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):
	st = input()
	x = int(input())
	n = len(st)
	arr = [-1 for j in range(n)]
	for j in range(n):
		if st[j] == '1':
			if j-x >= 0 and (arr[j-x] == -1 or arr[j-x] == 1):
				arr[j-x] = 1
			elif j+x < n and (arr[j+x] == -1 or arr[j+x] == 1):
				arr[j+x] = 1
			else:
				print(-1)
				break
		else:
			if j-x >= 0:
				if arr[j-x] == -1 or arr[j-x] == 0:
					arr[j-x] = 0
				else:
					print(-1)
					break
			if j + x < n:
				if arr[j+x] == -1 or arr[j+x] == 0:
					arr[j+x] = 0
				else:
					print(-1)
					break
	else:
		for k in arr:
			if k == -1 or k == 0:
				print(0,end='')
			else:
				print(1,end='')
		print()
