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
t=int(input())
output=[]
for i in range(t):
	s=input()
	x=int(input())
	w=[-1]*len(s)
	ans=0
	string=""
	for i in range(len(s)):
		if(s[i]=='0' and (i+x)<len(s)):
			w[i+x]=0
		if(s[i]=='0' and (i-x)>=0):
			w[i-x]=0
	for i in range(len(s)):
		if(s[i]=='1' and (i+x)<len(s) and (i-x)>=0 and (w[i-x]==-1 and w[i+x]==-1)):
			w[i-x]=1
			w[i+x]=1
		elif(s[i]=='1' and (i+x)<len(s) and (i-x)>=0 and (w[i-x]==-1 and w[i+x]==0)):
			w[i-x]=1
		elif(s[i]=='1' and (i+x)<len(s) and (i-x)>=0 and (w[i-x]==0 and w[i+x]==-1)):
			w[i+x]=1
		elif(s[i]=='1' and (i+x)<len(s) and (i-x)>=0 and (w[i-x]==0 and w[i+x]==0)):
			ans=-1
		elif(s[i]=='1' and (i+x)<len(s) and (i-x)<0 and w[i+x]==-1):
			w[i+x]=1
		elif(s[i]=='1' and (i+x)<len(s) and (i-x)<0 and w[i+x]==0):
			ans=-1
		elif(s[i]=='1' and (i+x)>=len(s) and (i-x)>=0 and w[i-x]==-1):
			w[i-x]=1
		elif(s[i]=='1' and (i+x)>=len(s) and (i-x)>=0 and w[i-x]==0):
			ans=-1
		elif(s[i]=='1' and (i+x)>=len(s) and (i-x)<0):
			ans=-1
	if(ans==0):
		for i in range(len(s)):
			if(w[i]==-1):
				w[i]=0
		string=''.join([str(elem) for elem in w])
	else:
		string='-1'	
	output.append(string)
for i in range(t):
	print(output[i])
			
			
