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
# sys.stdin = open('input.txt', 'r') 
# sys.stdout = open('output.txt', 'w')
 
import math
import collections
from sys import stdin,stdout,setrecursionlimit
import bisect as bs
setrecursionlimit(2**20)
M = 10**9+7
    
T = int(stdin.readline())
# T = 1

for _ in range(T):
    # n = int(stdin.readline())
    # n,d,m = list(map(int,stdin.readline().split()))
    # a = list(map(int,stdin.readline().split()))
    # q = int(stdin.readline())
    # a = list(map(int,stdin.readline().split()))
    # b = list(map(int,stdin.readline().split()))
    s = stdin.readline().strip('\n')
    x = int(stdin.readline())
    n = len(s)
    a = [-1]*n
    res = True
    for i in range(n):
        if(s[i] == '1'):
            if((i-x) >= 0 and a[i-x] != 0):
                a[i-x] = 1
                continue
            if((i+x) < n):
                if(a[i+x] == 0):
                    res = False
                    break
                else:
                    a[i+x] = 1
                    continue
            res = False
            break
        else:
            if((i-x) >= 0):
                if(a[i-x] == 1):
                    res = False
                    break
                else:
                    a[i-x] = 0
            if((i+x) < n):
                if(a[i+x] == 1):
                    res = False
                    break
                else:
                    a[i+x] = 0
    ans = ''
    for i in range(n):
        if(a[i] != -1):
            ans = ans + str(a[i])
        else:
            ans = ans + '1'
    if(res): print(ans)
    else: print(-1)
    