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
# cook your dish here
# code
#    ___________________________________
#   |                                   |
#   |                                   |
#   |        _,     _   _     ,_        |
#   |    .-'` /     \'-'/     \ `'-.    |
#   |   /    |      |   |      |    \   |
#   |  ;      \_  _/     \_  _/      ;  |
#   | |         ``         ``         | |
#   | |                               | |
#   |  ;    .-.   .-.   .-.   .-.    ;  |
#   |   \  (   '.'   \ /   '.'   )  /   |
#   |    '-.;         V         ;.-'    |
#   |        `                 `        |
#   |                                   |
#   |___________________________________|
#   |                                   |
#   |  Author      :   Ramzz            |
#   |  Created On  :   21-07-2020       |
#   |___________________________________|
#
#    _ __ __ _ _ __ ___  ________
#   | '__/ _` | '_ ` _ \|_  /_  /
#   | | | (_| | | | | | |/ / / / 
#   |_|  \__,_|_| |_| |_/___/___|
#
import math
import collections
from sys import stdin,stdout,setrecursionlimit
import bisect as bs
setrecursionlimit(2**20)


for _ in range(int(stdin.readline())):
    s = stdin.readline().strip('\n')
    x = int(stdin.readline())
     #a = list(map(int, stdin.readline().rstrip().split()))
    
    n = len(s)
    
    a = [-1]*n
    
    chk = True
    
    for i in range(n):
        if(s[i] == '1'):
            if((i-x) >= 0 and a[i-x] != 0):
                a[i-x] = 1
                continue
            if((i+x) < n):
                if(a[i+x] == 0):
                    chk = False
                    break
                else:
                    a[i+x] = 1
                    continue
            chk = False
            break
        else:
            if((i-x) >= 0):
                if(a[i-x] == 1):
                    chk = False
                    break
                else:
                    a[i-x] = 0
            if((i+x) < n):
                if(a[i+x] == 1):
                    chk = False
                    break
                else:
                    a[i+x] = 0
    
    
    if(not chk):
        print(-1)
        continue
    
    w = ''
    for i in range(n):
        if(a[i] != -1):
            w += str(a[i])
        else:
            w += '1'
    
    print(w)