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.
//    A Computer is Like a mischievous genie.
//    It will give you exactly what you ask for,
//    but not always what you want
//    A code by Rahul Verma


import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedHashSet;
import java.util.LinkedList;
import java.util.List;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Set;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;


public class Main {


    static class Clock {

        protected long start, stop;

        public void start() {
            start = System.currentTimeMillis();
        }

        public void stop() {
            stop = System.currentTimeMillis();
        }

        public String getTime() {
            return ((stop - start) + " ms");
        }
    }


    public static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

    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[] nextSArray() {
            String sr[] = null;
            try {
                sr = br.readLine().trim().split(" ");
            } catch (IOException e) {
                e.printStackTrace();
            }
            return sr;
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }

            return str;
        }
    }


    static long powmodulo(long a, long p) {
        if (p == 0) {
            return 1 % mod;
        }
        if (p == 1) {
            return a % mod;
        }
        long ans = 1;
        while (p > 0) {
            if ((p & 1) > 0) {
                ans = (ans * a) % mod;
            }
            a = (a * a) % mod;
            p = p >> 1;
        }
        return ans % mod;
    }


    static long mod = 1000000007;

    static long gcd(long a, long b) {
        if (a == 0) {
            return b;
        }
        return gcd(b % a, a);
    }

    static long fast_powerNumbers(long a, long n) {
        if (n == 1) {
            return a;
        }
        long ans = fast_powerNumbers(a, n / 2);
        if (n % 2 == 0) {
            return (ans * ans);
        } else {
            return ((ans * ans) * (a));
        }
    }


    static void dfs_helper(int[][] arr, int i, int j, int team, int n, int m) {
        arr[i][j] = team;
        if (i - 1 >= 0 && arr[i - 1][j] == 1) {
            dfs(arr, i - 1, j, team, n, m);
        }
        if (j - 1 >= 0 && arr[i][j - 1] == 1) {
            dfs(arr, i, j - 1, team, n, m);
        }
        if (i + 1 < n && arr[i + 1][j] == 1) {
            dfs(arr, i + 1, j, team, n, m);
        }
        if (j + 1 < m && arr[i][j + 1] == 1) {
            dfs(arr, i, j + 1, team, n, m);
        }

    }

    static void dfs(int[][] arr, int i, int j, int team, int n, int m) {
        dfs_helper(arr, i, j, team, n, m);

    }

    static int parent[];
    static int rank[];

    static int find(int i) {
        if (parent[i] == -1) {
            parent[i] = i;
            return i;
        }

        if (parent[i] == i) {
            return i;
        } else {
            parent[i] = find(parent[i]);
        }
        return parent[i];

    }

    static void unite(int s1, int s2) {

        if (rank[s1] > rank[s2]) {
            parent[s2] = s1;
            rank[s1] += rank[s2];
        } else {
            parent[s1] = s2;
            rank[s2] += rank[s1];
        }
    }


    public static long arr[];
    public static int arr1[];

//    static void seive(int n) {
//        arr = new int[n + 1];
//        arr[0] = arr[1] = 1;
//        for (int i = 4; i <= n; i = i + 2) {
//            arr[i] = 1;
//        }
//        for (int i = 3; i * i <= n; i = i + 2) {
//            if (arr[i] == 0) {
//                for (int j = i * i; j <= n; j = j + i) {
//                    arr[j] = 1;
//                }
//
//            }
//        }
//    }

    static  void seive(int n)
    {
        arr1=new int[n+1];
        arr1[0]=arr1[1]=1;
        for (int i = 4; i <=n ; i+=2) {
            arr1[i]=1;
        }
        for (int i = 3; i*i <=n ; i+=2) {
            if (arr1[i] == 0)
            {
                for (int j = i*i; j <=n ; j+=i) {
                    arr1[j]=1;
                }
            }
        }

    }


    public static void fun(int arr[][])
    {
        int a=0;
        int b=arr.length-1;
        int n=arr.length;
        int temp= arr[a][0];
        int tempi=arr[a][1];
        while(a<n-1&&arr[a+1][0]<temp)
        {
            arr[a][0]=arr[a+1][0];
            arr[a][1]=arr[a+1][1];
            ++a;
        }

        arr[a][0]=temp;
        arr[a][1]=tempi;
//        for (int i = 0; i < n; i++) {
//            System.out.println(Arrays.toString(arr[i]));
//        }
        temp =arr[b][0];
       tempi=arr[b][1];
        while(b>0&&arr[b-1][0]>temp)
        {
            arr[b][0]=arr[b-1][0];
            arr[b][1]=arr[b-1][1];
            --b;
        }
        arr[b][0]=temp;
        arr[b][1]=tempi;
//        for (int i = 0; i < n; i++) {
//            System.out.println(Arrays.toString(arr[i]));
//        }
    }
    public static void main(String[] args) throws Exception {
        FastReader sc = new FastReader();

