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
from collections import *
import sys  

# "". join(strings)  
    
def ri():
    return int(input())
 
def rl():
    return list(map(int, input().split()))
    
t =ri()

for _ in range(t):
	s=[int(x) for x in input()]
	n=len(s)
	x=ri()
	w = [1]*n
	new_s=[-1]*n
	ans=1
	for i in range(n):
		if s[i]==0:
			if i-x>=0:
				w[i-x]=0
			if i+x<=n-1:
				w[i+x]=0
	for i in range(n):
		if (i-x>=0 and w[i-x]==1) or (i+x<=n-1 and w[i+x]==1):
			new_s[i]=1
		else:
			new_s[i]=0
	for i in range(n):
		if new_s[i]!=s[i]:
			ans=-1
			break
	if ans==-1:
		print(-1)
	else:
		print("".join([str(x) for x in w]))



