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
a=int(input())
for i in range(a):
    s=input()
    ans=[]
    flag=1
    for i in range(len(s)):
        ans.append(s[i])
    x=int(input())
    te=[1]*len(s)
    for i in range(len(s)):
        if(s[i]=='0'):
            if(i-x>=0):
                te[i-x]=0
            if(i+x<len(s)):
                te[i+x]=0
        else:
            a1=0
            if(i-x>=0 and te[i-x]==0):
                a1+=1
            if(i+x<len(s) and te[i+x]==0):
                a1+=1
            if(a1==2):
                flag=0
                break;
    for i in range(len(te)):
        if(s[i]=='1'):
            a1=0
            if(i+x<len(te)):
                if(te[i+x]==1):
                    a1+=1
            if(i-x>=0):
                if(te[i-x]==1):
                    a1+=1
            if(a1==0):
                flag=0
                break;
    if(flag==0):
        print(-1)
    else:
        print(''.join(map(str,te)))
            
