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
from __future__ import print_function, division
from sys import stdin, stdout
from fractions import gcd
# from math import *
from collections import *
from operator import itemgetter, mul
from functools import reduce
from copy import copy

rstr = lambda: stdin.readline().strip()
rstrs = lambda: [str(x) for x in stdin.readline().split()]
rint = lambda: int(stdin.readline())
rints = lambda: [int(x) for x in stdin.readline().split()]
arr_2d = lambda n: [rints() for i in range(n)]
out = []

for _ in range(int(input())):
    s, x = rstr(), rint()
    ans = ['1' for _ in range(len(s))]

    for i in range(len(s)):
        if s[i] == '0':
            if i - x >= 0:
                ans[i - x] = '0'
            if i + x < len(s):
                ans[i + x] = '0'

    for i in range(len(s)):
        if s[i] == '1':
            v = ['', '']
            if i - x >= 0:
                v[0] = ans[i - x]
            if i + x < len(s):
                v[1] = ans[i + x]

            if '1' not in v:
                ans = ['-1']
                break

    out.append(''.join(ans))

print('\n'.join(out))
