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 valid(a1):
    if a1>=0 and a1<len(a):
        return True 
    return False
for i in range(int(input())):
    a=input()
    b=int(input())
    ans=[-1 for j in a]
    for j in range(len(a)):
        if a[j]=='0':
            if valid(j-b):
                ans[j-b]=0 
            if valid(j+b):
                ans[j+b]=0 
    flag=True
    for j in range(len(a)):
        if a[j]=='1':
            temp1=0
            if valid(j-b):
                if ans[j-b]==-1 or ans[j-b]==1:
                    ans[j-b]=1 
                    temp1+=1 
            if valid(j+b):
                if ans[j+b]==-1 or ans[j+b]==1:
                    ans[j+b]=1 
                    temp1+=1 
            if temp1==0:
                flag=False 
    if flag:
        res=""
        for j in ans:
            if j==-1:
                res+=str(0)
            else:
                res+=str(j)
        print(res)
    else:
        print(-1)