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=sys.stdin.readline

t = int(input())

for _ in range(t):
    #p,f = list(map(int,input().split()))
    s = input().rstrip()
    x = int(input())
    
    n = len(s)
    ans = [1] * n
    
    for i in range(n):
        a = i+x
        b = i-x
        
        if s[i] == '0':
            if a>-1 and a<n:
                ans[a] = 0
                
            if b>-1 and b<n:
                ans[b] = 0
            
    ok = 1
    #print(ans, s)
    
    for i in range(n):
        a = i+x
        b = i-x
        
        #if i==1:
        #    print(i,a,b,ans[a],ans[b],s[i])
        
        tot = 0
        
        #this 0 couldnt happen
        if a>-1 and a<n:
            if ans[a]==1:
                tot += 1
            
            if ans[a]==1 and s[i] == '0':
                
                ok = 0
                break
                
        #this 0 couldnt happen
        if b>-1 and b<n:
            if ans[b]==1:
                tot += 1
            
            if ans[b]==1 and s[i] == '0':
                
                ok = 0
                break
            
        #if 0 came from 
        if s[i] == '1' and tot==0:
            ok = 0
            break
            
    if ok==1:
        print(''.join([str(x) for x in ans]))
    else:
        print(-1)