        Clock clock = new Clock();
        clock.start();
        int n=sc.nextInt();
        int k= sc.nextInt();
        int arr[][]=new int[n][2];

        for (int i = 0; i < n; i++) {
            arr[i][0]=sc.nextInt();
            arr[i][1]=i;
        }
        Arrays.sort(arr, new Comparator<int[]>() {
            @Override
            public int compare(int[] o1, int[] o2) {
                return Integer.compare(o1[0],o2[0]);
            }
        });
        int a=0;
        int b=n-1;
        int min=arr[n-1][0]-arr[0][0];
        ArrayList<Pair>al=new ArrayList<>();
        int steps=0;
        for (int i = 0; i < k; i++) {

            arr[n-1][0]-=1;
            arr[0][0]+=1;
            int aa =arr[0][1];
            int bb=arr[n-1][1];
            if(aa==bb)
                break;
            Arrays.sort(arr, new Comparator<int[]>() {
                @Override
                public int compare(int[] o1, int[] o2) {
                    return Integer.compare(o1[0],o2[0]);
                }
            });
            int x = Math.abs(arr[n-1][0]-arr[0][0]);
            if(min<x)
                break;
            else
                min=x;

            ++steps;
            al.add(new Pair(bb,aa));

//            for (int j = 0; j < n; j++) {
//                System.out.println(Arrays.toString(arr[j]));
//            }
//            System.out.println();
        }
       out.println(min+" "+steps);
        for(Pair p:al)
        {
            out.println((p.a+1)+" "+(p.b+1));
        }
        out.close();


    }


}


class Pair{

    long a,b;
    Pair(long a,long b)
    {
        this.a=a;
        this.b=b;
    }
}
class DSU
{
    int parent[];
    int rank[];

    long sum[] ;
    DSU(int n)
    {
        this.parent=new int[n];
        this.rank=new int[n];
        sum=new long[n];
        Arrays.fill(parent,-1);
        Arrays.fill(rank,1);

    }

    int find(int s1)
    {
        if(parent[s1]==-1)
            return s1;
        return parent[s1]=find(parent[s1]);
    }

    void unite(int s1,int s2)
    {
        int p1=this.find(s1);
        int p2=this.find(s2);
        if(p1==p2)
            return;
        if(rank[p1]>rank[p2])
        {
            parent[p2]=p1;
            rank[p1]+=rank[p2];
            // System.out.println(arr[p2]);

            sum[p1]+=sum[p2];
            //sum[p2]+=sum[p1];

        }
        else
        {
            parent[p1]=p2;
            rank[p2]+=rank[p1];
            //System.out.println(arr[p1]);
            sum[p2]+=sum[p1];
            //sum[p1]+=sum[p2];
        }
    }


}

class Gaph {

    HashMap<Integer, ArrayList<Integer>> hm;

    Gaph() {
        hm = new HashMap<>();
    }

    Gaph(int n) {

        hm = new HashMap<>();
        for (int i = 0; i < n; i++) {
            hm.put(i, new ArrayList<Integer>());
        }
    }

    // function for adding an edge.................................................
    public void addEdge(int a, int b, boolean isDir) {
        if (isDir) {
            if (hm.containsKey(a)) {
                hm.get(a).add(b);
            } else {
                hm.put(a, new ArrayList<>(Arrays.asList(b)));
            }
        } else {
            if (hm.containsKey(a)) {
                hm.get(a).add(b);
            } else if (!hm.containsKey(a)) {
                hm.put(a, new ArrayList<>(Arrays.asList(b)));
            }

            if (hm.containsKey(b)) {
                hm.get(b).add(a);
            } else if (!hm.containsKey(b)) {
                hm.put(b, new ArrayList<>(Arrays.asList(a)));
            }
        }
    }


}

// out.println(al.toString().replaceAll("[\\[|\\]|,]",""));