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.FileReader;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
public class C {
    public static void main(String[] args){
        Scan scan = new Scan();
        int T = scan.nextInt();
        for(int t = 0; t< T; t++) {
            char[] s= scan.next().toCharArray();
            int x = scan.nextInt();
            char[] out = new char[s.length];
            char[] check = new char[s.length];
            for(int i = 0; i < s.length; i++){
                out[i] = '1';
                if(i-x >= 0) {
                    if (s[i - x] == '0')
                        out[i] = '0';
                }
                if(i+x<s.length) {
                    if (s[i + x] == '0')
                        out[i] = '0';
                }
            }
            for(int i = 0; i < s.length; i++){
                check[i] = '0';
            }
            for(int i = 0; i < s.length; i++){
                if(out[i] == '1'){
                    if(i-x>=0)
                        check[i-x]='1';
                    if(i+x<s.length)
                        check[i+x]='1';
                }
            }
            boolean same = true;
            for(int i = 0; i < s.length; i++){
                if(check[i]!=s[i]) {
                    same = false;
                    break;
                }
            }
            if (same){
                System.out.println(out);
            }
            else System.out.println("-1");

        }
    }
}
class Scan {
    BufferedReader br;
    StringTokenizer st;

    public Scan() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }

    public Scan(String f) {
        try {
            br = new BufferedReader(new FileReader(f));
        } catch (Exception ignored) {
        }
    }

    public String next() {
        if (st == null || !st.hasMoreElements())
            try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception ignored) {
            }
        return st.nextToken();
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public long nextLong() {
        return Long.parseLong(next());
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }

    public String nextLine() {
        try {
            return br.readLine();
        } catch (Exception ignored) {
            return "";
        }
    }
}