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
def parse(w,x):
    s=[]
    for i in range(len(w)):
        b=0
        if i>=x and w[i-x]==1:b=1
        if i<len(w)-x and w[i+x]==1:b=1
        s.append(b)
    return s
def u(r,i,v):
    if r[i]not in(-1,v):raise ArithmeticError
    r[i]=v
for _ in range(int(input())):
    s,x=list(map(int,input())),int(input())
    n=len(s)
    r=[-1]*n
    try:
        for i in range(n):
            if s[i]<1:
                if i>=x:u(r,i-x,0)
                if i+x<n:u(r,i+x,0)
        for i in range(x):
            if i+x<n:u(r,i+x,s[i])
            if n-i-1-x>=0:u(r,-i-1-x,s[-i-1])
        for i in range(x,n-x):
            if s[i]<1:continue
            if r[i-x]==0:u(r,i+x,1)
            elif r[i+x]==0:u(r,i-x,1)
            else:u(r,i-x,1),u(r,i+x,1)
        for i in range(n):r[i]=max(0,r[i])
        if parse(r,x)!=s:print(-1)
        else:print(''.join(map(str,r)))
    except ArithmeticError:print(-1)