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
#!/usr/bin/env pypy3

from sys import stdin, stdout
 
def input():
    return stdin.readline().strip()

def s_of(w):
	ret = []

	for i in range(len(w)):
		anchors = []
		for j in [i-x, i+x]:
			if 0 <= j < len(w):
				anchors += [w[j]]
		if 1 in anchors:
			ret += [1]
		else:
			ret += [0]

	return ret

def ans(S, x):
	ret = [1] * len(S)

	for i, s in enumerate(S):
		if s == '0':

			for j in [i-x, i+x]:
				if 0 <= j < len(ret): ret[j] = 0
	
	if ''.join(map(str, s_of(ret))) == S:
		return ''.join(map(str, ret))
	else:
		return '-1'

T = int(input())
for t in range(T):
	S = input()
	x = int(input())

	print(ans(S, x))