As you know, all the kids in Berland love playing with cubes. Little Petya has n towers consisting of cubes of the same size. Tower with number i consists of ai cubes stacked one on top of the other. Petya defines the instability of a set of towers as a value equal to the difference between the heights of the highest and the lowest of the towers. For example, if Petya built five cube towers with heights (8, 3, 2, 6, 3), the instability of this set is equal to 6 (the highest tower has height 8, the lowest one has height 2). 

The boy wants the instability of his set of towers to be as low as possible. All he can do is to perform the following operation several times: take the top cube from some tower and put it on top of some other tower of his set. Please note that Petya would never put the cube on the same tower from which it was removed because he thinks it's a waste of time. 

Before going to school, the boy will have time to perform no more than k such operations. Petya does not want to be late for class, so you have to help him accomplish this task.

Input

The first line contains two space-separated positive integers n and k (1 ≤ n ≤ 100, 1 ≤ k ≤ 1000) — the number of towers in the given set and the maximum number of operations Petya can perform. The second line contains n space-separated positive integers ai (1 ≤ ai ≤ 104) — the towers' initial heights.

Output

In the first line print two space-separated non-negative integers s and m (m ≤ k). The first number is the value of the minimum possible instability that can be obtained after performing at most k operations, the second number is the number of operations needed for that.

In the next m lines print the description of each operation as two positive integers i and j, each of them lies within limits from 1 to n. They represent that Petya took the top cube from the i-th tower and put in on the j-th one (i ≠ j). Note that in the process of performing operations the heights of some towers can become equal to zero.

If there are multiple correct sequences at which the minimum possible instability is achieved, you are allowed to print any of them.

Examples

Input

3 2
5 8 5


Output

0 2
2 1
2 3


Input

3 4
2 2 4


Output

1 1
3 2


Input

5 3
8 3 2 6 3


Output

3 3
1 3
1 2
1 3

Note

In the first sample you need to move the cubes two times, from the second tower to the third one and from the second one to the first one. Then the heights of the towers are all the same and equal to 6.
    			/*
    		     * Author- Priyam Vora
    		     * BTech 2nd Year DAIICT
    		     */
    		     
    		            
    		    import java.io.*;
    		    import java.math.*;
    		    import java.util.*;
import java.util.concurrent.ConcurrentHashMap;

import javax.print.attribute.SetOfIntegerSyntax;


    		     
    		    public class Practice{
    		    	private static InputStream stream;
    		    	private static byte[] buf = new byte[1024];
    		    	private static int curChar;
    		    	private static int numChars;
    		    	private static SpaceCharFilter filter;
    		    	private static PrintWriter pw;
    		    	private static long count = 0,mod=1000000007;
    		    //	private static TreeSet<Integer> ts=new TreeSet[200000];
    		    
    		        public static void main(String[] args) {
    		        	InputReader(System.in);
    		    		pw = new PrintWriter(System.out); 
    		            new Thread(null ,new Runnable(){
    		               public void run(){
    		                   try{
    		                       soln2();
    		                       pw.close();
    		                   } catch(Exception e){
    		                       e.printStackTrace();
    		                   }
    		               }
    		           },"1",1<<26).start();
    		       }
    		    
    		    	public static long gcd(long x, long y) {
    		    		if (x == 0)
    		    			return y;
    		    		else
    		    			return gcd( y % x,x);
    		    	}
    		    	public static String reverseString(String s) {
    		    		StringBuilder sb = new StringBuilder(s);
    		    		sb.reverse();
    		    		return (sb.toString());
    		    	}
    		    	
    		    	public static long pow(long n, long p) {
    		    		if(p==0)
    		    			return 1;
    		    		if(p==1)
    		    			return n%10;
    		    		if(p%2==0){
    		    			long temp=pow(n, p/2);
    		    		return (temp*temp)%10;
    		    		}else{
    		    			 	long temp=pow(n,p/2);
    		    			 	temp=(temp*temp)%10;
    		    			 	return(temp*n)%10;
    		    			 	
