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 heapq
import collections
def inputnum():
    return(int(input()))
def inputnums():
    return(map(int,input().split()))
def inputlist():
    return(list(map(int,input().split())))
def inputstring():
    return([x for x in input()])
def inputstringnum():
    return([ord(x)-ord('a') for x in input()])
def inputmatrixchar(rows):
    arr2d = [[j for j in input().strip()] for i in range(rows)] 
    return arr2d
def inputmatrixint(rows):
    arr2d = []
    for _ in range(rows):
        arr2d.append([int(i) for i in input().split()])
    return arr2d
    
t = int(input())
for q in range(t):
    s = inputstring()
    x = inputnum()
    n = len(s)
    w = ['1']*n
    for i in range(n):
        if s[i] == '0':
            if i+x < n:
                w[i+x] = '0'
            if i-x >= 0:
                w[i-x] = '0'
    done = False
    for i in range(n):
        if s[i] == '1':
            if (i-x < 0 or (i-x >= 0 and w[i-x] == '0')) and (i+x >= n or (i+x < n and w[i+x] == '0')):
                done = True
                break
    if done:
        print(-1)
    else:
        for c in w:
            print(c, end = '')
    print()