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())

while t:
    
    s=input()
    x=int(input())
    n=len(s)

    l1=['2' for i in range(0,n)]
    check=0

    for i in range(0,n):
        if (i+x<n and i-x>-1):
            if (s[i]=='0'):
                if (l1[i-x]=='1' or l1[i+x]=='1'):
                    check=1
                    break
                else:
                    l1[i-x]='0'
                    l1[i+x]='0'
            else:
                if (l1[i-x]!='0' or l1[i+x]!='0'):
                    if (l1[i-x]!='0'):
                        l1[i-x]='1'
                    elif (l1[i+x]!='0'):
                        l1[i+x]='1'
                else:
                    check=1
                    break
        elif (i+x<n):
            if (l1[i+x]=='2'):
                l1[i+x]=s[i]
            elif (l1[i+x]!=s[i]):
                check=1
                break
        elif (i-x>-1):
            if (l1[i-x]=='2'):
                l1[i-x]=s[i]
            elif (l1[i-x]!=s[i]):
                check=1
                break
        else:
            if (s[i]=='1'):
                check=1
                break
    
    if (check):
        print (-1)
    else:
        for i in range(0,n):
            if (l1[i]=='2'):
                l1[i]='1'

        w=''
        w=w.join(l1)

        print (w)

    # for i in range(0,x):
    #     if (i+x<n):
    #         l1[i+x]=s[i]

    # check=0

    # for i in range(n-1,n-x-1,-1):
    #     if (i-x>-1):
    #         if (l1[i-x]=='2'):
    #             l1[i-x]=s[i]
    #         elif (l1[i-x]!=s[i]):
    #             check=1
    #             break
    
    # if (check):
    #     print (-1)
    #     t=t-1
    #     continue
    
    # for i in range(min(x,n-x),max(x,n-x)):
    #     if (s[i]=='0'):
    #         if (i+x<n and i-x>0): 
    #             if (l1[i-x]=='1' or l1[i+x]=='1'):
    #                 check=1
    #                 break
    #             else:
    #                 l1[i-x]='0'
    #                 l1[i+x]='0'
    #         elif (i+x<n):
    #             if (l1[i+x]=='2'):
    #                 l1[i+x]=s[i]
    #             elif (l1[i+x]!=s[i]):
    #                 check=1
    #                 break
    #         elif (i-x>0):
    #             if (l1[i-x]=='2'):
    #                 l1[i-x]=s[i]
    #             elif (l1[i-x]!=s[i]):
    #                 check=1
    #                 break
    #     else:
    #         if (i+x<n and i-x>0):
    #             if (l1[i-x]=='0' and l1[i+x]=='0'):
    #                 check=1
    #                 break
    #             elif (l1[i-x]=='1' or l1[i+x]=='1'):
    #                 pass
    #             else:
    #                 if (l1[i-x]=='2' and l1[i+x]=='2'):
    #                     l1[i-x]='1'
    #                 elif (l1[i-x]=='2'):
    #                     l1[i-x]='1'
    #                 else:
    #                     l1[i+x]='1'
    #         elif (i+x<n):
    #             if (l1[i+x]=='2'):
    #                 l1[i+x]=s[i]
    #             elif (l1[i+x]!=s[i]):
    #                 check=1
    #                 break
    #         elif (i-x>0):
    #             if (l1[i-x]=='2'):
    #                 l1[i-x]=s[i]
    #             elif (l1[i-x]!=s[i]):
    #                 check=1
    #                 break
    #         else:
    #             check=1
    #             break

    # if (check):
    #     print (-1)
    #     t=t-1
    #     continue

    # for i in range(0,n):
    #     if l1[i]=='2':
    #         l1[i]='1'

    # w=''

    # w=w.join(l1)
    
    # print (w)

    t=t-1
#                     1             m     2                 m 3                   4
# 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6    
# 1 0 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0 1 0 0 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 0 0 1 1 0 1 1
# 30
# 0 0 1 1 1 1 0 1 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0
# ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^                           ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^