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 i in range(t):
    s=input()
    x=int(input())
    n=len(s)
    dp=[None for i in range(len(s))]
    # flag=0
    # for i in range(x):
    #     if i+x<n:
    #         ans[i+x]=s[i]
    #     elif s[i]!=0:
    #         flag=1
    #         break
    # if flag==0:
    #     print("-1")
    #     continue
    # for i in range(x):
    #     if n-i-1-x>=0:
    #         if ans[n-i-1-x]==None or ans[n-i-1-x]==s[n-1-i]:
    #             ans[n-1-i-x]=s[n-1-i]
    #         else:
    #             flag=1
    #             break
    #     elif s[n-i-1]!=0:
    #         flag=1
    #         break
    for i in range(n):
        ans=1
        if i-x>=0:
            ans&=int(s[i-x])
        if i+x<n:
            ans&=int(s[i+x])
        dp[i]=ans
    flag=0    
    for i in range(n):
        ans=0
        if i-x>=0:
            ans|=dp[i-x]
        if i+x<n:
            ans|=dp[i+x]
        if ans!=int(s[i]):
            flag=1
            break
    if flag==1:
        print("-1")
    else:
        print("".join([str(k) for k in dp]))
    
            