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:
/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */

import java.io.BufferedReader;
import java.io.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Comparator;
import java.util.PriorityQueue;
import java.util.StringTokenizer;

/**
 *
 * @author is2ac
 */
public class D_CF {

    public static void main(String[] args) throws IOException {
        FastScanner58 fs = new FastScanner58();
        //Reader fs = new Reader();
        PrintWriter pw = new PrintWriter(System.out);
        int t = fs.ni();
        //int t = 1;
        boolean flag = true;
        for (int tc = 0; tc < t; tc++) {
            int n = fs.ni();
            int k = fs.ni();
            int[] a = new int[n];
            int[] p = fs.intArray(k);
            int[] temp = fs.intArray(k);
            int[] b = new int[n];
            for (int i = 0; i < k; i++) {
                a[p[i]-1] = temp[i];
            }
            //position, temp
            PriorityQueue<int[]> pq = new PriorityQueue(new Comparator<int[]>(){
                public int compare(int[] a, int[] b) {
                    return a[1]-b[1];
                }
            });
            for (int i = 0; i < n; i++) {
                if (a[i]>0) {
                    pq.add(new int[] {i,i+a[i]});
                }
            }
            for (int i = 0; i < n; i++) {
                while (!pq.isEmpty()) {
                    if (pq.peek()[0]<i) {
                        pq.poll();
                    } else {
                    break;
                    }
                }
                int res = -1;
                if (pq.isEmpty()) {
                    res = -1;
                } else {
                    res = pq.peek()[1]-i;
                }
                b[i] = res;
            }
            pq.clear();
            for (int i = 0; i < n; i++) {
                if (a[i]>0) {
                    pq.add(new int[] {i,n-i-1+a[i]});
                }
            }
            for (int i = n-1; i > -1; i--) {
                while (!pq.isEmpty()) {
                    if (pq.peek()[0]>i) {
                        pq.poll();
                    } else {
                        break;
                    }
                }
                int res = -1;
                if (pq.isEmpty()) {
                    continue;
                } else {
                    res = pq.peek()[1]-(n-i-1);
                }
                if (b[i] == -1) b[i] = res;
                b[i] = Math.min(b[i],res);
            }
            StringBuilder sb = new StringBuilder();
            for (int i = 0; i < n; i++) {
                sb.append(b[i]);
                sb.append(" ");
            }
            pw.println(sb);
        }
        pw.close();
    }

    public static boolean isPrime(int n) {
        if (n == 1) {
            return false;
        }
        for (int i = 2; i <= (int) Math.sqrt(n); i++) {
            if (n % i == 0) {
                return false;
            }
        }
        return true;
    }

    public static int primes(int a) {
        int b = a;
        int ct = 0;
        for (int i = 2; i <= (int) Math.sqrt(b); i++) {
            if (a % i != 0) {
                continue;
            }
            if (!isPrime(i)) {
                continue;
            }
            int j = a / i;
            while (a % i == 0) {
                a /= i;
                ct++;
            }
            if (!isPrime(j)) {
                continue;
            }
            if (j == 1) {
                continue;
            }
            while (a % j == 0) {
                a /= j;
                ct++;
            }
        }
        return ct;
    }

    public static int dis(int a, int b, int n) {
        //for a to get to b
        if (a < b) {
            return b - a;
        }
        b += n;
        return b - a;
    }

    public static long gcd(long n1, long n2) {
        if (n2 == 0) {
            return n1;
        }
        return gcd(n2, n1 % n2);
    }
}

class GFG {

    // A utility function to get the
    // middle index of given range.
    static int getMid(int s, int e) {
        return s + (e - s) / 2;
    }

    /*
    * A recursive function to get the sum
    of values in given range of the array.
    * The following are parameters
      for this function.
    *
    * st -> Pointer to segment tree
    * node -> Index of current node in
    *         the segment tree.
    * ss & se -> Starting and ending indexes
    *         of the segment represented
    *         by current node, i.e., st[node]
    * l & r -> Starting and ending indexes
    *         of range query
     */
    static long MinUtil(long[] st, int ss,
            int se, int l,
            int r, int node) {

        // If segment of this node is completely
        // part of given range, then return
        // the max of segment
        if (l <= ss && r >= se) {
            return st[node];
        }

        // If segment of this node does not
        // belong to given range
        if (se < l || ss > r) {
            return (long) (1e11);
        }

        // If segment of this node is partially
        // the part of given range
        int mid = getMid(ss, se);

        return Math.min(
                MinUtil(st, ss, mid, l, r,
                        2 * node + 1),
                MinUtil(st, mid + 1, se, l, r,
                        2 * node + 2));
    }

    /*
    * A recursive function to update the
    nodes which have the given index in their
    * range. The following are parameters
    st, ss and se are same as defined above
    * index -> index of the element to be updated.
     */
    static void updateValue(long arr[], long[] st, int ss,
            int se, int index,
            long value,
            int node) {
        if (index < ss || index > se) {
            //System.out.println("Invalid Input");
            return;
        }

        if (ss == se) {

            // update value in array and in
            // segment tree
            arr[index] = value;
            st[node] = value;
        } else {
            int mid = getMid(ss, se);

            if (index >= ss && index <= mid) {
                updateValue(arr, st, ss, mid,
                        index, value,
                        2 * node + 1);
            } else {
                updateValue(arr, st, mid + 1, se, index,
                        value, 2 * node + 2);
            }

            st[node] = Math.min(st[2 * node + 1],
                    st[2 * node + 2]);
        }
        return;
    }

