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
for q in range(int(input())):
	s = input()
	s = '2' + s
	x = int(input())
	n = len(s) - 1
	w = [2] * (n + 1)
	res = 1
	for i in range(1, n + 1):
		if s[i] == '1':
			# 3 state
			if i > x:
				if i + x > n:
					if w[i - x] == 2:
						w[i - x] = 1
					elif w[i - x] == 0:
						res = 0
						break
				else:
					if w[i - x] == 0:
						if w[i + x] == 2:
							w[i + x] = 1
						elif w[i + x] == 0:
							res = 0
							break
					if w[i + x] == 0:
						if w[i - x] == 2:
							w[i - x] = 1
						elif w[i - x] == 0:
							res = 0
							break
			else:
				if i + x > n:
					res = 0
					break
				else:
					if w[i + x] == 2:
						w[i + x] = 1
					elif w[i + x] == 0:
						res = 0
						break


		else:
			# 1 state
			if i > x:
				if w[i - x] == 2:
					w[i - x] = 0
				elif w[i - x] == 1:
					res = 0
					break
			if i + x <= n:
				if w[i + x] == 2:
					w[i + x] = 0
				elif w[i + x] == 1:
					res = 0
					break
	if res == 0:
		print(-1)
	else:
		for o in range(1, n + 1):
			if w[o] == 2:
				w[o] = 1
		print(*w[1:], sep = "")
