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
from sys import stdin, stdout
input = stdin.readline
#print = stdout.write

for _ in range(int(input())):
	s = input()
	x = int(input())
	n = len(s) - 1
	ans = [''] * n
	for i in range(n):
		if i >= x and i + x < n:
			#print('a')
			if ans[i - x]:
				if ans[i - x] == '1' and s[i] == '0':
					print(-1)
					break
				if s[i] == '0':
					ans[i + x] = '0'
				elif ans[i - x] == '0':
					ans[i + x] = '1'
			else:
				ans[i - x] = s[i]
				if s[i] == '0':
					ans[i + x] = '0'
		elif i >= x:
			#print('b')
			if ans[i - x]:
				if ans[i - x] != s[i]:
						print(-1)
						break
			ans[i - x] = s[i]
		elif i + x < n:
			#print('c')
			ans[i + x] = s[i]
		elif s[i] == '1':
			print(-1)
			break
	else:
		for i in range(n):
			if not ans[i]:
				ans[i] = '0'
		print(''.join(ans))
				
