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):
    t -=1
    f = 0
    s = input()
    x = int(input())
    w = ['1']*len(s)
    n = len(s)
    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 s[i] == '1':
            if not ((i-x>=0 and w[i-x]=='1') or (i+x<n and w[i+x]=='1')):
                f = 1
                break

    if f==1:
        print(-1)
    else:
        print("".join(w))













    # for i in range(x):
    #     w[i+x] = s[i]
    # print(w)

    # for i in range(x):
    #     if w[n-1-x-i] == None:
    #         w[n-1-x-i] = s[n-1-i]
    #     else:
    #         if w[n-1-x-i] != s[n-1-i]:
    #             f = 1
    #             break
    
    # if f==1:
    #     print(-1)
    #     continue

    # for i in range(n):
    #     if w[i]==None:
    #         w[i] = '0'
    
    # for i in range(x,n-x):
    #     if s[i]==0 and (w[i-x]==1 and w[i+x]==1):
    #         f = 1
    #         break
    #     if s[i]==1 and (w[i-x]==0 and w[i+x]==0):
    #         f = 1
    #         break
    # if f == 1:
    #     print(-1)
    #     continue
    # else:
    #     print("".join(w))