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 functools import reduce
import os
import sys
from collections import *
#from fractions import *
from math import *
from bisect import *
from heapq import *
from io import BytesIO, IOBase
input = lambda: sys.stdin.readline().rstrip("\r\n")
def value(): return tuple(map(int, input().split())) # multiple values
def arr(): return [int(i) for i in input().split()] # array input
def sarr(): return [int(i) for i in input()] #array from string
def starr(): return [str(x) for x in input().split()] #string array
def inn(): return int(input()) # integer input
def svalue(): return tuple(map(str, input().split())) #multiple string values
def parr(): return [(value()) for i in range(n)] # array of pairs
mo = 1000000007
inf=1e18
div=998244353
# ----------------------------CODE------------------------------#
for _ in range(inn()):
    a=[int(x) for x in input()]
    n=len(a)
    x=inn()
    ans=[-1]*(n)
    for i in range(n):
        if(a[i]==0):
            if(i-x>=0):
                ans[i-x]=0
            if(i+x<n):
                ans[i+x]=0
    valid=True
    #print(*a[50:90],sep="")
    #print(*ans[50:90],sep="")
    for i in range(n):
        if(a[i]==1):
            valid1=True
            valid2=True
            in1=False
            in2=False
            if(i-x>=0):
                in1=True
                if(ans[i-x]==0):
                    #print(i,i-x)
                    valid1=False
                else:
                    ans[i-x]=1
            if(i+x<n):
                in2=True
                if(ans[i+x]==0):
                    #print(i,i+x)
                    valid2=False
                else:
                    ans[i+x]=1
            if((not valid1 or in1==False) and (not valid2 or in2==False)):
                valid=False
                break
    if(valid):
        for i in range(n):
            if(ans[i]==-1):
                ans[i]=1
        print(*ans,sep="")
    else:
        print(-1)




