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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.Deque;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.Map.Entry;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Random;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

public class hacker49 {

	static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    }
	static long[] x= {1,1,1,0,0,0,-1,-1,-1};
	static long[] y= {1,-1,0,-1,0,1,1,-1,0};
	public static void main(String[] args) {
		OutputStream outputStream =System.out;
	    PrintWriter out =new PrintWriter(outputStream);
		FastReader s=new FastReader();
     int n=s.nextInt();
     long k=s.nextLong();
     long[] a=new long[n];
     HashSet<Long> e=new HashSet<>();
     for(int i=0;i<n;i++) {
    	 a[i]=s.nextLong();
    	 e.add(a[i]);
     }
         sf(a);
         Arrays.sort(a);
         int g=e.size();
    long[] b=new long[g+1];
    long[] c=new long[g+1];
    long d=a[0];
    c[1]=d;
    long f=1;
    int j=1;
    for(int i=1;i<n;i++) {
    	if(a[i]==d) {
    		f++;
    	}else {
    		
    		c[j]=d;
    		b[j]=f;
    		f=1;
    		j++;
    		d=a[i];
    	}
    }
        c[j]=d;
        b[j]=f;
//        for(int i=1;i<=n;i++) {
//        	System.out.println(b[i]+" "+c[i]);
//        }
        long sum=0;
        long ans=Long.MAX_VALUE;
        long freq=-1;
        long[] pre=new long[g+1];
        long[] pre2=new long[g+1];
        for(int i=1;i<=g;i++) {
        	if(i==1) {
        		pre[1]=0;
        		sum+=b[i];
        		pre2[i]=sum;
        	}else {
        		pre[i]=pre[i-1]+(sum-b[i-1])*(c[i]-c[i-1])+(b[i-1]*(c[i]-c[i-1]));
        	sum+=b[i];
        	pre2[i]=sum;
        	}
        }
//        for(int i=1;i<=n;i++) {
//        	out.print(pre[i]+" ");
//        }
//        out.println();
//        for(int i=1;i<=n;i++) {
//        	out.print(pre2[i]+" ");
//        }
        int i=-1;
        j=-1;
        
        int y=lower_bound(pre,k,g);
//        System.out.println(y);
        if(y>=g) {
        out.println(pre2[g]+" "+c[g]);
        }else {
        	freq=pre2[y];
        	ans=c[y];
        	j=y+1;
        	i=1;
        	long sum1=-1;
        	while(j<=g) {
        		sum1=pre[j]-(pre[i]+(pre2[i]-b[i])*(c[j]-c[i]));
        		while(sum1>k) {
        			sum1-=b[i]*(c[j]-c[i]);
        			i++;
        		}
        		long r=k-sum1;
        		long u=c[j]-c[i-1];
        		long l=(r/u);
//        		System.out.println(l);
        		
        		l+=pre2[j]-pre2[i-1];
//        		System.out.println(l);
//        		System.out.println(l+" "+c[j]);
        		if(l>freq) {
        			freq=l;
        			ans=c[j];
        		}else if(sum1==freq) {
        			ans=Math.min(ans, c[j]);
        		}
        		j++;
        	}
        	out.println(freq+" "+ans);
        }
			out.close();
	}
	public static int upper_bound(long[] a ,long x,int n) {
		int l=-1;
		int r=n;
		while(r>l+1) {
			int mid=(l+r)/2;
			if(a[mid]>=x) {
				r=mid;
			}else {
				l=mid;
			}
		}
		return r;
				
	}
	public static int lower_bound(long[] a ,long x,int n) {
		int l=0;
		int r=n+1;
		while(r>l+1) {
			int mid=(l+r)/2;
			if(a[mid]<=x) {
				l=mid;
			}else {
				r=mid;
			}
		}
		return l;
				
