A piece of paper contains an array of n integers a1, a2, ..., an. Your task is to find a number that occurs the maximum number of times in this array.

However, before looking for such number, you are allowed to perform not more than k following operations — choose an arbitrary element from the array and add 1 to it. In other words, you are allowed to increase some array element by 1 no more than k times (you are allowed to increase the same element of the array multiple times).

Your task is to find the maximum number of occurrences of some number in the array after performing no more than k allowed operations. If there are several such numbers, your task is to find the minimum one.

Input

The first line contains two integers n and k (1 ≤ n ≤ 105; 0 ≤ k ≤ 109) — the number of elements in the array and the number of operations you are allowed to perform, correspondingly.

The third line contains a sequence of n integers a1, a2, ..., an (|ai| ≤ 109) — the initial array. The numbers in the lines are separated by single spaces.

Output

In a single line print two numbers — the maximum number of occurrences of some number in the array after at most k allowed operations are performed, and the minimum number that reaches the given maximum. Separate the printed numbers by whitespaces.

Examples

Input

5 3
6 3 4 0 2


Output

3 4


Input

3 4
5 5 5


Output

3 5


Input

5 3
3 1 2 2 1


Output

4 2

Note

In the first sample your task is to increase the second element of the array once and increase the fifth element of the array twice. Thus, we get sequence 6, 4, 4, 0, 4, where number 4 occurs 3 times.

In the second sample you don't need to perform a single operation or increase each element by one. If we do nothing, we get array 5, 5, 5, if we increase each by one, we get 6, 6, 6. In both cases the maximum number of occurrences equals 3. So we should do nothing, as number 5 is less than number 6.

In the third sample we should increase the second array element once and the fifth element once. Thus, we get sequence 3, 2, 2, 2, 2, where number 2 occurs 4 times.
import java.io.*;
import java.math.BigInteger;
import java.util.*;
 
 
 
 public class Main {
	public static InputReader in;
    public static PrintWriter pw;
 
 
 
	public static void main(String args[]) {
		new Thread(null, new Runnable() {
            public void run() {
                try{
                    solve();
                }
                catch(Exception e){
                    e.printStackTrace();
                }
            }
        }, "1", 1 << 26).start();
    }
	//static HashSet<Integer> set;
	static ArrayList<Integer> g[];
	static ArrayList<Integer> h[];
	//static boolean visited[];
	static long edje=0;
    static boolean vis[];
	static int col[];
	//static boolean[] visited;
	static int Parent[];
	static int Ans=0;
	static int min=Integer.MAX_VALUE;
	static boolean visited[];
	static int degree[];
	static int f[];
	static  int size[];
	//static int n;
	static int edjes=0;
	static int start=-1;
	static int end=-1;
	static boolean bool=false;
	static int Total=0;
	static int nums[];
	//static int a[];
	static int parent[];
	static int min1=Integer.MAX_VALUE;
	static HashSet set;
	//static int ans[];
	static int time1[];
	static int time2[];
	static int k=0;
//	static  HashSet<Integer>[] s;
	static int sum=0;
	static StringBuilder tmp=new StringBuilder();
	static HashMap<String,Integer> hm;
	static int ans[];
	static int val[];
	static  TreeSet<Integer> tp;
	static boolean vis2[][];
static int an2s=Integer.MAX_VALUE;
static  Stack<String> sr=new Stack();
static int n;
static String s[];
static int cnto=0;
static HashMap<Integer,Integer> map=new HashMap<Integer,Integer>();
public static void solve(){
		
	
		 in = new InputReader(System.in);
		 pw = new PrintWriter(System.out);
	     int n=in.nextInt();
         int x=in.nextInt();
         int a[]=in.nextIntArray(n);
         Arrays.sort(a);
         long sum[]=new long[n];
         sum[0]=(long)a[0];
         for(int i=1;i<n;i++)
        	 sum[i]=(long)a[i]+sum[i-1];
         //for(int i=0;i<n;i++)
        	// System.out.println(sum[i]);
         long fr[]=new long[n];
         long max=0;
        for(int i=0;i<n;i++)
         {
         //i=2;
        	 int high=i-1;
        	 int low=0;
        	 long ans=-1;
        	 while(low<=high)
        	 {
        		 int mid=(low+high)/2;
        		 long remain=(mid==0)?0:sum[mid-1];
        		 long sm=sum[i]-remain-a[i];
        		 long term=Math.abs(mid-i);
        		 long xx=(term*a[i])-(sm);
        		 //System.out.println(term+" "+sm+" "+xx+" "+mid);
        		 if(Math.abs(xx)<=x)
        		 {
        			 ans=term+1;
        			 high=mid-1;
        		 }
        		 else
        		 {
        			 
        			 low=mid+1;
        		 }
        			 
        	 }
        	 fr[i]=ans;
        	 max=Math.max(max, ans);
         }
         for(int i=0;i<n;i++)
         {
        	 if(fr[i]==max)
        	 {
        		 System.out.println(fr[i]+" "+a[i]);
        		 System.exit(0);
        	 }
         }
         System.out.println(1+" "+a[0]);
}
	
	public static void dfs2(int curr,int par,boolean visited[])
	{
		visited[curr]=true;
		cnto++;
		for(int x:g[curr])
		{
			if(!visited[x])
			{
				dfs2(x,par,visited);
			}
		}
	}
      public static void dfs(int i,int j,int x,int y)
      {
    	 int lev=1;
         Queue<String> Q=new LinkedList<String>();
         vis2[i][j]=true;
         Q.add(i+" "+j);
         while(!Q.isEmpty())
         {
        	 int cnt=Q.size();
            	while(cnt>0)
        	{
          String p=Q.poll();
          
