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())):
    ar=input().rstrip()
    x=int(input())
    n=len(ar)
    ans=[1]*(n)
    for j in range(n):
        if(ar[j]=="0"):
            if(j-x>=0):
                ans[j-x]=0
            if (j + x)<n:
                ans[j+x] = 0
    mk = ['0']*n
    for i in range(n):
        if(ans[i]==1):
            if (i - x >= 0):
                mk[i-x]='1'
            if (i + x < n):
                mk[i+x]='1'
    mk=''.join(mk)
    if (mk == ar):
        for i in ans:
            print(i,end="")
        print()
    else:
        print("-1")
