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 i in range(int(input())):
    s = input()
    x = int(input())
    n = len(s)
    w = ['#'] * n
    flag = True
    for j in range(n):
        if j + 1 - x <= 0:
            if j + 1 + x > n:
                if s[j] == '1':
                    flag = False
                    break
            else:
                if s[j] == '0':
                    if w[j + x] not in ['0', '#']:
                        flag = False
                        break
                    w[j + x] = '0'
                else:
                    if w[j + x] not in ['1', '#']:
                        flag = False
                        break
                    w[j + x] = '1'
        else:
            if j + 1 + x > n:
                if s[j] == '0':
                    if w[j - x] not in ['0', '#']:
                        flag = False
                        break
                    w[j - x] = '0'
                else:
                    if w[j - x] not in ['1', '#']:
                        flag = False
                        break
                    w[j - x] = '1'
            else:
                if s[j] == '0':
                    if w[j + x] not in ['#', '0'] or w[j - x] not in ['#', '0']:
                        flag = False
                        break
                    w[j + x] = w[j - x] = '0'
                else:
                    if w[j + x] == '0':
                        if w[j - x] == '0':
                            flag = False
                            break
                        w[j - x] = '1'
                    elif w[j - x] == '0':
                        w[j + x] = '1'
    if not flag:
        print(-1)
        continue
    for j in range(n):
        if w[j] == '#':
            w[j] = '1'
    print(''.join(w))