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 math
# from collections import Counter
# from collections import defaultdict
# from collections import deque
# from bisect import bisect_left as bl, bisect_right as br
# from itertools import accumulate,permutations as perm,combinations as comb
# import heapq
# from functools import reduce
# from fractions import Fraction
# import sys

def main():
	for _ in range(Iint()):
		s=list(map(int,input()))
		x=Iint()
		n=len(s)
		w=[1 for i in s]
		for i in range(n):
			if s[i]==0:
				if i>=x:
					w[i-x]=0
				if i+x<len(s):
					w[i+x]=0
		newString=[]
		for i in range(n):
			temp=0
			if i>=x and w[i-x]==1:
				temp=1
			if i+x<len(s) and w[i+x]==1:
				temp=1
			newString.append(temp)
			#print(n,s,newString)
		if newString==s:
			Plist(w)
		else:
			print(-1)



	
def I(): return input()

def Iint(): return int(input())

def Ilist(): return list(map(int, input().split()))   # int list

def Imap(): return map(int, input().split())   # int map

def Plist(li, s=''): print(s.join(map(str, li)))   # non string list

if __name__ == '__main__':
    main()