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
n=int(input())
for i in range(1,n+1):
	s=input()
	nn=len(s)
	x=int(input())
	ans="1"*(nn)
	for i in range(nn):
		if s[i]=='0':
			if (i - x >= 0):
				index=i-x
				ans=ans[:index] + '0' + ans[index + 1:]
			if (i+x < nn):
				index=i+x
				ans=ans[:index] + '0' + ans[index + 1:]
	ff=0
	for i in range(nn):
		flag=False
		flag = flag or (i - x >= 0 and ans[i - x] == '1')
		flag = flag or (i + x < nn and ans[i + x] == '1')
		# print(flag)
		# print(s[i], "cdsvfbgnh")
		if not flag:
			# print("ewfegrtmbdb")
			# print(s[i])
			if s[i]=='1':
				# print("m aagya")
				print("-1")
				ff=1
				break
	if ff==0:
		print(ans)
	


