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 sys
from collections import defaultdict as dd
from collections import deque
from functools import *
from fractions import Fraction as f
from copy import *
from bisect import *	
from heapq import *
from math import *
from itertools import permutations ,product
 
def eprint(*args):
    print(*args, file=sys.stderr)
zz=1
 
#sys.setrecursionlimit(10**6)
if zz:
	input=sys.stdin.readline
else:	
	sys.stdin=open('input.txt', 'r')
	sys.stdout=open('all.txt','w')
def inc(d,c):
	d[c]=d[c]+1 if c in d else 1
def bo(i):
	return ord(i)-ord('A')	
def li():
	return [int(xx) for xx in input().split()]
def fli():
	return [float(x) for x in input().split()]	
def comp(a,b):
	if(a>b):
		return 2
	return 2 if a==b else 0		
def gi():	
	return [xx for xx in input().split()]
def fi():
	return int(input())
def pro(a): 
	return reduce(lambda a,b:a*b,a)		
def swap(a,i,j): 
	a[i],a[j]=a[j],a[i]	
def si():
	return list(input().rstrip())	
def mi():
	return 	map(int,input().split())	
def gh():
	sys.stdout.flush()
def isvalid(i,j):
	return 0<=i<n and 0<=j<n	
def graph(n,m):
	for i in range(m):
		x,y=mi()
		a[x].append(y)
		a[y].append(x)
t=fi()

				

while t>0:
	t-=1
	s=si()
	n=len(s)
	x=fi()
	ans=[2 for i in range(n)]
	flag=0
	for i in range(n):
		if s[i]=='0':

			if i+x<n: 
				if ans[i+x]==1:
					flag=1
					break
				else:
					ans[i+x]=0

			if i-x>=0:
				if ans[i-x]==1:
					flag=1
					break
				else:
					ans[i-x]=0
		else:
			c=0
			valid=0
			if i+x<n: 
				if ans[i+x]==0:
					c+=1
				valid+=1
			if i-x>=0:
				if ans[i-x]==0:
					c+=1
				valid+=1	
			if c==valid :
				flag=1
				break
			if valid==1:
				if i-x>=0:
					ans[i-x]=1
				elif i+x<n:
					ans[i+x]=1
			elif valid==2 and c==1:
				if ans[i-x]:
					ans[i-x]=1
				else:
					ans[i+x]=1
	for i in range(n):
		if ans[i]==2:
			ans[i]=1
		ans[i]=str(ans[i])						
					
	print("".join(ans) if flag==0 else -1)			