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
import math
import bisect
from sys import stdin, stdout
from math import gcd, floor, sqrt, log2, ceil
from collections import defaultdict as dd
from bisect import bisect_left as bl, bisect_right as br
from bisect import insort
from collections import Counter
from collections import deque
from heapq import heappush,heappop,heapify
from itertools import permutations,combinations
mod = int(1e9)+7

 
ip = lambda : int(stdin.readline())
inp = lambda: map(int,stdin.readline().split())
ips = lambda: stdin.readline().rstrip()
                   
t = ip()
for _ in range(t):
    s = ips()
    x = ip()
    n = len(s)
    ans = [None]*n
    flag = True
    for i in range(x):
        pos = i+x
        if pos<n:
            if ans[pos] == None:
                ans[pos] = s[i]
            else:
                if ans[pos] != s[i]:
                    flag = False
                    break
    for i in range(n-x,n):
        pos = i-x
        if pos>=0:
            if ans[pos] == None:
                ans[pos] = s[i]
            else:
                if ans[pos] != s[i]:
                    flag = False
                    break
    for i in range(n):
        if s[i] == '0':
            if i+x<n:
                if ans[i+x] == None:
                    ans[i+x] = '0'
                else:
                    if ans[i+x] == '0':
                        pass
                    else:
                        flag = False
                        break
            if i-x>=0:
                if ans[i-x] == None:
                    ans[i-x] = '0'
                else:
                    if ans[i-x] == '0':
                        pass
                    else:
                        flag = False
                        break
        if i-x<0 and i+x>=n:
            if s[i] == '1':
                flag = False
                break
                    
    if flag:
        for i in range(n):
            if ans[i] == None:
                ans[i] = '1'
        ans = ''.join(ans)
        ch = [None]*n
        for i in range(n):
            if i-x<0 and i+x>=n:
                ch[i] = '0'
            else:
                if i-x>= 0:
                    if ans[i-x] == '1':
                        ch[i] = '1'
                if i+x<n:
                    if ans[i+x] == '1':
                        ch[i] = '1'
                if ch[i] == None:
                    ch[i] = '0'
        ch = ''.join(ch)
        if s == ch:
            print(ans)
        else:
            print(-1)
    else:
        print(-1)
        
    
                
        
