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
def solve():
	n = len(s)
	w = ['1']*n

	for i in range(n):
		if s[i] == '0':
			if i-x>=0: w[i-x] = '0'
			if i+x<n: w[i+x] = '0'

	for i in range(n):
		if s[i] == '1':
			if i-x>=0 and w[i-x] == '1': continue
			elif i+x<n and w[i+x] == '1': continue
			else: return [-1]
	return w


for _ in range(int(input())):
	# n, k = map(int, input().split())
	# l = [list(map(int, input().split())) for i in range(n)]
	# l = list(map(int, input().split()))
	s = list(str(input()))
	x = int(input())
	for i in solve():
		print(i, end='')
	print()