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 True:
    if t == 0:
        break
    t -=1 
    a = input()
    n = len(a)
    x = int(input())
    w = ['1' for i in range(n+1)]
    s = ['1']
    for i in a:
        s.append(i)
    for i in range(1,n+1):
        # print(i,w[1:])
        if (i > x and s[i] == '1') :
            if(w[i-x] != '0'):
                w[i-x] = '1'
        if ((i + x) <= n and s[i] == '1'):
            if(w[i+x] != 0):
                w[i+x] = '1'
        if(s[i] == '0'):
            if(i> x):
                w[i-x] = '0'
            if(i+x <= n):
                w[i+x] = '0'
    
    poss = True

    for i in range(1,n+1):
        if ((i>x and w[i-x] == '1') or (i+x <= n and w[i+x] == '1')) :
            if(s[i]!='1'):
                poss = False
                break
        else:
            if(s[i]!='0'):
                poss = False
                break

            

    if poss:       
        print(''.join(w[1:]))
    else:
        print(-1)

    