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

# Fast IO
def input():
	a = sys.stdin.readline()
	if a[-1] == "\n": a = a[:-1]
	return a
def print(*argv):
	n = len(argv)
	for i in range(n):
		if i == n-1: sys.stdout.write(str(argv[i]) + "\n")
		else: sys.stdout.write(str(argv[i]) + " ")
def lcm(x, y):
	from math import gcd
	return (x * y) / (gcd(x, y))

def solve(s, x):
	l = len(s)
	w = [1] * l

	for i in range(l):
		if s[i] == "0":
			if i - x >= 0:
				w[i - x] = 0
			if i + x <= l-1:
				w[i + x] = 0

	for i in range(l):
		if s[i] == "1":
			if i - x >= 0 and i + x <= l-1:
				if w[i-x] + w[i+x] == 0: return -1
			elif i - x >= 0 and w[i-x] == 0: return -1
			elif i + x <= l-1 and w[i+x] == 0: return -1
			elif i -x < 0 and i + x > l-1: return -1
 
	return  "".join(list(map(str, w)))


for _ in range(int(input())): # Multicase
	s = input()
	x = int(input())
	print(solve(s, x))
