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

#
# s[i] == 0    <=>    w[i-x] == 0 and w[i+x] == 0
# s[i] == 1    <=>    w[i-x] == 1 or  w[i+x] == 1
#

t = int(input())

def solve():
    w = input()
    n = len(w)
    x = int(input())

    print("[LOG] solve(w=", w, ", x=", x, ")", file=sys.stderr)

    def is_zero(pos):
        if pos <= 0 or pos > n:
            return True

        before = pos + x <= n and w[pos + x - 1] == '0'
        after = pos - x >= 1 and w[pos - x - 1] == '0'

        print("[LOG] is_zero(", pos, ") returns (", before, ", ", after, \
             ") =", before or after, file=sys.stderr)
        return before or after

    for i in range(1, n + 1):
        if w[i - 1] == '1':
            if is_zero(i - x) and is_zero(i + x):
                print(-1)
                break
    else:
        for i in range(1, n + 1):
            print(0 if is_zero(i) else 1, end='')
        print()

for _ in range(t):
    solve()