    		    		}
    		    	}
    		     
    		    		
    		     
    		    	public static boolean isPrime(int n) {
    		    		// Corner cases
    		    		if (n <= 1)
    		    			return false;
    		    		if (n <= 3)
    		    			return true;
    		     
    		    		// This is checked so that we can skip 
    		    		// middle five numbers in below loop
    		    		if (n % 2 == 0 || n % 3 == 0)
    		    			return false;
    		     
    		    		for (int i = 5; i * i <= n; i = i + 6)
    		    			if (n % i == 0 || n % (i + 2) == 0)
    		    				return false;
    		     
    		    		return true;
    		    	}
    		     
    		    	// To Get Input
    		    	// Some Buffer Methods
    		     
    		    	public static void InputReader(InputStream stream1) {
    		    		stream = stream1;
    		    	}
    		     
    		    	private static boolean isWhitespace(int c) {
    		    		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    		    	}
    		     
    		    	private static boolean isEndOfLine(int c) {
    		    		return c == '\n' || c == '\r' || c == -1;
    		    	}
    		     
    		    	private static int read() {
    		    		if (numChars == -1)
    		    			throw new InputMismatchException();
    		    		if (curChar >= numChars) {
    		    			curChar = 0;
    		    			try {
    		    				numChars = stream.read(buf);
    		    			} catch (IOException e) {
    		    				throw new InputMismatchException();
    		    			}
    		    			if (numChars <= 0)
    		    				return -1;
    		    		}
    		    		return buf[curChar++];
    		    	}
    		     
    		    	private static int nextInt() {
    		    		int c = read();
    		    		while (isSpaceChar(c))
    		    			c = read();
    		    		int sgn = 1;
    		    		if (c == '-') {
    		    			sgn = -1;
    		    			c = read();
    		    		}
    		    		int res = 0;
    		    		do {
    		    			if (c < '0' || c > '9')
    		    				throw new InputMismatchException();
    		    			res *= 10;
    		    			res += c - '0';
    		    			c = read();
    		    		} while (!isSpaceChar(c));
    		    		return res * sgn;
    		    	}
    		     
    		    	private static long nextLong() {
    		    		int c = read();
    		    		while (isSpaceChar(c))
    		    			c = read();
    		    		int sgn = 1;
    		    		if (c == '-') {
    		    			sgn = -1;
    		    			c = read();
    		    		}
    		    		long res = 0;
    		    		do {
    		    			if (c < '0' || c > '9')
    		    				throw new InputMismatchException();
    		    			res *= 10;
    		    			res += c - '0';
    		    			c = read();
    		    		} while (!isSpaceChar(c));
    		    		return res * sgn;
    		    	}
    		     
    		    	private static String nextToken() {
    		    		int c = read();
    		    		while (isSpaceChar(c))
    		    			c = read();
    		    		StringBuilder res = new StringBuilder();
    		    		do {
    		    			res.appendCodePoint(c);
    		    			c = read();
    		    		} while (!isSpaceChar(c));
    		    		return res.toString();
    		    	}
    		     
    		    	private static String nextLine() {
    		    		int c = read();
    		    		while (isSpaceChar(c))
    		    			c = read();
    		    		StringBuilder res = new StringBuilder();
    		    		do {
    		    			res.appendCodePoint(c);
    		    			c = read();
    		    		} while (!isEndOfLine(c));
    		    		return res.toString();
    		    	}
    		     
    		    	private static int[] nextIntArray(int n) {
    		    		int[] arr = new int[n];
    		    		for (int i = 0; i < n; i++) {
    		    			arr[i] = nextInt();
    		    		}
    		    		return arr;
    		    	}
    		     
