void reverse(int a[]) {
        int i, k, t;
        int n = a.length;
        for (i = 0; i < n / 2; i++) {
            t = a[i];
            a[i] = a[n - i - 1];
            a[n - i - 1] = t;
        }
    }

    static final Random random = new Random();

    //Method for sorting
    static void ruffleSort(int[] arr) {
        int n = arr.length;
        for (int i = 0; i < n; i++) {
            int j = random.nextInt(n);
            int temp = arr[j];
            arr[j] = arr[i];
            arr[i] = temp;
        }
        Arrays.sort(arr);
    }

    static void sortadv(long[] a) {
        ArrayList<Long> l = new ArrayList<>();
        for (long value : a) {
            l.add(value);
        }
        Collections.sort(l);
        for (int i = 0; i < l.size(); i++)
            a[i] = l.get(i);
    }

    //Method for checking if a number is prime or not
    static boolean isPrime(int n) {
        if (n <= 1) return false;
        if (n <= 3) return true;
        if (n % 2 == 0 || n % 3 == 0) return false;
        for (int i = 5; i * i <= n; i = i + 6)
            if (n % i == 0 || n % (i + 2) == 0)
                return false;
        return true;
    }

    public static void main(String[] args) throws java.lang.Exception {
        OutputStream outputStream = System.out;
        out = new PrintWriter(outputStream);
        scan = new FastReader();
        //for fast output sometimes
        StringBuilder sb = new StringBuilder();
        int t = ni();
        while (t-- != 0) {
            int n=ni();
            int k=ni();
            int[] a=new int[k];
            int[] temp=new int[k];
            iIA(a);
            iIA(temp);
            long dp[]=new long[n];
            Arrays.fill(dp,Integer.MAX_VALUE);
            for(int i=0;i<k;i++){
                dp[a[i]-1]=temp[i];
            }
            //iPA(dp);
            for(int i=1;i<n;i++){
                dp[i]=Math.min(dp[i-1]+1,dp[i]);
            }
            //iPA(dp);
            for(int i=n-2;i>=0;i--){
                dp[i]=Math.min(dp[i+1]+1,dp[i]);
            }
            lPA(dp);
            //pn("");
        }

        out.flush();
        out.close();
    }
}