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 bisect import bisect_left as bl
from bisect import bisect_right as br
from heapq import heappush,heappop,heapify
import math
from collections import *
from functools import reduce,cmp_to_key
import sys
input = sys.stdin.readline

from itertools import accumulate

M = mod = 998244353
def factors(n):return sorted(set(reduce(list.__add__, ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0))))
def inv_mod(n):return pow(n, mod - 2, mod)
 
def li():return [int(i) for i in input().rstrip('\n').split()]
def st():return input().rstrip('\n')
def val():return int(input().rstrip('\n'))
def li2():return [i for i in input().rstrip('\n')]
def li3():return [int(i) for i in input().rstrip('\n')]



for _ in range(val()):
    l = [0] + li3()
    x = val()
    n = len(l) - 1
    ans = [None] * (n + 1)
    flag = 0

    # print(l, n, x)
    for i in range(1, n + 1):
        # print(ans, i)
        if l[i] == 1:
            if i > x and (ans[i - x] == 1 or ans[i - x] == None):
                ans[i - x] = 1
            elif i + x <= n:
                ans[i + x] = 1
            else:
                flag = 1
                break
        else:
            if (i <= x or (ans[i - x] == None or ans[i - x ] == 0)) and (i + x > n or (ans[i + x] == None)):
                if i > x:ans[i - x] = 0
                if i + x <= n:ans[i + x] = 0
            else:
                flag = 1
                break
    for i in range(1, n + 1):
        if ans[i] == None:ans[i] = 1  
    if flag:
        print(-1)
    else:
        print(*ans[1:n + 1], sep = '')