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 _ in range (t) :
	s = str(input())
	n = len(s)
	ans = [None] * n
	x = int(input())
	cek = False
	for i in range (n): 
		if s[i] == '0':
			if i >= x:
				ans[i-x] = '0'
			if i+x < n:
				ans[i+x] = '0'
	for i in range (n):
		if s[i] == '1':
			if i >= x and ans[i-x] != '0':
				ans[i-x] = '1'
				continue
			if i+x < n and ans[i+x] != '0':
				ans[i+x] = '1'
			else :
				print(-1)
				cek = True
				break
	if cek : continue
	for i in range (n):
		if ans[i] == None:
			ans[i] = '1'
	print(*ans, sep='')


