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
tests = int(input())
for t in range(tests):
    string = list(input())
    x = int(input())
    string_len = len(string)
    res = [-1 for _ in range(string_len)]
    
    check=True
    for idx, item in enumerate(string):
        if item == '0':
            if (idx >= x):
                if res[idx-x] == -1 or res[idx-x] == 0:
                    res[idx-x] = 0
                else:
                    check = False
                    break
            if (idx <= string_len-x-1):
                if res[idx+x] == -1 or res[idx+x] == 0:
                    res[idx+x] = 0
                else:
                    check = False
                    break
        if item == '1':
            if (idx >= x):
                if res[idx-x] == -1 or res[idx-x] == 1:
                    res[idx-x] = 1
                else:
                    if (idx <= string_len-x-1) and (res[idx+x] == -1 or res[idx+x] == 1):
                        res[idx+x] = 1
                    else:
                        check = False
                        break
            elif (idx <= string_len-x-1):
                if res[idx+x] == -1 or res[idx+x] == 1:
                    res[idx+x] = 1
                else:
                    check = False
                    break
            else:
                check = False
                break
                
    if not check:
        print(-1)
    else:
        for idx in range(string_len):
            if res[idx] == -1:
                res[idx] = 1
        res = list(map(str, res))
        print(''.join(res))