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 collections import Counter, defaultdict, deque
import bisect
from sys import stdin, stdout
from itertools import repeat
import math

# sys.stdin = open('input')

def inp(force_list=False):
    re = map(int, raw_input().split())
    if len(re) == 1 and not force_list:
        return re[0]
    return re

def inst():
    return raw_input().strip()

def gcd(x, y):
   while(y):
       x, y = y, x % y
   return x

mod = 1000000007

def my_main():
    T = inp()
    pr = []
    for _ in range(T):
        st = inst()
        x = inp()
        n = len(st)
        ans = ['1'] * n
        for idx, c in enumerate(st):
            if c=='0':
                if idx+x<n:
                    ans[idx+x] = '0'
                if idx-x>=0:
                    ans[idx-x] = '0'
        ok = 1
        for idx, c in enumerate(st):
            if c=='1':
                have = 0
                if idx+x<n and ans[idx+x]=='1':
                    have = 1
                if idx-x>=0 and ans[idx-x]=='1':
                    have = 1
                if have == 0:
                    ok = 0
        if ok:
            pr.append(''.join(ans))
        else:
            pr.append('-1')


    print '\n'.join(pr)






my_main()
