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
#THIS CODE IS MADE BY "harshest2019"
from sys import *
ws=lambda:map(int,stdin.readline().strip().split())
li=lambda:list(map(int,stdin.readline().strip().split()))
mod=1000000007
def ncr(n, r, p): 
    num = den = 1 
    for i in range(r): 
        num = (num * (n - i)) % p 
        den = (den * (i + 1)) % p 
    return (num * pow(den, p - 2, p)) % p

def gcd(a,b):
    if (b == 0): 
         return a 
    return gcd(b, a%b)
def prod(l):
    ans=1
    for i in range(len(l)):
        ans=ans*l[i]
    return ans
#CODE STARTS HERE
for testcases in range(int(input())):
    a=list(map(int,list(stdin.readline().strip())))
    b=int(input())
    c=len(a)
    ans=[1]*c
    for i in range(c):
        if(a[i]==0):
            if(i+b<c):
                ans[i+b]=0
            if(i-b>=0):
                ans[i-b]=0
    flag=1
    for i in range(c):
        flags=0
        if((i+b)<c):
            flags+=ans[i+b]
        if((i-b)>=0):
            flags+=ans[i-b]
        if(a[i]==1 and flags==0):
            flag=-1
            break
    if(flag==-1):
        print(-1)
    else:
        for m in ans:
            print(m,end='')
    print()