    		    	private static int[][] next2dArray(int n, int m) {
    		    		int[][] arr = new int[n][m];
    		    		for (int i = 0; i < n; i++) {
    		    			for (int j = 0; j < m; j++) {
    		    				arr[i][j] = nextInt();
    		    			}
    		    		}
    		    		return arr;
    		    	}
    		    	private static char[][] nextCharArray(int n,int m){
    		    		char [][]c=new char[n][m];
    		    		for(int i=0;i<n;i++){
    		    			String s=nextLine();
    		    			for(int j=0;j<s.length();j++){
    		    				c[i][j]=s.charAt(j);
    		    			}
    		    		}
    		    		return c;
    		    	}
    		     
    		    	private static long[] nextLongArray(int n) {
    		    		long[] arr = new long[n];
    		    		for (int i = 0; i < n; i++) {
    		    			arr[i] = nextLong();
    		    		}
    		    		return arr;
    		    	}
    		     
    		    	private static void pArray(int[] arr) {
    		    		for (int i = 0; i < arr.length; i++) {
    		    			pw.print(arr[i] + " ");
    		    		}
    		    		pw.println();
    		    		return;
    		    	}
    		     
    		    	private static void pArray(long[] arr) {
    		    		for (int i = 0; i < arr.length; i++) {
    		    			pw.print(arr[i] + " ");
    		    		}
    		    		pw.println();
    		    		return;
    		    	}
    		     
    		    	private static void pArray(boolean[] arr) {
    		    		for (int i = 0; i < arr.length; i++) {
    		    			pw.print(arr[i] + " ");
    		    		}
    		    		pw.println();
    		    		return;
    		    	}
    		     
    		    	private static boolean isSpaceChar(int c) {
    		    		if (filter != null)
    		    			return filter.isSpaceChar(c);
    		    		return isWhitespace(c);
    		    	}
    		     
    		    	private interface SpaceCharFilter {
    		    		public boolean isSpaceChar(int ch);
    		    	}


     		        
     		       private static void soln2(){
    		  
     		        int n=nextInt();
     		        int k=nextInt();
     		        
     		        Pair p[]=new Pair[n];
     		        for(int i=0;i<n;i++ ){
     		        	p[i]=new Pair(nextInt(), i+1);
     		        }
     		      
     		  
     		        	Arrays.sort(p);
     		           long min_diff=p[n-1].val-p[0].val;
     		        	int c=0;
     		        	while(k-->0){
     		        		if(p[n-1].val==p[0].val)
     		        			break;
     		        		p[n-1].val--;
     		        		p[0].val++;
     		        		int ind1=p[n-1].ind;
     		        		int ind2=p[0].ind;
     		        		Arrays.sort(p);
     		        		long diff=p[n-1].val-p[0].val;
     		        		if(min_diff>=diff){
     		        			min_diff=diff;
     		        		}
     		        		else{
     		        			break;
     		        		}
     		        	
     		        	pw.println(ind1+" "+ind2);
     		        	
     	c++;	        		
     		        	}
     		        	System.out.println(min_diff+" "+c);
     		        }    		    
    		    	
    			
    		    	
    		    	 		    	
    		    }
    		    class Node{
    		    	int val;
    		    	int ind;
    		    	
    		    	Node(int val,int ind){
    		    		this.val=val;
    		    		this.ind=ind;
    		    	}
    		    	
    		    }
    		    
    		    
    		    class Pair implements Comparable<Pair>{
 	     			   
               	    	
        				int ind,val;
        				Pair(int val,int ind){
        				this.ind=ind;
        				this.val=val;
        				}
    					@Override
    					public int compareTo(Pair o) {
    						