          String s[]=p.split(" ");
          i=Integer.parseInt(s[0]);
          j=Integer.parseInt(s[1]);
          vis2[i][j]=true;
          
          if(i==n&&j==n)
          {
        	  an2s=Math.min(lev,an2s);
          }
    	  if(i+x<=n&&j+y<=n&&!vis2[i+x][j+y])
    	  {
    		  vis2[i+x][j+y]=true;
    		  Q.add((i+x)+" "+(j+y));
    	  }
    	  if(i+y<=n&&j+x<=n&&!vis2[i+y][j+x])
    	  {
    		  vis2[i+y][j+x]=true;
    		  Q.add((i+y)+" "+(j+x));
    	  }
    	  if(i-x>=1&&j+y<=n&&!vis2[i-x][j+y]){
    		vis2[i-x][j+y]=true;
    		  Q.add((i-x)+" "+(j+y));
    	  }
    	  if(i-y>=1&&j+x<=n&&!vis2[i-y][j+x]){
    		  vis2[i-y][j+x]=true;
    		  Q.add((i-y)+" "+(j+x));
    	  }
    	  if(i-x>=1&&j-y>=1&&!vis2[i-x][j-y]){
    		 vis2[i-x][j-y]=true;
    		  Q.add((i-x)+" "+(j-y));
    	  }
    	  if(i-y>=1&&j-x>=1&&!vis2[i-y][j-x]){
    		vis2[i-y][j-x]=true;
    		  Q.add((i-y)+" "+(j-x));
    	  }
    	  if(i+x<=n&&j-y>=1&&!vis2[i+x][j-y]){
    		vis2[i+x][j-y]=true;
    		  Q.add((i+x)+" "+(j-y));
    	  }
    	  if(i+y<=n&&j-x>=1&&!vis2[i+y][j-x]){
    		vis2[i+y][j-x]=true;
    		  Q.add((i+y)+" "+(j-x));
    	  }
          
    	  cnt--;
         }
        	lev++;
         }
       
      }
	
	
 
 
	/*
	 SubTree Checker DFS (TO CHECK IF X IS IN A SUBTREE OF Y)
	public static void dfs(int curr)
	{
		visited[curr]=true;
		time1[curr]=glob++;
		for(int x:g[curr])
		{
		if(!visited[x])
			dfs(x);
		}
		time2[curr]=glob++;
	}
    
	
	
 
    /*NO OF EDJES IN WHOLE CONNECTED COMPONENTS
  
	public static void dfs1(int curr)
	{
		visited[curr]=true;
		for(int next:g[curr])
		{
			edje++;
			if(!visited[next])
				dfs1(next);
		}
	}
	/*SUM OF ALL SUBTREE NODE'S VLAUES DFS
	public static void dfs(int curr,int prev)
		{
		val[curr]=1;
			for(int x:g[curr])
			{
				if(x!=prev)
				{
		            dfs(x,curr);
		            val[curr]+=val[x];
					
			    }
			}
		}*/
	
		public static long power(long a,long b)
		{
			long result=1;
			while(b>0)
			{
				if(b%2==1)
					result*=a;
				a=a*a;
				b/=2;
			}
			return result;
		}
				public static long pow(long n,long p,long m)
	{
		 long  result = 1;
		  if(p==0)
		    return 1;
		if (p==1)
		    return n;
		while(p!=0)
		{
		    if(p%2==1)
		        result *= n;
		    if(result>=m)
		    result%=m;
		    p >>=1;
		    n*=n;
		    if(n>=m)
		    n%=m;
		}
		return result;
	}
	static class Pair implements Comparable<Pair>{
	int num;
		int cost;
		Pair(int mr,int i){
	     	num=mr;
			cost=i;
			
		}
		@Override
		public int compareTo(Pair o) {
		      //  if(o.dis<this.dis)
		        	return 1;
		       // else
		        //	return -1;
			
			}
		
	}
	public static long gcd(long a, long b) {
		  if (b == 0) return a;
		  return gcd(b, a%b);
		}
	static class InputReader {
 
		private InputStream stream;
		private byte[] buf = new byte[8192];
		private int curChar, snumChars;
		private SpaceCharFilter filter;
 
		public InputReader(InputStream stream) {
			this.stream = stream;
		}
 
		public int snext() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
 
		public   int nextInt() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
 
		public long nextLong() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
 
		public int[] nextIntArray(int n) {
			int a[] = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}
 
		public String readString() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = snext();
			} while (!isSpaceChar(c));
			return res.toString();
		}
 
		public boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
 
		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	}
}
 
