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
import sys

# input = sys.stdin.readline
ll = lambda: list(map(int, input().split()))
lls = lambda: list(map(str, input().split()))
fin = lambda: list(map(float, input().split()))
st = lambda: input()
v = lambda: map(int, input().split())
ii = lambda: int(input())
mod = (10 ** 9) + 7
from math import *
# from fractions import *
from datetime import datetime
from collections import *
import math

# print(log(8,3))
for _ in range(ii()):
    s = st()
    x = ii()
    ans = ["1"] * len(s)
    f = 1
    for i in range(len(s)):
        if (s[i] == "0"):
            if (i - x >= 0):
                ans[i - x] = "0"
            if ((i + x) < len(s)):
                ans[i + x] = "0"
        #print("".join(ans), "ans")
    sol = ["0"] * len(s)
    for i in range(len(s)):
        if ((i - x >= 0 and ans[i - x] == "1") or ((i + x) < len(s) and ans[i + x] == "1")):
            sol[i] = "1"
    #print("".join(sol), "sol")
    if (s == "".join(sol)):
        print("".join(ans))
    else:
        print(-1)
