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.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.StringTokenizer;

public class C {
	
	public static void main(String[] args) throws InterruptedException {
		FastScanner fs=new FastScanner();
		int t=fs.nextInt();
		test:while(t-->0) {
		String s=fs.next();
		char[] bin = s.toCharArray();
		int x =fs.nextInt();
	    int n=bin.length;
	    char[] temp=new char[n];
	    Arrays.fill(temp, '1');
		for(int i=0;i<n;i++) {
			if(bin[i]=='0') {
				if(isValid(i-x,n)) temp[i-x]='0';
				if(isValid(i+x,n)) temp[i+x]='0';
			}
		}
		boolean works=true;
		for(int i=0;i<n;i++) {
			if(bin[i]=='1') {
				if(isValid(i-x,n)&&temp[i-x]=='1')continue;
				if(isValid(i+x,n)&&temp[i+x]=='1')continue;
				works=false;
			}
			if(!works) {
				break;
			}
		}
		if(!works) {
			System.out.println(-1);
		}
		else {
			System.out.println(temp);
		}
		}
		}
	static boolean isValid(int x,int n) {
		return x>=0&&x<n;
	}
	
	
	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 class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		
		public String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
			
		}
		
		public int nextInt() {
			return Integer.parseInt(next());
		}
		
		public int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		
		public long nextLong() {
			return Long.parseLong(next());
		}
		
		public long[] readLongArray(int n) {
			long[] a=new long[n];
			for (int i=0; i<n; i++) a[i]=nextLong();
			return a;
		}
	}

}
