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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */

/**
 *
 * @author wilso
 */
public class codeforces3 {
    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        PrintWriter pw = new PrintWriter(System.out);
        int t = sc.ni();
        for (int rep = 0; rep < t; rep++) {
            int N = sc.ni();
            int K = sc.ni();
            long[][] ref = new long[K][2];
            //[pos, val]
            for (int i = 0;i < ref.length; i++) {
                ref[i][0] = sc.nl();
            }
            for (int i = 0; i < ref.length; i++) {
                ref[i][1] = sc.nl();
            }
            pw.println(solve(N, ref));
        }
        pw.close();
    }

    public static String solve(int N, long[][] ref) {
        Map<Integer, Long> map = new HashMap();
        for (long[] x : ref) {
            map.put((int)(x[0] - 1), x[1]);
        }
        long[] pf = new long[N];
//        Arrays.fill(pf, Long.MAX_VALUE);
        long curr = (long)(1e10 + 1);
        for (int i = 0; i < pf.length; i++) {
            if (map.containsKey(i)) {
                curr = Math.min(curr, map.get(i));
            }
            pf[i] = curr;
            curr++;
        }
        long[] sf = new long[N];
        curr = (long)(2e10 + 1);
        for (int i = sf.length - 1;i >= 0; i--) {
            if (map.containsKey(i)) {
                curr = Math.min(curr, map.get(i));
            }
            sf[i] = curr;
            curr++;
        }
        
        
        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < N; i++) {
            sb.append(Math.min(pf[i], sf[i]) + " ");
        }
        return sb.toString();
        
    }
    
    static long pow(long num, long exp, long mod){
        long ans=1;
        for(int i=1;i<=exp;i++){
            ans=(ans*num)%mod;
        }
        return ans;
    }
    static boolean isPrime(int n)
    {
 
        // Check if number is less than
        // equal to 1
        if (n <= 1)
            return false;
 
        // Check if number is 2
        else if (n == 2)
            return true;
 
        // Check if n is a multiple of 2
        else if (n % 2 == 0)
            return false;
 
        // If not, then just check the odds
        for (int i = 3; i <= Math.sqrt(n); i += 2) 
        {
            if (n % i == 0)
                return false;
        }
        return true;
    }
    static int gcd(int a, int b)
    {
        if (a == 0)
            return b; 
        return gcd(b % a, a); 
    }
     
    // method to return LCM of two numbers
    static int lcm(int a, int b) {
        return (a / gcd(a, b)) * b;
    }
    static Map<Integer, Integer> primeFactorization(int x) {
        //first divide by 2
        Map<Integer, Integer> map = new HashMap();
        int count = 0;
        while (x % 2 == 0) {
            x /=2;
            count++;
        }
        //insert 2
        if (count > 0) map.put(2, count);
        for (int divisor = 3; divisor * divisor <= x; divisor += 2) {
            int cnt = 0;
            while (x % divisor == 0) {
                x /= divisor;
                cnt++;
            }
            if (cnt > 0) map.put(divisor, cnt);
        }
        if (x > 1) {
            map.put(x, 1);
        }
        return map;
    }
    static Map<Long, Integer> primeFactorization(long x) {
        //first divide by 2
        Map<Long, Integer> map = new HashMap();
        int count = 0;
        while (x % 2 == 0) {
            x /=2;
            count++;
        }
        //insert 2
        if (count > 0) map.put((long)(2), count);
        for (long divisor = 3; divisor * divisor <= x; divisor += 2) {
            int cnt = 0;
            while (x % divisor == 0) {
                x /= divisor;
                cnt++;
            }
            if (cnt > 0) map.put(divisor, cnt);
        }
        if (x > 1) {
            map.put(x, 1);
        }
        return map;
    }
    public static void sort(int[] arr) {
        Random rgen = new Random();
        for (int i = 0; i < arr.length; i++) {
            int r = rgen.nextInt(arr.length);
            int temp = arr[i];
            arr[i] = arr[r];
            arr[r] = temp;
        }
        Arrays.sort(arr);
    }
 
    public static void sort(long[] arr) {
        Random rgen = new Random();
        for (int i = 0; i < arr.length; i++) {
            int r = rgen.nextInt(arr.length);
            long temp = arr[i];
            arr[i] = arr[r];
            arr[r] = temp;
        }
        Arrays.sort(arr);
    }
    /* */
    //printing methods
    /* */
    //WOW!
    /* */
    public static void printArr(PrintWriter pw, int[] arr) {
        StringBuilder sb = new StringBuilder();
        for (int x : arr) {
            sb.append(x + "");
        }
        sb.setLength(sb.length() - 1);
        pw.println(sb.toString());
    }
    public static void printArr2d(PrintWriter pw, int[][] arr) {
        StringBuilder sb = new StringBuilder();
        for (int[] row : arr) {
            for (int x : row) {
                sb.append(x + " ");
            }
            sb.setLength(sb.length() - 1);
            sb.append("\n");
        }
        pw.println(sb.toString());
    }
}
class FastScanner {
    BufferedReader br;
    StringTokenizer st;

    public FastScanner() {
        br = new BufferedReader(new InputStreamReader(System.in), 32768);
        st = null;
    }

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

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

    int[] intArray(int N) {
        int[] ret = new int[N];
        for (int i = 0; i < N; i++)
            ret[i] = ni();
        return ret;
    }

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

    long[] longArray(int N) {
        long[] ret = new long[N];
        for (int i = 0; i < N; i++)
            ret[i] = nl();
        return ret;
    }

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

    String nextLine() {
        String str = "";
        try {
            str = br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return str;
    }
}
class MultiSet {
    TreeMap<Long, Integer> map = new TreeMap<>();
    private int size = 0;
    public MultiSet() {
    }
    public void add(Long val) {
        map.put(val, map.getOrDefault(val, 0) + 1);
        size++;
    }
    public void remove(Long val) {
        map.put(val, map.get(val) - 1);
        if (map.get(val) == 0) {
            map.remove(val);
        }
        size--;
    }
    public int size() {
        return size;
    }
    public Long higher(Long val) {
        return map.higherKey(val);
    }
    public Long lower(Long val) {
        return map.lowerKey(val);
    }
    public Long ceiling(Long val) {
        return map.ceilingKey(val);
    }
    public Long floor(Long val) {
        return map.floorKey(val);
    }
    public Long first() {
        return map.firstKey();
    }
    public Long last() {
        return map.lastKey();
    }
    public boolean isEmpty() {
        return map.isEmpty();
    }
}