Consider the following process. You have a binary string (a string where each character is either 0 or 1) w of length n and an integer x. You build a new binary string s consisting of n characters. The i-th character of s is chosen as follows:

  * if the character w_{i-x} exists and is equal to 1, then s_i is 1 (formally, if i > x and w_{i-x} =  1, then s_i =  1); 
  * if the character w_{i+x} exists and is equal to 1, then s_i is 1 (formally, if i + x ≤ n and w_{i+x} =  1, then s_i =  1); 
  * if both of the aforementioned conditions are false, then s_i is 0. 



You are given the integer x and the resulting string s. Reconstruct the original string w.

Input

The first line contains one integer t (1 ≤ t ≤ 1000) — the number of test cases.

Each test case consists of two lines. The first line contains the resulting string s (2 ≤ |s| ≤ 10^5, each character of s is either 0 or 1). The second line contains one integer x (1 ≤ x ≤ |s| - 1).

The total length of all strings s in the input does not exceed 10^5.

Output

For each test case, print the answer on a separate line as follows:

  * if no string w can produce the string s at the end of the process, print -1; 
  * otherwise, print the binary string w consisting of |s| characters. If there are multiple answers, print any of them. 

Example

Input


3
101110
2
01
1
110
1


Output


111011
10
-1
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class C {
    public static void main(String[] args) {
        long timeStart = System.nanoTime();
        Utility.FastReader fr = new Utility.FastReader();
        Solver solver = new Solver(fr);
        int t = fr.nextInt();
        while (t-- > 0) {
            solver.solve();
        }
        long timeEnd = System.nanoTime();
//        System.out.println("Completed in :" + ((double) (timeEnd - timeStart) / 1000000) + " miliseconds");
    }

    static class Solver {
        Utility.FastReader fr;

        public Solver(Utility.FastReader fr) {
            this.fr = fr;
        }

        void solve() {
            String s=fr.next();
            char[] c=new char[s.length()+1];
            for(int i=1; i<=s.length(); ++i)
                c[i]=s.charAt(i-1);
            int x=fr.nextInt();
            int n=s.length();
            boolean possible=true;
            boolean[] canBeOne=new boolean[n+1];
            Arrays.fill(canBeOne, true);
            for(int i=1; i<=n; ++i){
                if(c[i]=='0'){
                    if(i>x){
                        canBeOne[i-x]=false;
                    }
                    if(i+x<=n){
                       canBeOne[i+x]=false;
                    }
                }
            }
            for(int i=1; i<=n; ++i){
                if(c[i]=='1'){
                    if(i>x){
                        if(canBeOne[i-x]) continue;
                    }
                    if(i+x<=n){
                        if(canBeOne[i+x]) continue;
                        else{
                            possible=false;
                            break;
                        }
                    }
                    else{
                        possible=false;
                        break;
                    }
                }
            }
            if(!possible)
                System.out.println(-1);
            else{
                for(int i=1; i<=n; ++i){
                    if(canBeOne[i]){
                        System.out.print(1);
                    }
                    else{
                        System.out.print(0);
                    }
                }
                System.out.println();
            }
        }
    }

    static class Utility {
        static void sort(int[] a) {
            ArrayList<Integer> list = new ArrayList<>();
            for (int i : a) list.add(i);
            Collections.sort(list);
            for (int i = 0; i < a.length; i++) a[i] = list.get(i);
        }

        static void shuffleArray(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;
            }
        }

        static void shuffleArray(int[] arr) {
            int n = arr.length;
            Random rnd = new Random();
            for (int i = 0; i < n; ++i) {
                int tmp = arr[i];
                int randomPos = i + rnd.nextInt(n - i);
                arr[i] = arr[randomPos];
                arr[randomPos] = tmp;
            }
        }

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

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

        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;
            }
        }
    }
}

