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.
import java.io.*;
import java.util.*;

public class B implements Runnable{
	public static void main (String[] args) {new Thread(null, new B(), "_cf", 1 << 28).start();}

	public void run() {
		FastScanner fs = new FastScanner();
		PrintWriter out = new PrintWriter(System.out);
		System.err.println("Go!");

		int n = fs.nextInt(), k = fs.nextInt();
		int[] a = fs.nextIntArray(n);
		int[] b = new int[n];
		int max = 0;
		int val = -1, res = Integer.MAX_VALUE;
		for(int i : a) max = Math.max(max, i);
		for(int min = 0; min <= max; min++) {
			int lo = 0, hi = max, ret = -1;
			for(int bs = 0; bs < 50 && lo <= hi; bs++) {
				int mid = (lo+hi)/2;
				int have = 0, added = 0;
				for(int i = 0; i < n; i++) {
					if(a[i] < min) {
						have -= min-a[i];
						b[i] = min;
					}
					else if(a[i] > min+mid) {
						added += a[i] - (min+mid);
						have += a[i] - (min+mid);
						b[i] = min+mid;
					}
					else {
						b[i] = a[i];
					}
				}
				if(added > k) {
					lo = mid+1; continue;
				}
				for(int i = 0; i < n && have > 0; i++) {
					int add = Math.min((min+mid)-b[i], have);
					have -= add;
				}
				if(have == 0) {
					ret = mid;
					hi = mid-1;
				}
				else if(have < 0) {
					for(int i = 0; i < n; i++) if(b[i] > min) {
						int add = Math.min(-have, b[i]-min);
						added += add;
						have += add; b[i] -= add;
					}
					if(have == 0 && added <= k) {
						ret = mid;
						hi = mid-1;
					}
					else {
						lo = mid+1;
					}
				}
				else {
					lo = mid+1;
				}
			}
			if(ret != -1 && ret < res) {
				res = ret;
				val = min;
			}
		}

		int[][] moves = new int[k][2];
		int ptr = 0;
		for(int big = 0; big < n; big++) {
			if(a[big] <= val+res) continue;
			for(int small = 0; small < n && a[big] > val+res; small++) if(small != big && a[small] < val) {
				int goFor = val-a[small];
				while(goFor > 0 && a[big] > val+res) {
					goFor--;
					a[big]--; a[small]++;
					moves[ptr][0] = big+1; moves[ptr][1] = small+1;
					ptr++;
				}
			}
			for(int small = 0; small < n && a[big] > val+res; small++) if(small != big) {
				int goFor = val+res-a[small];
				while(goFor > 0 && a[big] > val+res) {
					goFor--;
					a[big]--; a[small]++;
					moves[ptr][0] = big+1; moves[ptr][1] = small+1;
					ptr++;
				}
			}
		}
		for(int small = 0; small < n; small++) if(a[small] < val) {
			for(int big = 0; big < n && a[small] < val; big++) if(big != small) {
				int goFor = a[big]-val;
				while(goFor > 0 && a[small] < val) {
					goFor--;
					a[small]++; a[big]--;
					moves[ptr][0] = big+1; moves[ptr][1] = small+1;
					ptr++;
				}
			}
		}
		out.printf("%d %d\n", res, ptr);
		for(int i = 0; i < ptr; i++) {
			out.printf("%d %d\n", moves[i][0], moves[i][1]);
		}
		
		out.close();
	}

	class FastScanner {
		public int BS = 1<<16;
		public char NC = (char)0;
		byte[] buf = new byte[BS];
		int bId = 0, size = 0;
		char c = NC;
		double num = 1;
		BufferedInputStream in;

		public FastScanner() {
			in = new BufferedInputStream(System.in, BS);
		}

		public FastScanner(String s) throws FileNotFoundException {
			in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
		}

		public char nextChar(){
			while(bId==size) {
				try {
					size = in.read(buf);
				}catch(Exception e) {
					return NC;
				}                
				if(size==-1)return NC;
				bId=0;
			}
			return (char)buf[bId++];
		}

		public int nextInt() {
			return (int)nextLong();
		}

		public long nextLong() {
			num=1;
			boolean neg = false;
			if(c==NC)c=nextChar();
			for(;(c<'0' || c>'9'); c = nextChar()) {
				if(c=='-')neg=true;
			}
			long res = 0;
			for(; c>='0' && c <='9'; c=nextChar()) {
				res = (res<<3)+(res<<1)+c-'0';
				num*=10;
			}
			return neg?-res:res;
		}

		public double nextDouble() {
			double cur = nextLong();
			return c!='.' ? cur:cur+nextLong()/num;
		}

		public String next() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c>32) {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public String nextLine() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c!='\n') {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public boolean hasNext() {
			if(c>32)return true;
			while(true) {
				c=nextChar();
				if(c==NC)return false;
				else if(c>32)return true;
			}
		}
		
		public int[] nextIntArray(int n) {
			int[] res = new int[n];
			for(int i = 0; i < n; i++) res[i] = nextInt();
			return res;
		}
		
	}

}