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

def solve():
	T = int(input())

	def f(s, x):
		res = ["0" for i in range(len(s))]
		for i in range(len(res)):
			if (i - x >= 0 and s[i - x] == "1" or i + x < len(s) and s[i + x] == "1"):
				res[i] = "1"
			else:
				res[i] = "0"

		return "".join(res)

	for i in range(T):
		w = input()
		x = int(input())

		n = len(w)
		s = ["1" for _ in range(n)]
		for i, c in enumerate(w):
			l_index, r_index = i - x, i + x

			if c == "0":
				if l_index >= 0: 
					s[l_index] = "0"
				if r_index < n:
					s[r_index] = "0"

		ns = "".join(s)

		if f(ns, x) == w:
			print(ns)
		else:
			print(str(-1))

solve()