	}
	static long get=0;
	static int[] ans=new int[200001];
//	static int[] dx= {2,2,-2,-2,-1,-1,1,1};
//	static int[] dy= {1,-1,-1,1,-2,2,-2,2};
//	static int[][] vis1=new int[101][101];
//	static boolean valid(int x,int y,int n) {
//		if(x>=1 && x<=n && y>=1 && y<=n) {
//			return true;
//		}
//		return false;
//	}
//	static void dfs(int x,int y,char[][] a,int n,char t) {
//		a[x][y]=t;
//		vis1[x][y]=1;
//		for(int i=0;i<8;i++) {
//			if(valid(x+dx[i],y+dy[i],n) && vis1[x+dx[i]][y+dy[i]]==0) {
//				dfs(x+dx[i],y+dy[i],a,n,(t=='W')?'B':'W');
//			}
//		}
//	}

	static int[] h=new int[200001];
	static int[] subtree=new int[200001];
	static int[] vis=new int[200001];
	static HashMap<Integer,pair> e=new HashMap<>();
	static ArrayList<Integer>[] f1=new ArrayList[200001];	
	static PriorityQueue<pair> q=new PriorityQueue<>();	
	static ArrayList<pair>[] f=new ArrayList[200001];   
	static void bfs() {
		Queue<node> q=new LinkedList<>();
		q.add(new node(1,0));
		h[1]=0;
		vis[1]=1;
		while(!q.isEmpty()) {
			node p=q.poll();
//			h[p.a]=p.b;
			for(int i=0;i<f1[p.a].size();i++) {
				if(vis[f1[p.a].get(i)]==0) {
					q.add(new node(f1[p.a].get(i),p.b+1));
					h[f1[p.a].get(i)]=p.b+1;
					vis[f1[p.a].get(i)]=1;
				}
			}
		}
	}
	static int dfs(int node) {
		int c=1;
		vis[node]=1;
		for(int i=0;i<f1[node].size();i++) {
			if(vis[f1[node].get(i)]==0) {
				c+=dfs(f1[node].get(i));
			}
		}
		subtree[node]=c;
		return c;
	}
	static void dfs2(int node,int v) {
		vis[node]=1;
		if(ans[node]==1) {
			get+=v;
		}
		for(int i=0;i<f1[node].size();i++) {
			if(vis[f1[node].get(i)]==0) {
				dfs2(f1[node].get(i),v+((ans[node]==0)?1:0));
			}
		}
	}
static long m=-1;
static void sf(long[] arr){
        int n = arr.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i){
            long tmp = arr[i];
            int randomPos = i + rnd.nextInt(n-i);
            arr[i] = arr[randomPos];
            arr[randomPos] = tmp;
        }   
}

	static class pair implements Comparable<pair>{
		private int a;
		private int b;
		private int c;
		
		pair(int a,int b,int c){
			this.a=a;
//			this.f=f;
			this.b=b;
			this.c=c;
//			this.d=d;
//			this.e=e;
		}
		public int compareTo(pair o) {
			if(o.c!=this.c) {
			return Integer.compare(o.c, this.c);}
		else {
				return Integer.compare(this.b,o.b);
			}
		}
//		
		
	}
	static class node{
		private int a;
		private int b;
		node(int a,int b){
			this.a=a;
			this.b=b;
		}
	}

//	public static int upper_bound(long[] a ,long x,int n) {
//		int l=-1;
//		int r=n;
//		while(r>l+1) {
//			int mid=(l+r)/2;
//			if(a[mid]<x) {
//				l=mid;
//			}else {
//				r=mid;
//			}
//		}
//		return r;
//				
//	}
//	public static int lower_bound(long[] a ,long x,int m) {
//		int l=0;
//		int r=m+1;
//		while(r>l+1) {
//			int mid=(l+r)/2;
//			if(a[mid]>=x) {
//				r=mid;
//			}else {
//				l=mid;
//			}
//		}
//		return r;
//				
//	}
	public static long lb(int n,long[] pre,long k,long a,long b,long x,long y) {
		long l=0;
		long r=n+1;
		while(l<r) {
			long mid=(l+r)/2;
			long sum=0;
			long gcd=GCD(a,b);
			long g=mid/(a*b/gcd);
			long a1=mid/a;
			long b1=mid/b;
			sum+=(pre[(int) g]*(x+y))/100;
			if(x>=y) {
				sum+=((pre[(int) a1]-pre[(int) g])*x)/100;
				sum+=(((pre[(int)(a1+b1-g)]-pre[(int)(a1)])*y))/100;
			}else {
				sum+=((pre[(int) b1]-pre[(int) g])*y)/100;
				sum+=(((pre[(int)(a1+b1-g)]-pre[(int)(b1)])*x))/100;
			}
			if(sum>=k) {
				r=mid;
			}else {
				l=mid+1;
			}
//			System.out.println(mid+" "+h);
		}
		
		return r;
				
