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
input = sys.stdin.readline
I = lambda : list(map(int,input().split()))

t,=I()
for _ in range(t):
	s=input().strip()
	x,=I()
	n=len(s)
	w=['1']*len(s)
	pos=1
	for i in range(n):
		if s[i]=='0':
			if i>=x:
				w[i-x]='0'
			if i<=n-x-1:
				w[i+x]='0'
	con=""
	for i in range(n):
		st=0
		if i>=x:
			st+=int(w[i-x])
		if i<=n-x-1:
			st+=int(w[i+x])
		con+='1' if st else '0'
	if con!=s:
		pos=0
	#print(con,s,w)
	if pos:
		print(''.join(w))
	else:
		print(-1)