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 answer(A,x):
    dp=[-1]*len(A)
    for i in range(len(A)):
        if i+1-x>0 and i+1+x<=len(A):
            if A[i]=="0":
                if dp[i-x]==-1:
                    dp[i-x]="0"
                else:
                    if dp[i-x]!=A[i]:
                        return -1
                if dp[i+x]==-1:
                    dp[i+x]="0"
                else:
                    if dp[i+x]!=A[i]:
                        return -1
            else:
                if dp[i-x]==-1:
                    dp[i-x]="1"
                else:
                    if dp[i-x]=="0":
                        dp[i+x]="1"
                    
        elif i+1-x>0:
            if dp[i-x]==-1:
                dp[i-x]=A[i]
            else:
                if dp[i-x]!=A[i]:
                    return -1
                
        elif i+1+x<=len(A):
            if dp[i+x]==-1:
                dp[i+x]=A[i]
            else:
                if dp[i+x]!=A[i]:
                    return -1
                
        else:
            if A[i]=="1":
                return -1
            
    

    
    for i in range(len(A)):
        if dp[i]==-1:
            dp[i]="1"
            
    
    return "".join(dp)


t=int(input())
for i in range(t):
    s=input()
    n=int(input())
    print(answer(s,n))