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
from math import sqrt
from collections import defaultdict
inpt = sys.stdin.readline

def inp():
    return(int(inpt()))

def inlist():
    return(list(map(int,inpt().split())))

def instr():
    s = inpt()
    return(list(s[:len(s)-1]))

def invr():
    return(map(int,inpt().split()))

class Graph:

    def __init__(self,n):
        self.n = n
        self.graph = defaultdict(list)
        self.marked = defaultdict(int)
    
    def addEdge(self,u,v):
        self.graph[u].append(v)
        self.graph[v].append(u)

    def dfs(self,u):

        self.marked[u] = 1

        for i in self.graph[u]:
            if(self.marked[i] == 0):
                self.dfs(i)

def main():
        
        t = inp()

        for l in range(t):

            s = instr()
            x = inp()

            w = ['1']*len(s)

            for i in range(len(s)):
                if(s[i] == '0'):
                    if(i-x>=0):
                        w[i-x] = '0'
                    if(i+x<len(s)):
                        w[i+x] = '0'

            chk = True
            
            for i in range(len(s)):
                if(s[i] == '1'):
                    if((i-x<0 or w[i-x]=='0') and (i+x>=len(s) or w[i+x]=='0')):
                        chk = False
                        break

            if(chk):
                for i in range(len(w)):
                    print(w[i],end='')
                print()
            else:
                print(-1)

main() 

