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 _ in range(t):
    s = input()
    n = len(s)
    w = [-1 for i in range(n)]
    x = int(input())
    possible = True
    # if n == 47:
    #     print("s: {}".format(s))
    #     print(x)
    # for i in range(x, n):
    #     imx = i - x
    #     ipx = i + x
    #     if s[i] == '1':
    #         if imx >= 0:
    #             w[imx] = '1'
    #     elif imx >= 0:
    #         w[imx] = '0'
    #
    # for i in range(x, n):
    #     ipx = i + x
    #     imx = i - x
    #     if s[i] == '0':
    #         if ipx < n:
    #             w[ipx] = '0'
    #     else:
    #         if imx >= 0 and ipx < n:
    #             if w[imx] == '0':
    #                 w[ipx] = '1'
    for i in range(n):
        imx = i - x
        ipx = i + x
        if s[i] == '1':
            if imx >= 0 and w[imx] == -1:
                w[imx] = '1'
            if ipx < n:
                w[ipx] = '1'
        else:
            if imx >= 0:
                w[imx] = '0'
            if ipx < n:
                w[ipx] = '0'

    for i in range(n):
        if w[i] == -1:
            w[i] = '0'

    for i in range(n):
        ipx = i + x
        imx = i - x
        if s[i] == '1':
            if imx >= 0 and ipx < n and w[imx] != '1' and w[ipx] != '1':
                possible = not possible
                break
            elif imx >= 0 and ipx >= n and w[imx] != '1':
                possible = not possible
                break
            elif ipx < n and imx < 0 and w[ipx] != '1':
                possible = not possible
                break
            elif ipx >= n and imx < 0:
                possible = not possible
                break
        else:
            if imx >= 0 and ipx < n and (w[imx] != '0' or w[ipx] != '0'):
                possible = not possible
                break
            elif imx >= 0 and ipx >= n and w[imx] != '0':
                possible = not possible
                break
            elif ipx < n and imx < 0 and w[ipx] != '0':
                possible = not possible
                break
    if not possible:
        print(-1)
        # print(''.join(w))
        # print()
    else:
        print(''.join(w))

# 10101111101000110 100111110000000111101110011011
# 00111101110011011 000000000000010101111101000110
