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
#!/usr/bin/env python3
import io
import os
import sys

input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline

def prdbg(*args, **kwargs):
    print(*args, **kwargs, file=sys.stderr)
    pass

def get_str():
    return input().decode().strip()

def rint():
    return map(int, input().split())

def oint():
    return int(input())

t = oint()

for _ in range(t):
    s = get_str()
    x = oint()
    n = len(s)
    w = [-1]*n
    for i in range(n):
        if s[i] == '0':
            if i-x >= 0:
                w[i-x] = 0
            if i+x < n:
                w[i+x] = 0
    flag = 0
    for i in range(n):
        if s[i] == '1':
            if i-x >= 0 and w[i-x] == -1 or i+x < n and w[i+x] == -1:
                pass
            else:
                flag = 1
    if flag:
        print(-1)
        continue
    for i in range(n):
        if w[i] == -1:
            w[i] = 1
    print(''.join(map(str, w)))

