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 
input = lambda:sys.stdin.readline().strip()
t = int(input())
while t:
    t-=1
    s = input()
    n = len(s)
    x = int(input())
    w = [""]*n
    for i in range(n):
        if s[i]=='0':
            if i-x>=0:
                w[i-x] = '0'
            if i+x<n:
                w[i+x] = '0'
    for i in range(n):
        if w[i]=="":
            w[i] = '1'
    temp = [""]*n
    for i in range(n):
        ok = True
        if i-x>=0:
            if w[i-x]=='1':
                temp[i] = '1'
                ok = False
        if i+x<len(s):
            if w[i+x]=='1':
                temp[i] = '1'
                ok = False
        if ok:
            temp[i] = '0'
    # print(w,"w")
    if "".join(temp)==s:
        print("".join(w))
    else:
        print(-1)