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
// package codeForces2;


import java.util.*;

import java.awt.Point;
import java.io.*;
import java.math.BigInteger;
public class Solutions {
	 
//	static ArrayList<ArrayList<Integer>>list=new ArrayList<ArrayList<Integer>>();
	static FastScanner scr=new FastScanner();
	static PrintStream out=new PrintStream(System.out);
	public static void main(String []args) {
		int T=scr.nextInt();
		t:for(int t=0;t<T;t++) {
			String s=scr.next();
			int x=scr.nextInt();
			char c[]=s.toCharArray();
			int n=s.length();
			char res[]=new char[n];
			Arrays.fill(res,'1');
			for(int i=0;i<n;i++) {
				if(c[i]=='0') {
					if(i-x>=0) {
						res[i-x]='0';
					}
					if(i+x<n) {
						res[i+x]='0';
					}
				}
			}
			for(int i=0;i<n;i++) {
				if(c[i]=='1') {
					if(i-x>=0 && res[i-x]=='1') {
						continue;
					}
					if(i+x<n && res[i+x]=='1') {
						continue;
					}
					out.println(-1);
					continue t;
				}
			}
			out.println(res);
		}
	}
	static int []reverse(int a[]){
		int n=a.length;
		int b[]=new int[n];
		int index=0;
		for(int i=n-1;i>=0;i--) {
			b[index]=a[i];
		}
		return b;
	}
	static boolean isPrime(int n) {
		for(int i=2;i*i<=n;i++) {
			if(n%i==0) {
				return false;
			}
		}
		return true;
	}
	static void swap(int a[],int i,int j) {
		int temp=a[i];a[i]=a[j];
		a[j]=temp;
	}
	static long modPow(long base,long exp,long mod) {
		if(exp==0) {
			return 1;
		}
		if(exp%2==0) {
			long res=(modPow(base,exp/2,mod));
			return (res*res)%mod;
		}
		return (base*modPow(base,exp-1,mod))%mod;
	}
	static long gcd(long a,long b) {
		if(b==0) {
			return a;
		}
		return gcd(b,a%b);
	}
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		int[] sort(int a[]) {
			Arrays.sort(a);
			return a;
		}
		int []reverse(int a[]){
			int b[]=new int[a.length];
			int index=0;
			for(int i=a.length-1;i>=0;i--) {
				b[index]=a[i];
			}
			return b;
		}
		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		long[] readLongArray(int n) {
			long  [] a=new long  [n];
			for (int i=0; i<n; i++) a[i]=nextLong();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}
	static int MAX=Integer.MAX_VALUE;
	static int MIN=Integer.MIN_VALUE;
}class triplet{
	int x;
	int y;
	int z;
	triplet(int fisrt,int second,int third){
		this.x=fisrt;
		this.y=second;
		this.z=third;
	}
}
class pair{
	int x=0;
	int y=0;
	pair(int first,int second){
		this.x=first;
		this.y=second;
	}
}