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
for _ in range(int(input())):
    s=[]
    for x in input():
        s.append(int(x))
    n=int(input())
    ans=[None]*len(s)
    #print(len(s),99999999999999999999999)
    for i in range(len(s)):
        if i-n>=0 and i+n<len(s):
            if s[i]==0:
                if ans[i-n]==1:
                    #print(ans)
                    ans=-1
                    #print(1,i)
                    break
                ans[i-n]=ans[i+n]=0
            else:
                if ans[i-n]==0:
                    ans[i+n]=1
                else:
                    ans[i-n]=1
        elif i-n<0 and i+n>=len(s):
            if s[i]==1:
                ans=-1
                #print(2,i)
                break
        elif i-n>=0:
            if ans[i-n]==None:
                ans[i-n]=s[i]
            else:
                if ans[i-n]!=s[i]:
                    ans=-1
                    #print(3,i)
                    break
        else:
            ans[i+n]=s[i]
    if ans==-1:
        print(-1)
        continue
    for i,x in enumerate(ans):
        if x==None:
            x=1
        ans[i]=str(x)
    print(''.join(ans))