  
    					

    					return val-o.val;
    					}
               		
        		    
    			/*	public int hashCode() {
					//	return 0;
    	    			int hu = (int) (row ^ (row >>> 32));
    	    			int hv = (int) (col ^ (col >>> 32));
    	    			return 31 * hu + hv;
    	    		}
    				public boolean equals(Object o) {
    	    			Pair other = (Pair) o;
    	    		return row == other.row && col == other.col;
    	    		}
    		*/
    		    	}
    		        class Graph{
    		        	private static int V,level[][],count=-1,lev_dfs[],degree=0,no_vert_conn_comp=0;
    		        	private Stack <Integer>st=new Stack();
    		        	private static LinkedList<Integer > adj[];
    		        	private boolean[][] Visite;
    		        	private static boolean [] Visited;
    		        	private static HashSet<Integer> Vis=new HashSet();
    		        	private static Stack<Integer> topo_sort=new Stack<>();
    		        	private static HashMap<String,Integer> hm=new HashMap<>();
    		  private static HashSet<String> hs=new HashSet();
    		private static HashSet<String > exist=new HashSet();
    		private static int a[];

    		
    		    Graph(int V){
    		    V++;
    		    this.V=(V);
    		    adj=new LinkedList[V];
    		    Visite=new boolean[100][100];
    		    
    	 	    Visited=new boolean[V];
    		    level=new int[100][100];
    		    lev_dfs=new int[V]; 
    		   for(int i=0;i<V;i++)
    			   adj[i]=new LinkedList<Integer>();
    		a=new int[V+1];
    		    }
    		   
    		    void setup(int d[]){
  
    		    	a=Arrays.copyOf(d, d.length);
    		    	
    		    }
    		    void ans(){
    		    	StringBuilder sb=new StringBuilder();
    		    	for(int i=1;i<a.length;i++){
    		    		sb.append(a[i]+" ");
    		    	}
    		    	System.out.println(sb);
    		    }
    		   void addEdge(int v,int w){
    		    
    		    	if(adj[v]==null){
    		    		adj[v]=new LinkedList();
    		    	}
    		    	adj[v].add(w);
    		    
    		    	
    		    
    		    	  	
    		    }
    		  
    		    public static int BFS2(int startVert){
    		    	Visited=new boolean[V];
    		    	for(int i=1;i<V;i++){
    		    		lev_dfs[i]=-1;
    		    	}
    		    //	System.out.println(startVert);
    		    	Queue<Integer> q=new LinkedList<Integer>();
    		    	q.add(startVert);
    		    	
    		    	lev_dfs[startVert]=0;
    		    	while(!q.isEmpty()){
    		    		int top=q.poll();
    		    		
    		    		Iterator<Integer> i= adj[top].listIterator();
    		    		while(i.hasNext()){
    		    			int n=i.next();
    		    	//		System.out.println(top+" "+n);
    		    			if(!Visited[n]){
    		    				q.add(n);
    		    				Visited[n]=true;
    		    				lev_dfs[n]=lev_dfs[top]+1;
    		    			
    		    			}
    		    		}
    		    	}
    		    
    		    //	q.clear();
    		    	return -1;
    		    }
    		    public static int getAn(){
    		    	if(ans==Long.MAX_VALUE)
    		    		ans=-1;
    		    	return 0;
    		    }
    		    public int getEd(){
    		    	return degree/2;
    		    }
    		    public void get(int from,int to){
    		    	int h=lev_dfs[from]-lev_dfs[to];
    		    	if(h<=0){
    		    		System.out.println(-1);
    		    	}else{
    		    		System.out.println(h-1);
    		    	}
    		    }
    		    private static boolean check(int x,int y,char c[][]){
    			
    				if((x>=0 && y>=0) && (x<c.length && y<c[0].length) && c[x][y]!='#'){
    					
    					return true;
    				}
    				return false;
    			}
    		    public int BFS(int x,int y,int k,char[][] c)
    		    {
    		    	 LinkedList<Pair> queue = new LinkedList<Pair>();
    		        //Visited[s]=true;
    		   //     queue.add(new Pair(x,y));
    		       int count=0;
    		   level[x][y]=-1;
    		   c[x][y]='M';
    		        while (!queue.isEmpty())
    		        {
    		            Pair temp = queue.poll();
    		        
