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.*;
import java.lang.*;
 public class B {

static FastReader  sc  = new FastReader();
static PrintWriter out = new PrintWriter(System.out);

public static void main(String[] args) throws Exception {

  int t = sc.nextInt();
  while (t-- > 0)
  B.go();
  out.flush();
}

// >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Code Starts <<<<<<<<<<<<<<<<<<<<<<<<<<<<< //
static int mod=(int)1e9+7;
static class helper{
	int x;long y;
	helper(int x,long  y){
		this.x=x;
		this.y=y;
	}

}

static void go() throws Exception {
	int n=sc.nextInt(),k=sc.nextInt();
	int a[]=sc.intArray(k);
	int t[]=sc.intArray(k);
	ArrayList<ArrayList<Integer>> aa=new ArrayList<>();
	for(int i=0;i<n;i++) {
		aa.add(new ArrayList<>());
	}
	for(int i=1;i<n;i++) {
		aa.get(i).add(i-1);
		aa.get(i-1).add(i);
	}
	PriorityQueue<helper> pq=new PriorityQueue<>((o1,o2)->Long.compare(o1.y, o2.y));
	
	for(int i=0;i<k;i++) {
		pq.add(new helper(a[i]-1,t[i]));
	}
	long dis[]=new long[n];
	Arrays.fill(dis, Integer.MAX_VALUE);
	for(int i=0;i<k;i++) {
		dis[a[i]-1]=t[i];
	}

	boolean vis[]=new boolean[n];
	while(pq.isEmpty()==false) {
				helper x=pq.poll();
				if(vis[x.x]==false) {
					vis[x.x]=true;
					for(int i:aa.get(x.x)) {
						if(dis[i]>dis[x.x]+Math.abs(x.x-i)) {
							dis[i]=dis[x.x]+Math.abs(x.x-i);
							pq.add(new helper(i,dis[i]));
						}
						
					}
				}
	}
	for(int i=0;i<dis.length;i++) {
		out.print(dis[i]+" ");
	}
	out.println();
}
static void   print(char a[][]) {

	for(int i=0;i<a.length;i++) {
		for(int j=0;j<a[i].length;j++) {
			out.print(a[i][j]);
		}
		out.println();
	}
}

// >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Code Ends <<<<<<<<<<<<<<<<<<<<<<<<<<<<< //


static long gcd(long a,long b){
    if(b==0){
        return a;
    }return gcd(b,a%b);
}
static long fact[];
static long invfact[];
static long ncr(int n,int k) {
	if(k<0||k>n) {
		return 0;
	}
	long x=fact[n]%mod;
	long y=invfact[k]%mod;
	long yy=invfact[n-k]%mod;
	long ans=(x*y)%mod;
	ans=(ans*yy)%mod;
	return ans;
}
static int prime[]=new int[40006];
static void sieve() {
	Arrays.fill(prime, 1);
	prime[0]=0;
	prime[1]=0;
	for(int i=2;i*i<=40005;i++) {
		if(prime[i]==1) {
		for(int j=i*i;j<=40005;j+=i) {
			prime[j]=0;
		}
		}
	}
	
//	for(int i=1;i<1000005;i++) {prime[i]=prime[i]+prime[i-1];}
}
static void sort(long [] a) {
  ArrayList<Long> aa = new ArrayList<>();
  for (long  i : a) {
    aa.add(i);
  }Collections.sort(aa);  for (int i = 0; i < a.length; i++)
    a[i] = aa.get(i);	  }
static void sort(int [] a) {
  ArrayList<Integer> aa = new ArrayList<>();
  for (int  i : a) {
    aa.add(i);
  } Collections.sort(aa); for (int i = 0; i < a.length; i++)
    a[i] = aa.get(i); }
static long pow(long x, long y) {
  long res = 1l;
  while (y != 0) {
    if (y % 2 == 1) {
      res = (x%mod * res%mod)%mod; } y /= 2; x = (x%mod * x%mod)%mod;
  } return res%mod;  }

//>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Fast IO <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< //

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());
  }
	int[] intArray(int n) {
		int a[]=new int[n];
		for(int i=0;i<n;i++)a[i]=sc.nextInt();
		return a;
	}
	long[] longArray(int n) {
		long a[]=new long[n];
		for(int i=0;i<n;i++)a[i]=sc.nextLong();
		return a;
	}String nextLine() {
    String str = "";
    try {
      str = br.readLine();
    } catch (IOException e) {
      e.printStackTrace();
    }
    return str;
  }}
}

/*
 * imp log method using math function is somewhat inaccurate to check power of
 * two
 *
 */