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.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.Map.Entry;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Random;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

public class hacker49 {

	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 void main(String[] args) {
		OutputStream outputStream =System.out;
	    PrintWriter out =new PrintWriter(outputStream);
		FastReader s=new FastReader();
 int t=s.nextInt();
 while(t>0) {
	int n=s.nextInt();
	int m=s.nextInt();
	long[] dp1=new long[n+1];
	long[] dp2=new long[n+2];
	dp2[n+1]=Long.MAX_VALUE;
	long[] pos=new long[n+1];
	long[] a=new long[m+1];
	for(int i=1;i<=m;i++) {
		a[i]=s.nextLong();
	}
	for(int i=1;i<=m;i++) {
		long temp=s.nextLong();
		pos[(int) a[i]]=temp;
	}
	dp1[0]=Long.MAX_VALUE;
	for(long i=1;i<=n;i++) {
		if(pos[(int) i]==0) {
			dp1[(int) i]=dp1[(int) (i-1)];
		}else {
			dp1[(int) i]=Math.min(dp1[(int) (i-1)], pos[(int) i]-i);
		}
	}
	for(long i=n;i>=1;i--) {
		if(pos[(int) i]==0) {
			dp2[(int) i]=dp2[(int) (i+1)];
		}else {
			dp2[(int) i]=Math.min(dp2[(int) (i+1)], pos[(int) i]+i);
		}
	}
	for(long i=1;i<=n;i++) {
		long d1=0;
		long d2=0;
		if(dp1[(int) i]==Long.MAX_VALUE) {
			d1=Long.MAX_VALUE;
		}else {
			d1=dp1[(int) i]+i;
		}
		if(dp2[(int) i]==Long.MAX_VALUE) {
			d2=Long.MAX_VALUE;
		}else {
			d2=dp2[(int) i]-i;
		}
		long ans=Math.min(d1, d2);
		out.print(ans+" ");
//		out.print(ans+" ");
	}
	out.println();
t--;			 
 }
		 
		out.close();
	}
	static int[] par=new int[200001];
	static int[] ans=new int[200001];
	static int[] deg=new int[200001];
	static ArrayList<Integer>[] f1=new ArrayList[200001];
	static int[] vis1=new int[200001];
	static void sf(long[] arr){
        int n = arr.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i){
            long tmp = arr[i];
            int randomPos = i + rnd.nextInt(n-i);
            arr[i] = arr[randomPos];
            arr[randomPos] = tmp;
        }   
}
	public static int upper_bound(long[] a ,long x,int n) {
		int l=-1;
		int r=n;
		while(r>l+1) {
			int mid=(l+r)/2;
			if(a[mid]<x) {
				l=mid;
			}else {
				r=mid;
			}
		}
		return r;
				
	}
	public static int lower_bound(long[] a ,long x,int n) {
		int l=-1;
		int r=n;
		while(r>l+1) {
			int mid=(l+r)/2;
			if(a[mid]<=x) {
				l=mid;
			}else {
				r=mid;
			}
		}
		return l;
				
	}
	
	static int[] t=new int[501];
	static class pair implements Comparable<pair>{
		private long a;
		private long b;
//		private int c;
		pair(long a,long b){
			this.a=a;
			this.b=b;
//			this.c=c;
		}
		public int compareTo(pair o) {
			return Long.compare(this.a,o.a);
		}
	}
	public static long[] merge_sort(long[] A, int start, int end) {
		if (end > start) {
			int mid = (end + start) / 2;
			long[] v = merge_sort(A, start, mid);
			long[] o = merge_sort(A, mid + 1, end);
			return (merge(v, o));
		} else {
			long[] y = new long[1];
			y[0] = A[start];
			return y;
		}
	}
	public static long[] merge(long a[], long b[]) {
//		int count=0;
		long[] temp = new long[a.length + b.length];
		int m = a.length;
		int n = b.length;
		int i = 0;
		int j = 0;
		int c = 0;
		while (i < m && j < n) {
			if (a[i] < b[j]) {
				temp[c++] = a[i++];
			
