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
t=int(input())
for i in range(t):
    s=input()
    b=[]
    for j in s:
        b.append(int(j))
    n=len(b)
    y=int(input())
    c=[1]*(n)
    j=0
    f=0
    while(j<n):
        if b[j]==0:
            if (j-y)>=0:
                c[j-y]=0
            if (j+y)<n:
                c[j+y]=0

        j+=1
    j=0
    while(j<n):
        if (j+y)<n and (j-y)>=0:
            r=c[j-y]|c[j+y]
        elif (j+y)<n:
            r=c[j+y]
        elif (j-y)>=0:
            r=c[j-y]
        else:
            r=0
        if r!=b[j]:
            f=1
            break
        j+=1
    if f==1:
        print(-1)
    else:
        s=""
        for j in c:
            s+=str(j)
        print(s)