	}
	
	
	
	public static long[] merge_sort(long[] A, int start, int end) {
		if (end > start) {
			int mid = (end + start) / 2;
			long[] v = merge_sort(A, start, mid);
			long[] o = merge_sort(A, mid + 1, end);
			return (merge(v, o));
		} else {
			long[] y = new long[1];
			y[0] = A[start];
			return y;
		}
	}
	public static long[] merge(long a[], long b[]) {
		
		long[] temp = new long[a.length + b.length];
		int m = a.length;
		int n = b.length;
		int i = 0;
		int j = 0;
		int c = 0;
		while (i < m && j < n) {
			if (a[i] < b[j]) {
				temp[c++] = a[i++];
			
			} else {
				temp[c++] = b[j++];
			}
		}
		while (i < m) {
			temp[c++] = a[i++];
		}
		while (j < n) {
			temp[c++] = b[j++];
		}
		return temp;
	}	
	public static int[] Create(int[] a,int n) {
		int[] b=new int[n+1];
		for(int i=1;i<=n;i++) {
			int j=i;
			int h=a[i];
			while(i<=n) {
				b[i]+=h;
				i=get_next(i);
			}
			i=j;
		}
		return b;
	}
public static int get_next(int a) {
	return a+(a&-a);
}
public static int get_parent(int a) {
	return a-(a&-a);
}
public static int query_1(int[] b,int index) {
	int sum=0;
	if(index<=0) {
		return 0;
	}
	while(index>0) {
		sum+=b[index];
		index=get_parent(index);
	}
	return sum;
}
public static int query(int[] b,int n,int l,int r) {
	int sum=0;
	sum+=query_1(b,r);
	sum-=query_1(b,l-1);
	return sum;
}
public static void update(int[] a,int[] b,int n,int index,int val) {
	int diff=val-a[index];
	a[index]+=diff;
	while(index<=n) {
		b[index]+=diff;
		index=get_next(index);
	}	
}
	
