There are n benches in the Berland Central park. It is known that a_i people are currently sitting on the i-th bench. Another m people are coming to the park and each of them is going to have a seat on some bench out of n available.

Let k be the maximum number of people sitting on one bench after additional m people came to the park. Calculate the minimum possible k and the maximum possible k.

Nobody leaves the taken seat during the whole process.

Input

The first line contains a single integer n (1 ≤ n ≤ 100) — the number of benches in the park.

The second line contains a single integer m (1 ≤ m ≤ 10 000) — the number of people additionally coming to the park.

Each of the next n lines contains a single integer a_i (1 ≤ a_i ≤ 100) — the initial number of people on the i-th bench.

Output

Print the minimum possible k and the maximum possible k, where k is the maximum number of people sitting on one bench after additional m people came to the park.

Examples

Input

4
6
1
1
1
1


Output

3 7


Input

1
10
5


Output

15 15


Input

3
6
1
6
5


Output

6 12


Input

3
7
1
6
5


Output

7 13

Note

In the first example, each of four benches is occupied by a single person. The minimum k is 3. For example, it is possible to achieve if two newcomers occupy the first bench, one occupies the second bench, one occupies the third bench, and two remaining — the fourth bench. The maximum k is 7. That requires all six new people to occupy the same bench.

The second example has its minimum k equal to 15 and maximum k equal to 15, as there is just a single bench in the park and all 10 people will occupy it.
import java.util.*;
import java.io.*;
import java.math.*;
public class k
{
    static class InputReader {
        public BufferedReader br;
        public StringTokenizer token;
        public InputReader(InputStream stream)
        {
            br=new BufferedReader(new InputStreamReader(stream),32768);
            token=null;
        }
 
        public String next()
        {
            while(token==null || !token.hasMoreTokens())
            {
                try
                {
                    token=new StringTokenizer(br.readLine());
                }
                catch(IOException e)
                {
                    throw new RuntimeException(e);
                }
            }
            return token.nextToken();
        }
 
        public int nextInt()
        {
            return Integer.parseInt(next());
        }
 
        public long nextLong()
        {
            return Long.parseLong(next());
        }
    }
    static class card{
        long a;
        int i;
        public card(long a,int i)
        {
            this.a=a;
            this.i=i;
        }
    }
    static class sort implements Comparator<pair>
    {
        public int compare(pair o1,pair o2)
        {
            if(o1.a!=o2.a)
            return (o1.a-o2.a)*-1;
            else
            return (o1.b-o2.b);
        }
    }
    /*static class sort1 implements Comparator<pair>
    {
    public int compare(pair o1,pair o2)
    {
    if(o1.a!=o2.a)
    return (int)(o1.a-o2.a);
    else
    return (o1.b-o2.b);
    }
    }*/
    static class extra{
        static void shuffle(int a[])
        {
            List<Integer> l=new ArrayList<>();
            for(int i=0;i<a.length;i++)
                l.add(a[i]);
            Collections.shuffle(l);
            for(int i=0;i<a.length;i++)
                a[i]=l.get(i);
        }
 
        static long gcd(long a,long b)
        {
            if(b==0)
                return a;
            else
                return gcd(b,a%b);
        }
 
        static boolean valid(int i,int j,int r,int c)
        {
            if(i>=0 && i<r && j>=0 && j<c)
                return true;
            else
                return false;
        }
        static boolean v[]=new boolean[100001];
        static List<Integer> l=new ArrayList<>();
        static int t;
        static void seive()
        {
            for(int i=2;i<100001;i++)
            {
                if(!v[i])
                {
                    t++;
                    l.add(i);
                    for(int j=2*i;j<100001;j+=i)
                        v[j]=true;
                }
            }
        }
 
        static int binary(long a[],long val,int n)
        {
            int mid=0,l=0,r=n-1,ans=0;
            while(l<=r)
            {
                mid=(l+r)>>1;
                if(a[mid]==val)
                {
                    r=mid-1;
                    ans=mid;
                }
                else if(a[mid]>val)
                    r=mid-1;
                else
                {
                    l=mid+1;
                    ans=l;
                }
            }
            return (ans+1);
        }
    }
    static class pair{
        int a;
        int b;
        public pair(int a,int n)
        {
            this.a=a;
            this.b=n;
        }
    }
    static InputReader sc=new InputReader(System.in);
    static PrintWriter out=new PrintWriter(System.out);
    public  static void main(String[] args) 
    {
        solver s=new solver();
        int t=1;
        while(t>0)
        {
            s.solve();
            t--;
        }
    }
    static class solver
    {
        void solve()
        {
            int n=sc.nextInt();
            int m=sc.nextInt();
            int a[]=new int[n];
            for(int i=0;i<n;i++)
            {
                a[i]=sc.nextInt();
            }
            new extra().shuffle(a);
            Arrays.sort(a);
            int max=a[n-1]+m;
            int  f=0;
            for(int i=0;i<n-1;i++)
            {
                if(m>=(a[n-1]-a[i]))
                {
                    m-=a[n-1]-a[i];
                }
                else 
                {
                    f=1;
                    break;
                }
            }
            int min=a[n-1];
            if(f==0)
            {
                if(m>0)
                {
                   min+=(m/n)+(((m%n)!=0)?1:0); 
                }
            }
            System.out.println(min+" "+max);
        }
    }
}
 