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.util.*;
import java.io.*;

public class C94C{
	static class FastReader {

        BufferedReader br;
        StringTokenizer st;

        private 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());
        }

	 int[] nextIntArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
	}

	int[] nextIntArrayOne(int n) {
				int[] a = new int[n+1];
				for (int i = 1; i < n+1; i++)
					a[i] = nextInt();
				return a;
	}

        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;
        }
    }

	public static void main(String[] args) {
		FastReader s =new FastReader();
		int t = s.nextInt();
		StringBuilder str = new StringBuilder();
		while(t-- >0) {
			char arr[] = s.nextLine().toCharArray();
			int x = s.nextInt();
			int n = arr.length;
			int w[] = new int[n];
			Arrays.fill(w, -1);
			
			boolean flag = true;
			
			for(int i = 0; i< n; i++) {
				
				int prv = i - x;
				int nxt = i + x;
				
				if(arr[i] == '0') {
					
					if(prv >= 0 && nxt < n) {
						
						if(w[prv] == 1) {
							flag = false;
							break;
						}
							
						w[prv] = 0;
						w[nxt] = 0;
						
						
					}else if(prv >= 0) {
						
						if(w[prv] == 1) {
							flag = false;
							break;
						}else {
							w[prv] = 0;
						}
						
					}else if(nxt < n) {
						w[nxt] = 0;	
					}else {
						w[i] = 0;
					}
					
					
					
				}else {
					
					if(prv >= 0 && nxt < n) {
						
						if(w[prv] == 0) {
							w[nxt] = 1;
						}
					}else if(prv >= 0) {
						
						if(w[prv] == 0) {
							flag = false;
							break;
						}else {
							w[prv] = 1;
						}
						
					}else if(nxt < n) {
						w[nxt] = 1;	
					}else {
						flag = false;
						break;
					}
					
					
					
					
				}
			}
			
 			
			if(flag) {
				
				for(int p : w) {
					if(p == -1) str.append(1);
					else
					str.append(p);
				}
				str.append("\n");
				
			}else {
				str.append("-1\n");
			}
			
		}
		System.out.println(str);
	}

	

}

