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 functools import reduce
from collections import Counter
import time
import datetime
from math import sqrt,gcd

# def time_t():
#     print("Current date and time: " , datetime.datetime.now())
#     print("Current year: ", datetime.date.today().strftime("%Y"))
#     print("Month of year: ", datetime.date.today().strftime("%B"))
#     print("Week number of the year: ", datetime.date.today().strftime("%W"))
#     print("Weekday of the week: ", datetime.date.today().strftime("%w"))
#     print("Day of year: ", datetime.date.today().strftime("%j"))
#     print("Day of the month : ", datetime.date.today().strftime("%d"))
#     print("Day of week: ", datetime.date.today().strftime("%A"))

def ip(): return int(sys.stdin.readline())

def sip(): return sys.stdin.readline()

def mip(): return map(int,sys.stdin.readline().split())

def mips(): return map(str,sys.stdin.readline().split())

def lip(): return list(map(int,sys.stdin.readline().split()))

def matip(n,m):
    lst=[]
    for i in range(n):
        arr = lip()
        lst.append(arr)
    return lst

def factors(n): # find the factors of a number
    return list(set(reduce(list.__add__, ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0))))

def minJumps(arr, n): #to reach from 0 to n-1 in the array in minimum steps
    jumps = [0 for i in range(n)]
    if (n == 0) or (arr[0] == 0):
        return float('inf')
    jumps[0] = 0
    for i in range(1, n):
        jumps[i] = float('inf')
        for j in range(i):
            if (i <= j + arr[j]) and (jumps[j] != float('inf')):
                jumps[i] = min(jumps[i], jumps[j] + 1)
                break
    return jumps[n-1]

def dic(arr): # converting list into dict of count
    return Counter(arr)

def check_prime(n):
    if n<2:
        return False
    for i in range(2,int(n**(0.5))+1,2):
        if n%i==0:
            return False
    return True 

# --------------------------------------------------------- #
# sys.stdin = open('input.txt','r')
# sys.stdout = open('output.txt','w')
# --------------------------------------------------------- #

t = ip()
while t:
    t-=1
    w = sip()
    x = ip()
    n = len(w)-1
    arr = [2]*n
    flag = 0
    for i in range(n):
        if w[i]=='0':
            if i+x<n:
                if arr[i+x]==2:
                    arr[i+x]=0
            if i-x>=0:
                if arr[i-x]==2:
                    arr[i-x]=0
                elif arr[i-x]==1:
                    flag = 1
                    break
        else:
            # what if both i+x and i-x both donot exist
            check = 0
            if i-x>=0:
                if arr[i-x]==2:
                    arr[i-x]=1
                elif arr[i-x]==0:
                    check+=1
            else:
                check+=1
            if i+x<n:
                if arr[i+x]==2:
                    if check==1:
                        arr[i+x]=1
            else:
                check+=1
            if check==2:
                flag = 1
                break
    if flag == 1:
        print(-1)
    else:
        for item in arr:
            if item==2:
                print(1,end='')
            else:
                print(item,end='')
        print()


