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
from sys import stdin,stdout
# 010,1
for _ in range(int(stdin.readline())):
    # n,mnl,mns=list(map(int, stdin.readline().split()))
    s=input()
    x=int(stdin.readline());n=len(s)
    ans=[' ']*n;f=1
    for i in range(n):
        if s[i]=='0':
            if i-x>=0:ans[i-x]='0'
            if i+x<n:ans[i+x]='0'
    # print(ans)
    for i in range(n):
        if s[i]=='1':
            left=right=0
            if i-x>=0:
                if ans[i-x]=='1' or ans[i-x]==' ':
                    left=1
                    ans[i-x]='1'
            if left==0 and i+x<n:
                if ans[i+x]==' ':
                    right=1
                    ans[i+x]='1'
            if right==left==0:
                f=0
                break
    # print(ans)
    ans=''.join(['0' if ch==' ' else ch for ch in ans])
    print(ans if f else -1)
