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 minp():
	return sys.stdin.readline().strip()

def mint():
	return int(minp())

def mints():
	return map(int, minp().split())

def check(s, n, v):
	for i in range(n):
		if s[i:i+n].count(v) == 0:
			return False
	return True

def solve():
	s = minp()
	x = mint()
	n = len(s)
	a = [None]*n
	for i in range(n):
		if i - x >= 0:
			if i + x < n:
				if s[i] == '0':
					if a[i + x] is not None and a[i + x] != '0':
						print(-1)
						return
					if a[i - x] is not None and a[i - x] != '0':
						print(-1)
						return
					a[i - x] = '0'
					a[i + x] = '0'
			else:
				if a[i - x] is not None and a[i - x] != s[i]:
					print(-1)
					return
				a[i - x] = s[i]
		elif i + x < n:
			if a[i + x] is not None and a[i + x] != s[i]:
				print(-1)
				return
			a[i + x] = s[i]
	for i in range(n):
		if a[i] is None:
			a[i] = '1'
	for i in range(n):
		c = '0'
		if i - x >= 0 and a[i - x] == '1':
			c = '1'
		elif i + x < n and a[i + x] == '1':
			c = '1'
		#print(a, a[i], c)
		if s[i] != c:
			print(-1)
			return
	print(''.join(a))

for i in range(mint()):
	solve()
