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
"""T=int(input())
for _ in range(0,T):
    n=int(input())
    a,b=map(int,input().split())
    s=input()
    s=[int(x) for x in input().split()]
    for i in range(0,len(s)):
        a,b=map(int,input().split())"""



T=int(input())
for _ in range(0,T):
    s=input()
    x=int(input())
    L=['1']*len(s)
    n=len(s)

    for i in range(0,len(s)):
        if(s[i]=='0'):
            if((i+x)<n):
                L[i+x]='0'
            if((i-x)>=0):
                L[i-x]='0'

    temp=''.join(L)
    temp=str(temp)

    kk=['0']*len(s)
    for i in range(0,len(L)):
        tt=0
        if((i+x)<n and L[i+x]=='1'):
            tt=1
        if((i-x)>=0 and L[i-x]=='1'):
            tt=1
        if(tt==0):
            kk[i]='0'
        else:
            kk[i]='1'

    kk=''.join(kk)
    kk=str(kk)

    if(s==kk):
        print(temp)
    else:
        print(-1)

    

