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 tt in range(int(input())):
    s=input()
    n=len(s)
    x=int(input())
    ans=[" " for i in range(n)]
    for i in range(n):
        if s[i] == "0":
            for j in [i-x,i+x]:
                if 0 <= j and j < n:
                    ans[j] = "0"
    good=True
 #   print(ans)
    for i in range(n):
        if s[i]=="0":
            if ans[i]!="0":
                ans[i]="1"
            continue
        l = (0 <= i - x) and (ans[i-x]!="0")
        r = (i + x < n) and (ans[i+x]!="0")
        if not l and not r:
            good = False
        if l:
            ans[i-x] = "1"
        if r:
            ans[i+x] = "1"
    print("".join(ans) if good and " " not in ans else -1)           