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:
// package com.company

/*
 * @author :: Yuvraj Singh
 * CS UNDERGRAD AT IT GGV BILASPUR
 */

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;
import static java.lang.Math.*;
import static java.util.Arrays.*;
import static java.lang.System.out;
import static java.lang.Long.MAX_VALUE;

public final class Main{

    FastReader in;
    StringBuffer sb;
    public static void main(String[] args) {
        new Main().run();
    }

    void run(){
        in= new FastReader();
        start();
    }

    void start(){
        sb= new StringBuffer();
        for(int t=in.nextInt();t>0;t--)
            solve();
        out.print(sb);
    }

    long MOD= 1000000007;
    void solve(){
        int n= in.nextInt();
        int k= in.nextInt();
        long[] a=longArr(k);
        long[] t=longArr(k);
        long[] ans= new long[n];
        for(int i=0;i<n;i++){
            ans[i]= Integer.MAX_VALUE;
        }
        for(int i=0;i<k;i++){
            ans[(int) (a[i]-1)]= t[i];
        }
        long[] left= new long[n];
        left[0]= ans[0];
        for(int i=1;i<n;i++) {
            left[i]= min(left[i-1]+1,ans[i]);
        }
        long[] right= new long[n];
        right[n-1]= ans[n-1];
        for(int i=n-2;i>=0;i--) {
            right[i]= min(right[i+1]+1,ans[i]);
        }
        for(int i=0;i<n;i++)
            sb.append(min(left[i], right[i])).append(" ");

        sb.append("\n");
    }

    int upper_bound(long[] arr, int key) {
        int i=0, j=arr.length-1;
        if (arr[j]<=key) return j+1;
        if(arr[i]>key) return i;
        while (i<j){
            int mid= (i+j)/2;
            if(arr[mid]<=key){
                i= mid+1;
            }else{
                j=mid;
            }
        }
        return i;
    }

    void sort(long[] A){
        int n = A.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i){
            long tmp = A[i];
            int randomPos = i + rnd.nextInt(n-i);
            A[i] = A[randomPos];
            A[randomPos] = tmp;
        }
        Arrays.sort(A);
    }

    long[] longArr(int n){
        long[] res= new long[n];
        for(int i=0;i<n;i++){
            res[i]= in.nextLong();
        }
        return res;
    }

    // sieve of eratosthenes code for precomputing whether numbers are prime or not up to MAX_VALUE
    long MAX= MAX_VALUE;
    int[] precomp= new int[(int) (MAX+1)];
    void sieve(){
        long n= MAX;
        boolean[] prime = new boolean[(int) (n+1)];
        for(int i=0;i<=n;i++)
            prime[i] = true;

        for(long p = 2; p*p <=n; p++)
        {
            // If prime[p] is not changed, then it is a prime
            if(prime[(int) p])
            {
                // Update all multiples of p
                for(long i = p*p; i <= n; i += p)
                    prime[(int) i] = false;
            }
        }

        // Print all prime numbers
        for(long i = 2; i <= n; i++)
        {
            if(prime[(int) i])
                precomp[(int) i]= 1;
        }
    }

    boolean isDigitSumPalindrome(long N) {
        // code here
        long sum= sumOfDigits(String.valueOf(N));
        long rev=0;
        long org= sum;
        while (sum!=0){
            long d= sum%10;
            rev = rev*10 +d;
            sum /= 10;
        }
        return org == rev;
    }

    long sumOfDigits(String n){
        long sum= 0;
        for (char c: n.toCharArray()){
            sum += Integer.parseInt(String.valueOf(c));
        }
        return sum;
    }

    long[] revArray(long[] arr) {
        int n= arr.length;
        int i=0, j=n-1;
        while (i<j){
            long temp= arr[i];
            arr[i]= arr[j];
            arr[j]= temp;
            i++;
            j--;
        }
        return arr;
    }

    long gcd(long a, long b){
        if (b==0)
            return a;
        return gcd(b, a%b);
    }
    long lcm(long a,long b){
        return (a*b)/gcd(a,b);
    }

    static class Pair{
        long first;
        long second;
        Pair(long x,long y){
            this.first=x;
            this.second=y;
        }
    }

    static class Compare {
        static void compare(ArrayList<Pair> arr, long n) {
            arr.sort(new Comparator<Pair>() {
                @Override
                public int compare(Pair p1, Pair p2) {
                    return (int) (p1.first - p2.first);
                }
            });
        }
    }

    public 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 (Exception e){
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        int nextInt(){
            return Integer.parseInt(next());
        }
        long nextLong(){
            return Long.parseLong(next());
        }
        double nextDouble(){
            return Double.parseDouble(next());
        }
        float nextFloat(){
            return Float.parseFloat(next());
        }
        String nextLine(){
            String str="";
            try{
                str=br.readLine();
            }catch (Exception e){
                e.printStackTrace();
            }
            return str;
        }
    }
}