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
import sys 
from collections import defaultdict as dd
from collections import Counter as cc
from queue import Queue
import math
import itertools
try:
	sys.stdin = open('input.txt', 'r') 
	sys.stdout = open('output.txt', 'w')
except:
	pass
# input = lambda: sys.stdin.buffer.readline().rstrip()

for _ in range(int(input())):
	w=input()
	e=len(w)
	x=int(input())
	k=['1']*e
	t=['0']*e
	for i in range(x,e):
		if w[i]=='0':
			k[i-x]='0'
	for i in range(e-x):
		if w[i]=='0':
			k[i+x]='0'
	for i in range(e):
		if (i>=x and k[i-x]=='1') or ((i+x)<e and k[i+x]=='1'):
			t[i]='1'
	t=''.join(t)
	k=''.join(k)
	if t==w:
		print(k)
	else:
		print(-1)
