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())
for i in range(t):
	s=input()
	x=int(input())
	w=["a"]*len(s)
	
	for j in range(len(s)):
		if s[j]=='0':
			if j>=x:
				w[j-x]="0"
			if j+x<len(s):
				w[j+x]="0"
	flag=0
	for j in range(len(s)):
		flag=0
		if s[j]=="1":
			if j>=x:
				if w[j-x]=="0":
					flag+=1
				else:
					w[j-x]="1"
			else:
				flag+=1
			if j+x<len(s):
				if w[j+x]=="0":
					flag+=1
				else:
					w[j+x]="1"
			else:
				flag+=1
		if flag==2:
			break
	if flag==2:
		print(-1)
	else:
		for j in range(len(w)):
			if w[j]=="a":
				w[j]="1"
		print("".join(w))
					
		
			
	
			 
			
