human
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 
=====
Give me a Python code to print the answer on a separate line as follows:?
assistant
#Here is Python code to print the answer on a separate line as follows:
.
collections import defaultdict as dc
import sys
from collections import Counter as cnt
from collections import deque as dq
from copy import copy,deepcopy
import itertools 
import math
mod=10**9 +7
# How to sort a list using two compare :
# instead of defining a function define class as a key
# class key(str):
#     def __lt__(x,y):
#         return int(x+y)>int(y+x)
def sinp():
    p=str(sys.stdin.readline())
    return p

def seive(n):
    p=[0]*(n+1)
    for i in range(2,n):           
        for j in range(2*i,n+1,i):
                p[i]=1
    return p

def inp(): 
    p=int(sys.stdin.readline())
    return p

def line():
    p=list(map(int,sys.stdin.readline().split()))
    return p

def read_mat():
    n=inp()
    a=[]
    for i in range(n):
        a.append(line())
    return a

def ind(a):
    return ord(a)-ord('A')

def digit(n):
    p=[int(i) for i in str(n)]
    return p

def check(p,n):
    l=str(p)
    s=''
    for i in range(n):
        s=s+bin(int(l[i]))[2:]
    s=s[:-n]
    if s=='':
        return 0
    return int(s,2)

def createcomb(a,n,i):
    if i==n:
        ans.append(a)
    else:
        for z in range(n):
            a.append(a[z])
            createcomb(a,n,z)  
            a.pop()          

def solve(a,n,a1,b1,c1):
    l=[]
    r=[]
    x=0
    for i in range(n):
        if a[i]>=x:
            l.append(i)
            x=a[i]
    x=0
    for i in range(n-1,-1,-1):
        if a[i]>=x:
            r.append(i)
            x=a[i]
    z=cnt(r)
    c=0
    p=len(l)
    q=len(r)
    for i in l:
        if z[i]:
            c+=1
    if p==a1 and q==b1 and c1==c:
        return 1
    return 0

def xor(a,b):
    s=''
    for i in range(len(a)):
        if a[i]=='1' and b[i]=='0':
            s+='1'
        elif b[i]=='1' and a[i]=='0':
            s+='1'
        else:
            s+='0'
    return s
for t in range(inp()):
    s=str(input())
    x=inp()
    n=len(s)
    w=list('_'*n)
    for i in range(n):
        if s[i]=='0':
            if i>=x:
                w[i-x]='0'
            if...