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
# #binary string recostruction:


# t = int(input()) # num of test cases

# for a in range(t):
# 	gut = 0
# 	s = list(input())
	
# 	x = int (input())
# 	#if s[l] = 0 -> both r 0
# 	#if s[l] = 1 -> at least 1 isn't 0
# 	n = len(s)
# 	w = list()
# 	for tt in range(n):
# 		w.append("1")
	
# 	for i in range(n):	# ver los 0's
# 		if "0"==s[i]:
# 			if (i>=x):
# 				w[i-x] = "0"
# 			if n> i+x : 
# 				w[i+x] = "0"
	
# 	for ii in range(n):	#si en la casilla hay un 1 debe haber al menos un 1 en las de w asociadas.
# 		if "1" == s[ii]:
# 			gut = 0 
# 			if (ii>=x and w[ii-x] != "0"):
# 				gut = 1
# 			if n> ii+x and w[ii+x] != "0" : 	
# 					gut = 1
# 			if (gut == 0):
# 				break
			
# 	if (gut == 1):
# 		print("".join(w))

# 	else:
# 		print(-1)

#binary string recostruction:


t = int(input()) # num of test cases

for a in range(t):
	s = list(input())
	x = int (input())
	n = len(s)
	w = list()
	for tt in range(n):
		w.append("1")
	
	for i in range(n):	# ver los 0's
		if "0"==s[i]:

			if (i>=x):
				w[i-x] = "0"

			if n> i+x : 
				w[i+x] = "0"
	
	def f(qq):
		
		ww = list()
		for ii in range(n):	#si en la casilla hay un 1 debe haber al menos un 1 en las de w asociadas.
				if (ii>=x and qq[ii-x] == "1" or n> ii+x and qq[ii+x] == "1"):
					ww.append("1")
				else:
					ww.append("0")

		return ww

	if (f(w) == s):
		print("".join(w))

	else:
		print(-1)