			} else {
				temp[c++] = b[j++];
			}
		}
		while (i < m) {
			temp[c++] = a[i++];
		}
		while (j < n) {
			temp[c++] = b[j++];
		}
		return temp;
	}
static ArrayList<Integer>[] f=new ArrayList[501];	
static int[] vis=new int[501];	
static PriorityQueue<pair> e1=new PriorityQueue<>();
static PriorityQueue<pair> e2=new PriorityQueue<>();
static void dfs(int node) {
		vis[node]=1;
//		e2.add(new pair(node));
//		e1.add(new pair(t[node]));
		for(int i=0;i<f[node].size();i++) {
			if(vis[f[node].get(i)]==0) {
				dfs(f[node].get(i));
			}
		}
	}
	
	public static int[] Create(int[] a,int n) {
		int[] b=new int[n+1];
		for(int i=1;i<=n;i++) {
			int j=i;
			int h=a[i];
			while(i<=n) {
				b[i]+=h;
				i=get_next(i);
			}
			i=j;
		}
		return b;
	}
public static int get_next(int a) {
	return a+(a&-a);
}
public static int get_parent(int a) {
	return a-(a&-a);
}
public static int query_1(int[] b,int index) {
	int sum=0;
	if(index<=0) {
		return 0;
	}
	while(index>0) {
		sum+=b[index];
		index=get_parent(index);
	}
	return sum;
}
public static int query(int[] b,int n,int l,int r) {
	int sum=0;
	sum+=query_1(b,r);
	sum-=query_1(b,l-1);
	return sum;
}
public static void update(int[] a,int[] b,int n,int index,int val) {
	int diff=val-a[index];
	a[index]+=diff;
	while(index<=n) {
		b[index]+=diff;
		index=get_next(index);
	}	
}
	
//	public static void Create(int[] a,pair[] segtree,int low,int high,int pos) {
//		if(low>high) {
//			return;
//		}
//		if(low==high) {
//			segtree[pos].b.add(a[low]);
//			return ;
//		}
//		int mid=(low+high)/2;
//		Create(a,segtree,low,mid,2*pos);
//		Create(a,segtree,mid+1,high,2*pos+1);
//		segtree[pos].b.addAll(segtree[2*pos].b);
//		segtree[pos].b.addAll(segtree[2*pos+1].b);
//	}
//	public static void update(pair[] segtree,int low,int high,int index,int pos,int val,int prev) {
//		if(index>high || index<low) {
//			return ;
//		}
//		if(low==high && low==index) {
//			segtree[pos].b.remove(prev);
//			segtree[pos].b.add(val);
//			return;
//		}
//			int mid=(high+low)/2;
//			 update(segtree,low,mid,index,2*pos,val,prev);
//			 update(segtree,mid+1,high,index,2*pos+1,val,prev);
//			 segtree[pos].b.clear();
//			  segtree[pos].b.addAll(segtree[2*pos].b);
//			  segtree[pos].b.addAll(segtree[2*pos+1].b);
//			  
//	}
//	public static pair query(pair[] segtree,int low,int high,int qlow,int qhigh ,int pos) {
//		if(low>=qlow && high<=qhigh) {
//			return segtree[pos];
//		}
//		if(qhigh<low || qlow>high) {
//			return new pair();
//		}
//		int mid=(low+high)/2;
//	  pair a1=query(segtree,low,mid,qlow,qhigh,2*pos);
//	  pair a2=query(segtree,mid+1,high,qlow,qhigh,2*pos+1);
//	  pair a3=new pair();
//	  a3.b.addAll(a1.b);
//	  a3.b.addAll(a2.b);
//	  return a3;
//	  
//	}
//	
//	public static int nextPowerOf2(int n) 
//	{ 
//	    n--; 
//	    n |= n >> 1; 
//	    n |= n >> 2; 
//	    n |= n >> 4; 
//	    n |= n >> 8; 
//	    n |= n >> 16; 
//	    n++;     
//	    return n; 
//	} 
//	
////	static class pair implements Comparable<pair>{
////		private int a;
////		private long b;
//////		private long c;
////		pair(int a,long b){
////			this.a=a;
////			this.b=b;
//////			this.c=c;
////		}
////		public int compareTo(pair o) {
//////		if(this.a!=o.a) {
//////			return Long.compare(this.a, o.a);
//////		}else {
////			return Long.compare(o.b,this.b);
//////		}
////		}
////	}
//	static class pair implements Comparable<pair>{
//		private int a;
//		private int b;
//		pair(int a,int b){
////			this.b=new HashSet<>();
//			this.a=a;
//			this.b=b;
//		}
//		public int compareTo(pair o) {
//			return Integer.compare(this.b, o.b);
//		}
//	}
	public static int lower_bound(ArrayList<Long> a ,int n,long x) {
		int l=0;
		int r=n;
		while(r>l+1) {
			int mid=(l+r)/2;
			if(a.get(mid)<=x) {
				l=mid;
			}else {
				r=mid;
			}
		}
		return l;		
	}

