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

def input():    return sys.stdin.readline().strip()
def iinput():   return int(input())
def rinput():   return map(int, sys.stdin.readline().strip().split()) 
def get_list(): return list(map(int, sys.stdin.readline().strip().split())) 
mod = int(1e9)+7


for _ in range(iinput()):
	s = input()
	n = len(s)
	x = iinput()
	w = ['1' for _ in range(n)]

	for i in range(n):
		if (s[i]=='0'):
			if (i>=x):
				w[i-x] = '0'
			if (i+x<n):
				w[i+x] = '0'
	
	ans = True
	for i in range(n):
		if ((i>=x and w[i-x]=='1') or (i+x<n and w[i+x]=='1')):
			if s[i]!='1':
				ans = False
				break
		else:
			if s[i]!='0':
				ans = False
				break		

	if ans == True:
		print("".join(w))
	else:
		print(-1)	