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.Arrays;
import java.util.StringTokenizer;

public class C {
    static void solve(String str, int x) {
        int[] res = new int[str.length()];
        Arrays.fill(res, 2);
        for(int i = 0; i < res.length; i++) {
            if(str.charAt(i) == '1') {
                if(i - x >= 0 && (res[i-x] == 2 || res[i-x] == 1)) {
                    res[i-x] = 1;
                } else {
                    if(i + x < str.length()) {
                        res[i+x]= 1;
                    } else {
                        System.out.println(-1);
                        return;
                    }
                }
            } else if(i - x >= 0 || i + x < str.length()){
                if(i - x >= 0 && i + x < str.length() ) {
                    if((res[i-x] == 2 || res[i-x] == 0) && (res[i+x] == 2 || res[i+x] == 0)) {
                        res[i-x] = 0;
                        res[i+x] = 0;
                    } else {
                        System.out.println(-1);
                        return;
                    }
                } else if(i - x >= 0) {
                    if(res[i-x] == 2 || res[i-x] == 0) {
                        res[i-x] = 0;
                    } else {
                        System.out.println(-1);
                        return;
                    }
                } else {
                    if(res[i+x] == 2 || res[i+x] == 0) {
                        res[i+x] = 0;
                    } else {
                        System.out.println(-1);
                        return;
                    }
                }
            }
        }

        for(int i = 0; i < res.length; i++) {
            if(res[i] == 2) {
                System.out.print(0);
            }else
            System.out.print(res[i]);
        }
        System.out.println();
    }
    public static void main(String[] args) {
        FastReader fastReader = new FastReader();

        int tests = fastReader.nextInt();
        for(int test = 1; test <= tests; test++) {
            String str = fastReader.next();
            int x = fastReader.nextInt();
            solve(str, x);
        }
    }
    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;
        }
    }
}
