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
# for _ in range(int(input())):
#     n=int(input())
#     s=input()
#     l=[]
#     for i in range(n):
#         l.append(s[2*i])
#     ans="".join(l)
#     print(ans)


# for _ in range(int(input())):
#     cap1, cap2 = map(int, input().split())
#     cnt1, cnt2 = map(int, input().split())
#     w1, w2 = map(int, input().split())
#     if w1 > w2:
#         cnt1, cnt2 = cnt2, cnt1
#         w1, w2 = w2, w1
#
#     if cnt1 >= cap1//w1 + cap2//w1:
#         print(cap1//w1 + cap2//w1)
#     else:
#

for _ in range(int(input())):
    flag=1
    s=input()
    x=int(input())
    n=len(s)
    l=['1' for i in range(n)]
    for i in range(n):
        if s[i]=='0' and i+x<n:
            l[i+x]='0'
        if s[i]=='0' and i-x>=0:
            l[i-x]='0'
    for i in range(n):
        if s[i]=='1':
            if (x+i<n and l[i+x]=='1') or (i-x>=0 and l[i-x]=='1'):
                continue
            else:
                print(-1)
                flag=0
                break
    if flag:
        print("".join(l))
