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
# Author Name: Ajay Meena
# Codeforce : https://codeforces.com/profile/majay1638
import sys
import math
import bisect
import heapq
from bisect import bisect_right
from sys import stdin, stdout

# -------------- INPUT FUNCTIONS ------------------


def get_ints_in_variables(): return map(
    int, sys.stdin.readline().strip().split())


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


def get_ints_in_list(): return list(
    map(int, sys.stdin.readline().strip().split()))
def get_list_of_list(n): return [list(
    map(int, sys.stdin.readline().strip().split())) for _ in range(n)]


def get_string(): return sys.stdin.readline().strip()

# -------------- SOLUTION FUNCTION ------------------


def Solution(s, n, x):
    # Write Your Code Here
    res = ["1" for _ in range(n)]
    flag = False
    for i in range(n):
        if s[i] == "0":
            if i-x >= 0:
                res[i-x] = "0"
            if i+x < n:
                res[i+x] = "0"
    constructStr = ["0" for _ in range(n)]
    for i in range(n):
        if i-x >= 0 and res[i-x] == "1":
            constructStr[i] = "1"
        elif i+x < n and res[i+x] == "1":
            constructStr[i] = "1"
        else:
            constructStr[i] = "0"
    # print(res, constructStr)
    for i in range(n):
        if s[i] != constructStr[i]:
            flag = True
            break
    if flag:
        print(-1)
    else:
        # print(res)
        print("".join(res))


def main():
    # Take input Here and Call solution function
    for _ in range(get_int()):
        s = get_string()
        x = get_int()
        Solution(s, len(s), x)


# calling main Function
if __name__ == '__main__':
    main()
