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())
while T>0:
    str = []
    w = input()
    x = int(input())
    n = len(w)-1
    flag = False
    for i in range(0, 2*n+1):
        str.append(-1)
    for i in range(0, x):
        for j in range(i, n+1, x):
            if j == i:
                if j +x > n and w[j] == '1':
                    flag = False
                    break
                elif j+x > n:
                    break
                str[j+x] = int(w[j])
                continue

            if w[j] == '0':
                if str[j-x] == 1:
                    flag = False
                    break
                str[j-x] = 0
                str[j+x] = 0

            else:
                if str[j-x] == 1:
                    continue
                if str[j-x] == -1:
                    str[j-x] = 1
                else:
                    str[j+x] = 1

    for i in range(0, n+1):
        if str[i] == -1:
            str[i] = 0
    res = ""

    for i in range(0, n+1):
        if (i-x >= 0 and str[i-x] ==1) or (i+x <= n and str[i+x] ==1 ):
            res+='1'
        else:
            res+='0'

    if res!=w:
        print(-1)
    else:
        for i in range (0, n+1):
            print(str[i], end="")
        print()
    T-=1