	public static int[] is_prime=new int[1000001];
	public static ArrayList<Long> primes=new ArrayList<>();
 	public static void sieve() {
		long maxN=1000000;
		for(long i=1;i<=maxN;i++) {
			is_prime[(int) i]=1;
		}
		is_prime[0]=0;
		is_prime[1]=0;
		for(long i=2;i*i<=maxN;i++) {
			if(is_prime[(int) i]==1) {
//				primes.add((int) i);
				for(long j=i*i;j<=maxN;j+=i) {
					is_prime[(int) j]=0;
				}
			}
		}
		for(long i=0;i<=maxN;i++) {
			if(is_prime[(int) i]==1) {
				primes.add(i);
			}
		}		
	}
	
	
//	public static pair[] merge_sort(pair[] A, int start, int end) {
//		if (end > start) {
//			int mid = (end + start) / 2;
//			pair[] v = merge_sort(A, start, mid);
//			pair[] o = merge_sort(A, mid + 1, end);
//			return (merge(v, o));
//		} else {
//			pair[] y = new pair[1];
//			y[0] = A[start];
//			return y;
//		}
//	}
//	public static pair[] merge(pair a[], pair b[]) {
//		pair[] temp = new pair[a.length + b.length];
//		int m = a.length;
//		int n = b.length;
//		int i = 0;
//		int j = 0;
//		int c = 0;
//		while (i < m && j < n) {
//			if (a[i].b >= b[j].b) {
//				temp[c++] = a[i++];
//			
//			} else {
//				temp[c++] = b[j++];
//			}
//		}
//		while (i < m) {
//			temp[c++] = a[i++];
//		}
//		while (j < n) {
//			temp[c++] = b[j++];
//		}
//		return temp;
//	}
	
	
//	public static long im(long a) {
//		return binary_exponentiation_1(a,mod-2)%mod;
//	}
	public static double bn1(double a,double n) {
		double res=1;
		while(n>0) {
			if(n%2!=0) {
//				res=((res)%(1000000007) * (a)%(1000000007))%(1000000007);
				res=(res*a);
				n--;
			}else {
//				a=((a)%(1000000007) *(a)%(1000000007))%(1000000007);
				a=(a*a);
				n/=2;
			}
		}
		return (res);
		
	}

	public static long bn(long a,long n) {
		long res=1;
		while(n>0) {
			if(n%2!=0) {
				res=res*a;
				n--;
			}else {
				a*=a;
				n/=2;
			}
		}
		return res;
		
	}

	public static long[] fac=new long[100001];
	public static void find_factorial() {
		fac[0]=1;
		fac[1]=1;
		for(int i=2;i<=100000;i++) {
			fac[i]=(fac[i-1]*i)%(mod);
		}
	}
	
	static long mod=1000000007;
	public static long GCD(long a,long b) {
		if(b==(long)0) {
			return a;
		}
		return GCD(b , a%b);
	}
	static long c=0;
	
		
	
}