    		            
    		        }
    		        return V;
    		    }
    		    static long ans=Long.MAX_VALUE;
    		    
    		   public static void dfs2(int startVert,int endVert,long need){
    			Visited[startVert]=true;
    			//System.out.println(startVert+" "+need);
    			   for(int x:adj[startVert]){
    				if(x==endVert ){
    					String to="";
    					to+=startVert+" "+x;
    					
    					if(hs.contains(to) && startVert!=x)
    					ans=Math.min(need+1, ans);
    					else
    						ans=Math.min(need, ans);
    				}
    				else{
    					String to="";
    					to+=startVert+" "+x;
    					boolean tmp=false;
    					if(hs.contains(to) )
    						tmp=true;
    					if(!Visited[x])
    					{
    					if(tmp)
    						dfs2(x, endVert, need+1);
    					else{
    						dfs2(x, endVert, need);
    					}
    					}
    					}
    			}
    			   
    			   
    		   }
    		     public long dfs(int startVertex){
    		    //	 getAns(startVertex);
    		    	 if(!Visited[startVertex])  {
    		    	
    		   return dfsUtil(startVertex);
    		  
    		    	//return getAns();
    		    	}
    		    	 
    		    
    		     
    		    return 0;
    		    	}
    		 private long dfsUtil(int startVertex) {//0-Blue 1-Pink
    			 int c=1;
    		TreeSet<Integer> index=new TreeSet();
    		TreeSet<Integer> ele=new TreeSet(Collections.reverseOrder());
    			 long cout=0;
    		      degree=0;
    		    	Visited[startVertex]=true;
    		    	lev_dfs[startVertex]=0;
    		      st.push(startVertex);
    		      int temp=-1;
    		    	    while(!st.isEmpty()){
    		    	
    		    	int top=st.pop();
    		    //	ts.add(top);
    		    	Iterator<Integer> i=adj[top].listIterator();

      		      index.add(top);
      		      ele.add(a[top]);
    		    while(i.hasNext()){
    		    //	System.out.println(top);
    		    	int n=i.next();
    		     if( !Visited[n]){
    		    				Visited[n]=true;
    		    				st.push(n);
    		    c++;
    		     }
    		         }
    		 }
    		    	   for(int x:index){
    		    		   a[x]=ele.first();
    		    		   ele.remove(ele.first());
    		    	  }
    		 
    		 //   System.out.println(temp);
    		    return 0;
    		    }
    		        
    		        }     
    		       	        
    		    class Dsu{
    		    	private int rank[], parent[] ,n;
    		    	private static int[] parent1;
    		    	Dsu(int size){
    		    		this.n=size+1;
    		    		rank=new int[n];
    		    		//parent=new int[n];
    		    		parent=new int[n];
    		    	makeSet();
    		
    		    	}
    		    	
    		    	void makeSet(){
    		    		for(int i=0;i<n;i++){
    		    			parent[i]=i;
    		    		}
    		    	}
    		    	
    		    	int find(int x){
    		    		if(parent[x]!=x){
    		    			
    		    			parent[x]=find(parent[x]);
    		    		}
    		    		return parent[x];
    		    	}
    		    
    		    	
    		    	void union(int x,int y){
    		    		int xRoot=find(x);
    		    		int yRoot=find(y);
    		    		
    		    		if(xRoot==yRoot)
    		    			return;
    		    		if(rank[xRoot]<rank[yRoot]){
    		    		parent[xRoot]=yRoot;	
    		    		}else if(rank[yRoot]<rank[xRoot]){
    		    			parent[yRoot]=xRoot;
    		    		}else{
    		    			parent[yRoot]=xRoot;
    		    			rank[xRoot]++;
    		    		}
    		    		
    		    	}

    		     
    		    }
    			