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())
for i in range(t):
    s = input()
    x = int(input())
    n = len(s)
    l = ['2'] * n
    check = True
    for i in range(n):
        
        if s[i] == '1':
            if i - x < 0 and i + x < n:
                if l[i + x] == '0':
                    check = False
                l[i + x] = '1'
            if i + x >= n and i - x >= 0:
                if l[i - x] == '0':
                    check = False
                l[i - x] = '1'
            
        else:
            if i - x >= 0 :
            
                if l[i - x] == '1':
                    check = False
            
                l[i - x] = '0'
               
                        
            if i + x < n:
                
                if l[i + x] == '1':
                    check = False
                
                l[i + x] = '0'
        
    nat = -1
   
    if check == True:
        for i in range(n):
            if s[i] == '1':
                t = 0
                z = 0
                if i - x >= 0:
                    z += 1
                    if l[i - x] == '0':
                        t += 1
                if i + x < n:
                    z += 1
                    if l[i + x] == '0':
                        t += 1
                if t == z:
                    check = False
        if check == True:
            nat = ''
 
        
            for i in range(n):
                if l[i] != '0':
                    nat += '1'
                else:
                    nat += '0'
    print(nat)
