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 = input()
    s = []
    for i in S:
        s.append(int(i))
    n = len(s)
    x = int(input())
    a = [0]*n
    b = [False]*n
    check=False
    for i in range(min(x,n)):
        if i+x<n:
            b[i+x]=True
            a[i+x]=s[i]
    for i in range(n-x,n):
        if i-x>=0:
            if not b[i-x]:
                b[i-x]=True
                a[i-x]=s[i]
            else:
                if a[i-x]!=s[i]:
                    check=True
                    break
    for i in range(x,n-x):
        if s[i]==0:
            if (b[i-x] and a[i-x]==1) or (b[i+x] and a[i+x]==1):
                check=True
                break
            else:
                b[i-x]=True
                b[i+x]=True
                a[i-x]=0
                a[i+x]=0
    for i in range(n-x,x):
        b[i]=True
        if s[i]==1:
            check=True
            break
    for i in range(n):
        if not b[i]:
            a[i]=1
    for i in range(x,n-x):
        if s[i]==1:
            if (b[i-x] or b[i+x]) and (a[i-x]+a[i+x]==0):
                check=True
                break
    if check:
        print("-1")
    else:
        for i in a:
            print(i,end='')
        print()