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 math, sys
from collections import defaultdict, Counter, deque
 
INF = float('inf')
MOD = 10 ** 9 + 7
 
def gcd(a, b):
	while b:
		a, b = b, a%b
	return a
 
def isPrime(n):
	if (n <= 1): 
		return False
	i = 2
	while i ** 2 <= n:
		if n % i == 0:
			return False
		i += 1
	return True
 
def primeFactors(n):
	factors = []
	i = 2
	while i ** 2 <= n:
		while n % i == 0:
			factors.append(i)
			n //= i 
		i += 1
	if n > 1:
		factors.append(n)
	return factors
 
def vars():
	return map(int, input().split())
 
def array():
	return list(map(int, input().split()))
 
 
 
def main():
	s = input()
	n = len(s)
	x = int(input())

	ans = ['1'] * n
	for i in range(n):
		if s[i] == '0':
			if i - x >= 0:
				ans[i - x] = '0'
			if i + x < n:
				ans[i + x] = '0'
			

	for i in range(n):
		c = 0
		if i - x >= 0:
			c |= int(ans[i - x])
		if i + x < n:
			c |= int(ans[i + x])

		if s[i] == '1' and not c:
			print(-1)
			return

		if s[i] == '0' and c:
			print(-1)
			return

	print(''.join(ans))
	return


if __name__ == "__main__":
	t = 1
	t = int(input())
	for _ in range(t):
		main()
