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
#: Author - Soumya Saurav
import sys,io,os,time
from collections import defaultdict
from collections import OrderedDict
from collections import deque
from itertools import combinations
from itertools import permutations
import bisect,math,heapq
alphabet = "abcdefghijklmnopqrstuvwxyz"

#input = sys.stdin.readline

########################################
for ii in range(int(input())):
	s = input()
	x = int(input())
	n = len(s)
	def legal(a,n):
		return a >= 0 and a < n
	ans = ["1"]*n
	f =1
	for i in range(n):
		if s[i] == "0":
			if legal(i-x,n): ans[i-x] = "0"
			if legal(i+x,n): ans[i+x] = "0"
	for i in range(n):
		if s[i] == "1":
			if legal(i-x,n) and ans[i-x] == "1": continue
			if legal(i+x,n) and ans[i+x] == "1": continue
			f = 0
	if f: print("".join(ans))
	else: print(-1)
			








