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
tc = int(input())
for t in range(tc):

    s = input()
    x = int(input())
    n = len(s)
    w = [-1 for _ in range(len(s))]
    later = []
    pos = True
    for i in range(len(s)):
        if i+x >= n and i-x < 0:
            if s[i] == '1':
                pos = False
                print(-1)
                break
            else:  # w[i]  = '0' | -1
                continue
        elif i+x >= n and i-x >= 0:
            if w[i-x] == -1:
                w[i-x] = s[i]
            else:
                if w[i-x] != s[i]:  # w[i-x] is '0' | '1'
                    pos = False
                    print(-1)
                    break
                else:
                    continue
        elif i+x < n and i-x < 0:
            if w[i+x] == -1:
                w[i+x] = s[i]
            else:
                if w[i+x] != s[i]:
                    pos = False
                    print(-1)
                    break
                else:
                    continue
        else:
            if s[i] == '0':
                if w[i+x] == '1' or w[i-x] == '1':
                    pos = False
                    print(-1)
                    break
                else:
                    w[i+x] = '0'
                    w[i-x] = '0'
            else:
                later.append(i)

    # print("later : ", later)
    if pos:
        for idx in later:
            if w[idx+x] == '0' and w[idx-x] == '0':
                pos = False
                print(-1)
                break
            else:
                if w[idx+x] == -1:
                    w[idx+x] = '1'
                if w[idx-x] == -1:
                    w[idx-x] = '1'
    if pos:
        for i in range(len(w)):
            if w[i] == -1:
                w[i] = '0'
        print("".join(w))