//	public static void Create(int[] a,pair[] segtree,int low,int high,int pos) {
//		if(low>high) {
//			return;
//		}
//		if(low==high) {
//			segtree[pos].b.add(a[low]);
//			return ;
//		}
//		int mid=(low+high)/2;
//		Create(a,segtree,low,mid,2*pos);
//		Create(a,segtree,mid+1,high,2*pos+1);
//		segtree[pos].b.addAll(segtree[2*pos].b);
//		segtree[pos].b.addAll(segtree[2*pos+1].b);
//	}
//	public static void update(pair[] segtree,int low,int high,int index,int pos,int val,int prev) {
//		if(index>high || index<low) {
//			return ;
//		}
//		if(low==high && low==index) {
//			segtree[pos].b.remove(prev);
//			segtree[pos].b.add(val);
//			return;
//		}
//			int mid=(high+low)/2;
//			 update(segtree,low,mid,index,2*pos,val,prev);
//			 update(segtree,mid+1,high,index,2*pos+1,val,prev);
//			 segtree[pos].b.clear();
//			  segtree[pos].b.addAll(segtree[2*pos].b);
//			  segtree[pos].b.addAll(segtree[2*pos+1].b);
//			  
//	}
//	public static pair query(pair[] segtree,int low,int high,int qlow,int qhigh ,int pos) {
//		if(low>=qlow && high<=qhigh) {
//			return segtree[pos];
//		}
//		if(qhigh<low || qlow>high) {
//			return new pair();
//		}
//		int mid=(low+high)/2;
//	  pair a1=query(segtree,low,mid,qlow,qhigh,2*pos);
//	  pair a2=query(segtree,mid+1,high,qlow,qhigh,2*pos+1);
//	  pair a3=new pair();
//	  a3.b.addAll(a1.b);
//	  a3.b.addAll(a2.b);
//	  return a3;
//	  
//	}
//	
//	public static int nextPowerOf2(int n) 
//	{ 
//	    n--; 
//	    n |= n >> 1; 
//	    n |= n >> 2; 
//	    n |= n >> 4; 
//	    n |= n >> 8; 
//	    n |= n >> 16; 
//	    n++;     
//	    return n; 
//	} 
//	
////	static class pair implements Comparable<pair>{
////		private int a;
////		private long b;
//////		private long c;
////		pair(int a,long b){
////			this.a=a;
////			this.b=b;
//////			this.c=c;
////		}
////		public int compareTo(pair o) {
//////		if(this.a!=o.a) {
//////			return Long.compare(this.a, o.a);
//////		}else {
////			return Long.compare(o.b,this.b);
//////		}
////		}
////	}
//	static class pair implements Comparable<pair>{
//		private int a;
//		private int b;
//		pair(int a,int b){
////			this.b=new HashSet<>();
//			this.a=a;
//			this.b=b;
//		}
//		public int compareTo(pair o) {
//			return Integer.compare(this.b, o.b);
//		}
//	}
	public static int lower_bound(ArrayList<Long> a ,int n,long x) {
		int l=0;
		int r=n;
		while(r>l+1) {
			int mid=(l+r)/2;
			if(a.get(mid)<=x) {
				l=mid;
			}else {
				r=mid;
			}
		}
		return l;		
	}
	public static int[] is_prime=new int[1000001];
	public static ArrayList<Long> primes=new ArrayList<>();
 	public static void sieve() {
		long maxN=1000000;
		for(long i=1;i<=maxN;i++) {
			is_prime[(int) i]=1;
		}
		is_prime[0]=0;
		is_prime[1]=0;
		for(long i=2;i*i<=maxN;i++) {
			if(is_prime[(int) i]==1) {
//				primes.add((int) i);
				for(long j=i*i;j<=maxN;j+=i) {
					is_prime[(int) j]=0;
				}
			}
		}
		for(long i=0;i<=maxN;i++) {
			if(is_prime[(int) i]==1) {
				primes.add(i);
			}
		}		
	}
//	public static pair[] merge_sort(pair[] A, int start, int end) {
//		if (end > start) {
//			int mid = (end + start) / 2;
//			pair[] v = merge_sort(A, start, mid);
//			pair[] o = merge_sort(A, mid + 1, end);
//			return (merge(v, o));
//		} else {
//			pair[] y = new pair[1];
//			y[0] = A[start];
//			return y;
//		}
//	}
//	public static pair[] merge(pair a[], pair b[]) {
//		pair[] temp = new pair[a.length + b.length];
//		int m = a.length;
//		int n = b.length;
//		int i = 0;
//		int j = 0;
//		int c = 0;
//		while (i < m && j < n) {
//			if (a[i].b >= b[j].b) {
//				temp[c++] = a[i++];
//			
//			} else {
//				temp[c++] = b[j++];
//			}
//		}
//		while (i < m) {
//			temp[c++] = a[i++];
//		}
//		while (j < n) {
//			temp[c++] = b[j++];
//		}
//		return temp;
//	}
	public static long im(long a) {
		return binary_exponentiation_1(a,mod-2)%mod;
	}
	public static long binary_exponentiation_1(long a,long n) {
		long res=1;
		while(n>0) {
			if(n%2!=0) {
				res=((res)%(mod) * (a)%(mod))%(mod);
				n--;
			}else {
				a=((a)%(mod) *(a)%(mod))%(mod);
				n/=2;
			}
		}
		return (res)%(mod);
		
	}

	public static double bn1(double a,double n) {
		double res=1;
		while(n>0) {
			if(n%2!=0) {
//				res=((res)%(1000000007) * (a)%(1000000007))%(1000000007);
				res=(res*a);
				n--;
			}else {
//				a=((a)%(1000000007) *(a)%(1000000007))%(1000000007);
				a=(a*a);
				n/=2;
			}
		}
		return (res);	
	}
	public static long bn(long a,long n) {
		long res=1;
		while(n>0) {
			if(n%2!=0) {
				res=res*a;
				n--;
			}else {
				a*=a;
				n/=2;
			}
		}
		return res;
		
	}
public static long[] fac=new long[300001];
public static void ff() {
		fac[0]=(long)1;
		fac[1]=(long)1;
		for(long i=2;i<=300000;i++) {
			fac[(int) i]=(fac[(int) (i-1)]*i)%(m);
		}
	}	
public static long mod=998244353;
public static long GCD(long a,long b) {
		if(b==(long)0) {
			return a;
		}
		return GCD(b , a%b);
	}
public static long c=0;	
}