Jon Snow and his Favourite Number



C. Jon Snow and his Favourite Number


time limit per test

 4 seconds


memory limit per test

 256 megabytes


input

 standard input


output

 standard output


Jon Snow now has to fight with White Walkers. He has n rangers, each of which has his own strength. Also Jon Snow has his favourite

number x. Each ranger can fight with a white walker only if the strength of the white walker equals his strength. He however thinks

that his rangers are weak and need to improve. Jon now thinks that if he takes the bitwise XOR of strengths of some of rangers with his favourite number x,

he might get soldiers of high strength. So, he decided to do the following operation k times:




  1. Arrange all the rangers in a straight line in the order of increasing strengths.


  2. Take the bitwise XOR (is written as )

    of the strength of each alternate ranger with x and update it's strength.


Suppose, Jon has 5 rangers with strengths [9, 7, 11, 15, 5] and

he performs the operation 1 time with x = 2.

He first arranges them in the order of their strengths, [5, 7, 9, 11, 15]. Then he does the following:




  1. The strength of first ranger is updated to ,

    i.e. 7.


  2. The strength of second ranger remains the same, i.e. 7.


  3. The strength of third ranger is updated to ,

    i.e. 11.


  4. The strength of fourth ranger remains the same, i.e. 11.


  5. The strength of fifth ranger is updated to ,

    i.e. 13.


The new strengths of the 5 rangers are [7, 7, 11, 11, 13]



Now, Jon wants to know the maximum and minimum strength of the rangers after performing the above operations k times. He wants your

help for this task. Can you help him?


Input


First line consists of three integers nkx (1 ≤ n ≤ 105, 0 ≤ k ≤ 105, 0 ≤ x ≤ 103)

— number of rangers Jon has, the number of times Jon will carry out the operation and Jon's favourite number respectively.


Second line consists of n integers representing the strengths of the rangers a1, a2, ..., an (0 ≤ ai ≤ 103).


Output


Output two integers, the maximum and the minimum strength of the rangers after performing the operation k times.


Examples


input


5 1 2
9 7 11 15 5

output


13 7

input


2 100000 569
605 986

output


986 605



#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstring>
#include<queue>
#include<vector>
#include<algorithm>
int maxi[100005];
int mini[100005];
using namespace std;
vector <int> a;
int main()
{
int m,k,n,data;
scanf("%d%d%d",&m,&k,&n);
for (int i=0;i<m;i++)
{
scanf("%d",&data);
a.push_back(data);
}
sort(a.begin(),a.end());
maxi[0]=a[m-1];
//
mini[0]=a[0];

for(int i=1;i<=k;i++)
{
sort(a.begin(),a.end());
maxi[i]=a[m-1];
mini[i]=a[0];
if (i>=3)
{
if(maxi[i]==maxi[i-1]&&mini[i]==mini[i-1]
&&maxi[i]==maxi[i-2]&&mini[i]==mini[i-2]
&&maxi[i]==maxi[i-3]&&mini[i]==mini[i-3])
{
cout<<a[m-1]<<" "<<a[0]<<endl;
return 0;
}
}
for(int j=0;j<a.size();j+=2)
{
a[j]^=n;
}
}
sort(a.begin(),a.end());
cout<<a[m-1]<<" "<<a[0]<<endl;
}

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