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.*;
import java.lang.Math;
import static java.lang.Math.max;
import static java.lang.Math.min;
import static java.lang.Math.abs;



public class Main {

     static PrintWriter pw;
     static Scanner sc;
     static StringBuilder ans;
     static long mod = 1000000000+7;

     static void pn(final Object arg) {      pw.print(arg);   pw.flush();      }     
      

     /*-------------- for input in an value ---------------------*/
     static int ni()     { return sc.nextInt();       }
     static long nl()    { return sc.nextLong();      }
     static double nd()  { return sc.nextDouble();    }
     static String ns()  { return sc.next();          }


     static void ap(int arg)           { ans.append(arg); }
     static void ap(long arg)          { ans.append(arg); }
     static void ap(String arg)        { ans.append(arg); }
     static void ap(StringBuilder arg) { ans.append(arg); }
     static void yes() { ap("Yes\n"); }
     static void no()  { ap("No\n"); }        


     /* for Dubuggin */
     static void printArr(int ar[])  {   for(int i : ar)     ap(i+ " ");    ap("\n"); }
     static void printArr(long ar[]) {   for(long i : ar)    ap(i+ " ");    ap("\n"); }     

     /*-------------- for input in an array ---------------------*/
     static void readIntegerArray(int arr[]){
          for(int i=0; i<arr.length; i++)arr[i] = ni();
     }
     static void readLongArray(long arr[]){
          for(int i=0; i<arr.length; i++)arr[i] = nl(); 
     }
     static void readStringArray(String arr[]){
          for(int i=0; i<arr.length; i++)arr[i] = ns(); 
     }    
     static void readDoubleArray(double arr[]){
          for(int i=0; i<arr.length; i++)arr[i] = nd();
     }


     /*-------------- File vs Input ---------------------*/
     static void runFile() throws Exception {
          sc = new Scanner(new FileReader("input.txt"));
          pw = new PrintWriter(new BufferedWriter(new FileWriter("output.txt")));
     }
     static void runIo() throws Exception  {
          pw =new PrintWriter(System.out);
          sc = new Scanner(System.in);
     }


     static boolean isPowerOfTwo (long x) { return x!=0 && ((x&(x-1)) == 0);}

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

     static long nCr(long n, long r) { // Combinations
          if (n < r)
               return 0;
          if (r > n - r) { // because nCr(n, r) == nCr(n, n - r)
               r = n - r;
          }
          long ans = 1L;
          for (long i = 0; i < r; i++) {
               ans *= (n - i);
               ans /= (i + 1);
          }
          return ans;
     }          

     static int countDigit(long n){return (int)Math.floor(Math.log10(n) + 1);} 

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

          for (long i = 5; i * i <= n; i = i + 6) 
          if (n % i == 0 || n % (i + 2) == 0) 
               return false; 

          return true; 
     }         

     static boolean sv[] = new boolean[10002];
      

     static void seive() {

            //true -> not prime
          // false->prime

          sv[0] = sv[1] = true; 
          sv[2] = false;
          for(int i = 0; i< sv.length; i++) {
               if( !sv[i] && (long)i*(long)i < sv.length ) {
                    for ( int j = i*i; j<sv.length ; j += i ) {                
                     sv[j] = true;
                    }
               }
          }

     }


     static long kadensAlgo(long ar[]) {

          int n = ar.length;

          long pre = ar[0];
          long ans = ar[0];                

          for(int i = 1; i<n; i++) {
               pre = Math.max(pre + ar[i], ar[i]);
               ans = Math.max(pre, ans);
          }
          return ans;
     }


     static long  binpow( long a,   long b) {

          long res = 1;
          while (b > 0) {
               if ( (b & 1) > 0){
                    res = (res * a);              
               }
               a = (a * a);
               b >>= 1;
          }

          return res;
     }

     static long factorial(long n)  {
          long res = 1, i;
          for (i = 2; i <= n; i++){
               res  =  ((res%mod) * (i%mod))%mod;
          }          
          return res;
     } 

     static int getCountPrime(int n) {
 
          int ans = 0;
 
          while (n%2==0) { 
               ans ++;
               n /= 2; 
          }  
 
          for (int i = 3; i *i<= n; i+= 2) {  
               while (n%i == 0) {  
                    ans ++;
                    n /= i; 
               }
          }
 
          if(n > 1 )
               ans++;
 
          return ans; 
     }    
     static void sort(long[] arr)    {
          /* because Arrays.sort() uses quicksort which is dumb
          Collections.sort() uses merge sort */
          ArrayList<Long> ls = new ArrayList<Long>();
          for(Long x: arr)
               ls.add(x);          
          Collections.sort(ls);
          for(int i=0; i < arr.length; i++)
               arr[i] = ls.get(i);

    }     

 
     
     static int upperBound(long ar[], long k, int l, int r) {
          
         while (l <= r) {
             int m = (l + r) >> 1 ;
             if (ar[m] > k) {
                 r = m - 1 ;
             } else {
                 l = m + 1 ;
             }
         }         
         return l ;
     }

     static int lowerBound(long ar[], long k, int l, int r) {
         
         while (l <= r) {
             int m = (l + r) >> 1 ;
             if (ar[m] >= k) {
                 r = m - 1 ;
             } else {
                 l = m + 1 ;
             }
         }
         return l ;
     } 

     static void findDivisor(int n, ArrayList<Integer> al) {

         for(int i = 1; i*i <= n; i++){
             if( n % i == 0){
                 if(n/i==i){
                     al.add(i);
                 }
                 else{
                     al.add(n/i);
                     al.add(i);
                 }
             }
         }

     }
 
     static class Pair{
        int u;
        int d;
        Pair(int u, int d){
            this.u = u;
            this.d = d;
        }
    }
     
  
     public static void main(String[] args)  throws Exception {
  
          // runFile();  
   
          runIo();              

          int t;
          t = 1;
  
          t =  sc.nextInt();
                
          ans = new StringBuilder();
          
          while( t-- > 0 ) {   
               solve();
          }                
          
          pn(ans+""); 
 
     }   



  
     public static void solve() {          
           
       int n = ni();
       int k = ni();
       int ar[] = new int[k];
       long temp[] = new long[k];
       readIntegerArray(ar);
       readLongArray(temp);

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

      for(int i= 0; i<k; i++) {
          ans[ar[i]] = temp[i];    
      }            

      long min = Integer.MAX_VALUE;
      long idx = 0;

      for(int i = 1; i<=n; i++) {

          if( ans[i] == 0 )
               ans[i] = min + idx;
          else {

               if( ans[i] < min + idx ) {
                    min = ans[i];
                    idx = 0;
               }
               else {
                    ans[i] = min+idx;
               }
          }

          idx++;

      }

      min = Integer.MAX_VALUE;
      idx = 0;

      for(int i = n; i>=1; i--) {

          if( ans[i] == 0 )
               ans[i] = min + idx;
          else {

               if( ans[i] < min + idx ) {
                    min = ans[i];
                    idx = 0;
               }
               else {
                    ans[i] = min+idx;
               }
          }

          idx++;

      }      

     
     for(int i = 1; i<=n;i++)
          ap(ans[i]+" ");

     ap("\n");


    } 

}