    // Return max of elements in range from
    // index l (query start) to r (query end).
    static long getMin(long[] st, int n, int l, int r) {

        // Check for erroneous input values
        if (l < 0 || r > n - 1 || l > r) {
            //System.out.printf("Invalid Input\n");
            return (long) (1e11);
        }

        return MinUtil(st, 0, n - 1, l, r, 0);
    }

    // A recursive function that constructs Segment
    // Tree for array[ss..se]. si is index of
    // current node in segment tree st
    static long constructSTUtil(long arr[],
            int ss, int se,
            long[] st, int si) {

        // If there is one element in array, store
        // it in current node of segment tree and return
        if (ss == se) {
            st[si] = arr[ss];
            return arr[ss];
        }

        // If there are more than one elements, then
        // recur for left and right subtrees and
        // store the max of values in this node
        int mid = getMid(ss, se);

        st[si] = Math.min(
                constructSTUtil(arr, ss, mid,
                        st, si * 2 + 1),
                constructSTUtil(arr, mid + 1,
                        se, st,
                        si * 2 + 2));

        return st[si];
    }

    /*
    * Function to construct segment tree from
    given array. This function allocates
    * memory for segment tree.
     */
    static long[] constructST(long arr[], int n) {

        // Height of segment tree
        int x = (int) Math.ceil(Math.log(n) / Math.log(2));

        // Maximum size of segment tree
        int max_size = 2 * (int) Math.pow(2, x) - 1;

        // Allocate memory
        long[] st = new long[max_size];

        // Fill the allocated memory st
        constructSTUtil(arr, 0, n - 1, st, 0);

        // Return the constructed segment tree
        return st;
    }
}

class BIT16 {

    long[] bit;

    public BIT16(int size) {
        bit = new long[size];
    }

    public void update(int ind, long delta) {
        while (ind < bit.length) {
            bit[ind] += delta;
            ind = ind + (ind & (-1 * ind));
        }
    }

    public long sum(int ind) {
        long s = 0;
        while (ind > 0) {
            s += bit[ind];
            ind = ind - (ind & (-1 * ind));
        }
        return s;
    }

    public long query(int l, int r) {
        return sum(r) - sum(l);
    }
}

class UnionFind18 {

    int[] id;

    public UnionFind18(int size) {
        id = new int[size];
        for (int i = 0; i < size; i++) {
            id[i] = i;
        }
    }

    public int find(int p) {
        int root = p;
        while (root != id[root]) {
            root = id[root];
        }
        while (p != root) {
            int next = id[p];
            id[p] = root;
            p = next;
        }
        return root;
    }

    public void union(int p, int q) {
        int a = find(p), b = find(q);
        if (a == b) {
            return;
        }
        id[b] = a;
    }
}

class Reader {

    final private int BUFFER_SIZE = 1 << 16;
    private DataInputStream din;
    private byte[] buffer;
    private int bufferPointer, bytesRead;

    public Reader() {
        din = new DataInputStream(System.in);
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }

    public Reader(String file_name) throws IOException {
        din = new DataInputStream(new FileInputStream(file_name));
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }

    public String readLine() throws IOException {
        byte[] buf = new byte[64];
        int cnt = 0, c;
        while ((c = read()) != -1) {
            if (c == '\n') {
                break;
            }
            buf[cnt++] = (byte) c;
        }
        return new String(buf, 0, cnt);
    }

    public int ni() throws IOException {
        int ret = 0;
        byte c = read();
        while (c <= ' ') {
            c = read();
        }
        boolean neg = (c == '-');
        if (neg) {
            c = read();
        }
        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0' && c <= '9');
        if (neg) {
            return -ret;
        }
        return ret;
    }

    public long nextLong() throws IOException {
        long ret = 0;
        byte c = read();
        while (c <= ' ') {
            c = read();
        }
        boolean neg = (c == '-');
        if (neg) {
            c = read();
        }
        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0' && c <= '9');
        if (neg) {
            return -ret;
        }
        return ret;
    }

    public double nextDouble() throws IOException {
        double ret = 0, div = 1;
        byte c = read();
        while (c <= ' ') {
            c = read();
        }
        boolean neg = (c == '-');
        if (neg) {
            c = read();
        }
        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0' && c <= '9');
        if (c == '.') {
            while ((c = read()) >= '0' && c <= '9') {
                ret += (c - '0') / (div *= 10);
            }
        }
        if (neg) {
            return -ret;
        }
        return ret;
    }

    private void fillBuffer() throws IOException {
        bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
        if (bytesRead == -1) {
            buffer[0] = -1;
        }
    }

    private byte read() throws IOException {
        if (bufferPointer == bytesRead) {
            fillBuffer();
        }
        return buffer[bufferPointer++];
    }

    public void close() throws IOException {
        if (din == null) {
            return;
        }
        din.close();
    }
}

class FastScanner58 {

    BufferedReader br;
    StringTokenizer st;

    public FastScanner58() {
        br = new BufferedReader(new InputStreamReader(System.in), 32768);
        st = null;
    }

    String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }

    int ni() {
        return Integer.parseInt(next());
    }

    int[] intArray(int N) {
        int[] ret = new int[N];
        for (int i = 0; i < N; i++) {
            ret[i] = ni();
        }
        return ret;
    }

    long nl() {
        return Long.parseLong(next());
    }

    long[] longArray(int N) {
        long[] ret = new long[N];
        for (int i = 0; i < N; i++) {
            ret[i] = nl();
        }
        return ret;
    }

    double nd() {
        return Double.parseDouble(next());
    }

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