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
import sys, math
#map(int, sys.stdin.readline().split())
#list(map(int, sys.stdin.readline().split()))

t = int(sys.stdin.readline())

for _ in range(t):
	s = [int(char) for char in sys.stdin.readline().replace("\n", "")]
	x = int(sys.stdin.readline())
	w = [1]*len(s)

	n = len(s)
	for i in range(len(s)):
		if s[i] == 0 and i>=x:
			w[i-x] = 0
		if s[i] == 0 and i+x<n:
			w[i+x] = 0
	valid = True
	for i in range(n):
		if s[i] == 1 and not((i+x<n and int(w[i+x]) == 1) or (i>=x and int(w[i-x]) == 1)):
			valid = False
			break
	if valid:
		for i in range(len(s)):
			print(w[i], end="")
		print()
	else:
		print(-1)

