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
import heapq
import cProfile
from collections import Counter, defaultdict, deque
from functools import reduce
import math


def get_int():
    return int(stdin.readline().strip())


def get_tuple():
    return map(int, stdin.readline().split())


def get_list():
    return list(map(int, stdin.readline().split()))


def solve():
    st = input()
    x = get_int()
    n = len(st)
    ans = [1]*n
    for i,v in enumerate(st):
        if v=='0':
            if i-x>=0: ans[i-x] = 0
            if i+x<n: ans[i+x] = 0
    for i,v in enumerate(st):
        if i-x>=0:
            if ans[i-x]==1:
                if v=='1': continue
                else: return False
        if i+x<n:
            if ans[i+x]==1:
                if v=='1': continue
                else: return False
        if v=='1': return  False

    return "".join([str(e) for e in ans])





def main():
    ans = solve()
    if ans: print(ans)
    else: print("-1")


TestCases = True

if TestCases:
    for i in range(get_int()):
        main()
else:
    main()
