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
import sys

t = int(input())

i = 0
for line in sys.stdin:
    if i == 0:
        s = line[:-1]
    else:
        x = int(line)
        impossible = False

        w = [-1 for _ in range(len(s))]
        for j in range(len(s)):
            if s[j] == "1":
                if j - x < 0:
                    if j + x < len(s):
                        w[j + x] = 1
                    else:
                        impossible = True
                        break
                elif j + x >= len(s):
                    if j - x >= 0:
                        if w[j - x] == 1 or w[j - x] == -1:
                            w[j - x] = 1
                        else:
                            impossible = True
                            break
                    else:
                        impossible = True
                        break
                else:
                    if w[j - x] == -1 or w[j - x] == 1:
                        w[j - x] = 1
                    else:
                        if w[j + x] == -1 or w[j + x] == 1:
                            w[j + x] = 1
                        else:
                            impossible = True
                            break
            else:
                if j - x >= 0:
                    if w[j - x] == 1:
                        impossible = True
                        break
                    w[j - x] = 0
                if j + x < len(s):
                    if w[j + x] == 1:
                        impossible = True
                        break
                    w[j + x] = 0

        if impossible:
            print(-1)
        else:
            for p in range(len(w)):
                if w[p] == -1:
                    w[p] = 1
            print(*w, sep="")

    i = 1 - i
