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 math import *
from collections import *
from random import *
from decimal import Decimal
from heapq import *
from bisect import *
import sys
input=sys.stdin.readline
sys.setrecursionlimit(10**5)
def lis():
    return list(map(int,input().split()))
def ma():
    return map(int,input().split())
def inp():
    return int(input())
def st1():
    return input().rstrip('\n')
t=inp()
while(t):
    t-=1
    s=st1()
    x=inp()
    n=len(s)
    r=[1 for i in range(n)]
    fl=0
    for i in range(n):
        if(i-x<0 and i+x>n-1 and s[i]=='1'):
            fl=1
            break
        if(s[i]=='0'):
            if(i-x>=0):
                r[i-x]=0
            if(i+x<=n-1):
                r[i+x]=0
    #print(r)
    for i in range(n):
        if(s[i]=='1'):
            loc=0
            if(i-x>=0):
                if(r[i-x]==1):
                    loc+=1
            if(i+x<=n-1):
                if(r[i+x]==1):
                    loc+=1
            if(loc==0):
                fl=1
                break

    if(fl):
        print(-1)
    else:
        for i in r:
            print(i,end='')
        print()
