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
t = int(input())

for ii in range(t):
	s = input()
	x = int(input())

	ans = [-1]*len(s)

	can = True
	for i in range(len(s)):

		back = i-x
		front = i+x
		sor = False
		if s[i] == "1":
			if back >= 0:
				if ans[back] == -1 or ans[back] == 1:
					ans[back] = 1
					sor = True

			if not sor:
				if front < len(ans):
					if ans[front] == -1 or ans[front] == 1:
						ans[front] = 1
						sor = True

			if not sor:
				can = False
				break

		else:
			if back >= 0:
				if ans[back] == 1:
					can = False
					break
				ans[back] = 0

			if front < len(ans):
				if ans[front] == 1:
					can = False
					break
				ans[front] = 0

		# print(ans)
	if not can:
		print(-1)

	else:
		for i in range(len(ans)):
			if ans[i] == -1:
				ans[i] = 1

			print(ans[i], end = "")

		print()
