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
"""
Code of Ayush Tiwari
Codeforces: servermonk
Codechef: ayush572000

"""

def solution():
    
    # This is the main code
    s=list(input())
    x=int(input())
    n=len(s)
    flag=0
    l=['2']*n
    for i in range(n):
        p=i-x
        q=i+x
        if (p<0 and q>n-1):
            if s[i]=='1':
                flag=1 
                break       
        elif p<0:
            if s[i]=='1':
                if l[q]=='0':
                    flag=1
                    break
                l[q]='1'
            else:
                if l[q]=='1':
                    flag=1
                    break
                l[q]='0'
        elif q>n-1:
            if s[i]=='1':
                if l[p]=='0':
                    flag=1
                    break
                l[p]='1'
            else:
                if l[p]=='1':
                    flag=1
                    break
                l[p]='0'
        else:
            if s[i]=='0':
                if l[p]=='1' or l[q]=='1':
                    flag=1
                    break
                l[p]='0'
                l[q]='0'
            else:
                if l[p]=='0' and l[q]=='0':
                    flag=1
                    break
                elif l[p]=='0' and l[q]=='2':
                    l[q]='1'
                elif l[p]=='2' and l[q]=='0':
                    l[p]='1'
    if flag:
        print(-1)
    else:
        ans=''
        for i in range(n):
            if l[i]=='2':
                ans+='1'
            else:
                ans+=l[i]
        print(ans)
t=int(input())
for _ in range(t):
    solution()