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.math.*;
import java.lang.*;

public class Main implements Runnable {
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1)
                throw new InputMismatchException();

            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }

                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        public int nextInt() {
            int c = read();

            while (isSpaceChar(c))
                c = read();

            int sgn = 1;

            if (c == '-') {
                sgn = -1;
                c = read();
            }

            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));

            return res * sgn;
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;

            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));

            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return readString();
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }

    public static void main(String args[]) throws Exception {
        new Thread(null, new Main(), "Main", 1 << 27).start();
    }

    static class Pair {
        long f;
        long s;
        int p;
        PrintWriter w;

        // int t;

        Pair(long f, long s) {
            // Pair(int f,int s, PrintWriter w){
            this.f = f;
            this.s = s;
            // this.p = p;
            // this.w = w;
            // this.t = t;

        }

        public static Comparator<Pair> wc = new Comparator<Pair>() {
            public int compare(Pair e1,Pair e2){

                // 1 for swap
                if(Math.abs(e1.f)-Math.abs(e2.f)!=0){
                    if(e1.f<=e2.f)return -1;
                    else return 1;
                }
                else{
                    if(e1.s<=e2.s)return -1;
                    else return 1;
                    // e1.w.println("##"+e1.f+" "+e2.f);
//                    return (Math.abs(e1.s)-Math.abs(e2.s));
                }


            }
        };
    }

    public Integer[] sort(Integer[] a) {
        Arrays.sort(a);
        return a;
    }

    public Long[] sort(Long[] a) {
        Arrays.sort(a);
        return a;
    }

    public static ArrayList<Integer> sieve(int N) {
        int i, j, flag;

        ArrayList<Integer> p = new ArrayList<Integer>();

        for (i = 1; i < N; i++) {

            if (i == 1 || i == 0)
                continue;

            flag = 1;

            for (j = 2; j <= i / 2; ++j) {
                if (i % j == 0) {
                    flag = 0;
                    break;
                }
            }
            if (flag == 1) {
                p.add(i);
            }
        }
        return p;
    }

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

    public static int gcd(int a, int b) {
        if (b == 0)
            return a;
        else
            return gcd(b, a % b);
    }

    //// recursive dfs
    public static int dfs(int s, ArrayList<Integer>[] g, long[] dist, boolean[] v, PrintWriter w, int p) {
        v[s] = true;
        int ans = 1;
        // int n = dist.length - 1;
        int t = g[s].size();
        // int max = 1;
        for (int i = 0; i < t; i++) {
            int x = g[s].get(i);
            if (!v[x]) {
                // dist[x] = dist[s] + 1;
                ans = Math.min(ans, dfs(x, g, dist, v, w, s));
            } else if (x != p) {
                // w.println("* " + s + " " + x + " " + p);
                ans = 0;
            }
        }
        // max = Math.max(max,(n-p));
        return ans;
    }

    //// iterative BFS
    public static int bfs(int s, ArrayList<Integer>[] g, long[] dist, boolean[] b, PrintWriter w, int p) {
        b[s] = true;
        int siz = 1;
        // dist--;
        Queue<Integer> q = new LinkedList<>();
        q.add(s);
        while (q.size() != 0) {
            int i = q.poll();
            Iterator<Integer> it = g[i].listIterator();
            int z = 0;
            while (it.hasNext()) {
                z = it.next();
                if (!b[z]) {
                    b[z] = true;
                    // dist--;
                    dist[z] = dist[i] + 1;
                    // siz++;
                    q.add(z);
                } else if (z != p) {
                    siz = 0;
                }
            }

        }
        return siz;
    }

    public static int lower(int a[], int x) { // x is the target value or key
        int l = -1, r = a.length;
        while (l + 1 < r) {
            int m = (l + r) >>> 1;
            if (a[m] >= x)
                r = m;
            else
                l = m;
        }
        return r;
    }

    public static int upper(int a[], int x) {// x is the key or target value
        int l = -1, r = a.length;
        while (l + 1 < r) {
            int m = (l + r) >>> 1;
            if (a[m] <= x)
                l = m;
            else
                r = m;
        }
        return l + 1;
    }

    public static int lower(ArrayList<Integer> a, int x) { // x is the target value or key
        int l = -1, r = a.size();
        while (l + 1 < r) {
            int m = (l + r) >>> 1;
            if (a.get(m) >= x)
                r = m;
            else
                l = m;
        }
        return r;
    }

    public static int upper(ArrayList<Integer> a, int x) {// x is the key or target value
        int l = -1, r = a.size();
        while (l + 1 < r) {
            int m = (l + r) >>> 1;
            if (a.get(m) <= x)
                l = m;
            else
                r = m;
        }
        return l + 1;
    }

    public static long power(long x, long y, long m) {
        if (y == 0)
            return 1;

        long p = power(x, y / 2, m) % m;
        p = (p * p) % m;

        if (y % 2 == 0)
            return p;
        else
            return (x * p) % m;
    }

    public void yesOrNo(boolean f) {
        if (f) {
            w.println("YES");
        } else {
            w.println("NO");
        }
    }

    // Arrays.sort(rooms, (room1, room2) -> room1[1] == room2[1] ? room1[0]-room2[0]
    // : room2[1]-room1[1]);
    // Arrays.sort(A, (a, b) -> Integer.compare(a[0] , b[0]));
    //////////////////////////////////////////////////////////////////////////////////////////////////////
    //////////////////////////////////////////////////////////////////////////////////////////////////////
    // code here
    int oo = (int) 1e9;
//    int[] parent;
//    int[] dist;
//    int[][] val;
//    boolean[][] vis;
//    ArrayList<Integer>[] g;
    // int[] col;
    HashMap<Long, Boolean> vis = new HashMap<Long, Boolean>();
    //char[][] g;
    // boolean[][] v;
//    Long[] a;
    // ArrayList<Integer[]> a;
    // int[][] ans;
//    long[][] dp;
    long mod;
//    int n;
//    int m;
//    int k;
//    long[][] pre;
    // StringBuilder[] a;
    // StringBuilder[] b;
    // StringBuilder ans;


    PrintWriter w = new PrintWriter(System.out);

    public void run() {

        InputReader sc = new InputReader(System.in);

        int defaultValue = 0;
        mod =  1000000007;

        int test = 1;
        test = sc.nextInt();
        while (test-- > 0) {
            int n = sc.nextInt();
            int k = sc.nextInt();

            long[] a = new long[k];
            long[] t = new long[k];
            long[] ans = new long[n+1];

            long[] pre = new long[n+1];
            long[] suf = new long[n+1];
            HashMap<Long,Long> hm = new HashMap<Long,Long>();

            for(int i=0;i<k;i++){
                a[i] = sc.nextLong();
            }
            for(int i=0;i<k;i++){
                t[i] = sc.nextLong();
                hm.put(a[i],t[i]);
            }

            long min = (long)1e16;


            for(int i=n;i>=0;i--){
                if(hm.containsKey((long)i)){
                    min = Math.min(min,hm.get((long)i)+i);
                }
                pre[i] = min;
            }



            min = (long)1e16;
            for(int i=0;i<=n;i++){
                if(hm.containsKey((long)i)){
                    min = Math.min(min,hm.get((long)i)+(n-i));
                }
                suf[i] = min;
            }


            for(int i=1;i<=n;i++){
                ans[i] = Math.min( pre[i]-i , suf[i]-(n-i) );
                w.print(ans[i]+" ");
            }
            w.println("");

        }

        w.flush();
        w.close();

    }







}