Problem: All our characters have hobbies. The same is true for Fedor. He enjoys shopping in the neighboring supermarket. 

The goods in the supermarket have unique integer ids. Also, for every integer there is a product with id equal to this integer. Fedor has n discount coupons, the i-th of them can be used with products with ids ranging from li to ri, inclusive. Today Fedor wants to take exactly k coupons with him.

Fedor wants to choose the k coupons in such a way that the number of such products x that all coupons can be used with this product x is as large as possible (for better understanding, see examples). Fedor wants to save his time as well, so he asks you to choose coupons for him. Help Fedor!

Input

The first line contains two integers n and k (1 ≤ k ≤ n ≤ 3·105) — the number of coupons Fedor has, and the number of coupons he wants to choose.

Each of the next n lines contains two integers li and ri ( - 109 ≤ li ≤ ri ≤ 109) — the description of the i-th coupon. The coupons can be equal.

Output

In the first line print single integer — the maximum number of products with which all the chosen coupons can be used. The products with which at least one coupon cannot be used shouldn't be counted.

In the second line print k distinct integers p1, p2, ..., pk (1 ≤ pi ≤ n) — the ids of the coupons which Fedor should choose.

If there are multiple answers, print any of them.

Examples

Input

4 2
1 100
40 70
120 130
125 180


Output

31
1 2 


Input

3 2
1 12
15 20
25 30


Output

0
1 2 


Input

5 2
1 10
5 15
14 50
30 70
99 100


Output

21
3 4 

Note

In the first example if we take the first two coupons then all the products with ids in range [40, 70] can be bought with both coupons. There are 31 products in total.

In the second example, no product can be bought with two coupons, that is why the answer is 0. Fedor can choose any two coupons in this example.

Solution (in JAVA):

Solution:
//package com.codeforces.competitions.year2017.round390div2;

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

public final class TaskC
{
	public static void main(String[] args)
	{
		InputReader in = new InputReader(System.in);
		PrintWriter out = new PrintWriter(System.out);
		Solver solver = new Solver(in, out);

		solver.solve();
		in.close();
		out.flush();
		out.close();
	}

	static class Solver
	{
		int n, k;
		Point[] pts;
		Q[] qs;
		InputReader in;
		PrintWriter out;

		void solve()
		{
			n = in.nextInt();
			k = in.nextInt();
			pts = new Point[n];

			for (int i = 0; i < n; i++)
				pts[i] = new Point(i, in.nextInt(), in.nextInt());

			Arrays.sort(pts, new Comparator<Point>()
			{
				@Override public int compare(Point o1, Point o2)
				{
					if (o1.l == o2.l)
						return Integer.compare(o1.r, o2.r);

					return Integer.compare(o1.l, o2.l);
				}
			});

			PriorityQueue<Integer> queue = new PriorityQueue<>();

			for (int i = 0; i < k; i++)
				queue.add(pts[i].r);

			int max = queue.peek() - pts[k - 1].l + 1;
			int ml, mr;

			ml = pts[k - 1].l;
			mr = queue.peek();

			for (int i = k; i < n; i++)
			{
				queue.poll();
				queue.add(pts[i].r);

				int curr = queue.peek() - pts[i].l + 1;

				if (curr > max)
				{
					max = curr;
					ml = pts[i].l;
					mr = queue.peek();
				}
			}

			if (max <= 0)
			{
				out.println(0);

				for (int i = 1; i <= k; i++)
					out.print(i + " ");
			}
			else
			{
				out.println(max);

				for (int i = 0; i < n && k > 0; i++)
				{
					if (pts[i].l <= ml && pts[i].r >= mr)
					{
						out.print(pts[i].id + 1 + " ");
						k--;
					}
				}
			}

			/*PriorityQueue<Integer> queue = new PriorityQueue<>(Collections.reverseOrder());

			for (int i = 0; i < k; i++)
				queue.add(pts[i].r);

			long rm, rM;

			rm = queue.peek();
			rM = pts[k - 1].l;

			for (int i = k; i < n; i++)
			{
				queue.add(pts[i].r);
				queue.poll();

				if (rm - rM < queue.peek() - pts[i].l)
				{
					rm = queue.peek();
					rM = pts[i].l;
				}
			}

			if (rm < rM)
			{
				out.println("0");

				for (int i = 1; i <= k; i++)
					out.print(i + " ");
			}
			else
			{
				out.println(rm - rM + 1);

				for (int i = 0; i < n; i++)
				{
					if (k == 0)
						break;

					if (pts[i].l <= rM && pts[i].r >= rm)
					{
						out.print(pts[i].id + 1 + " ");
						k--;
					}
				}
			}*/
		}

		void solve2()
		{
			n = in.nextInt();
			k = in.nextInt();
			pts = new Point[n];

			for (int i = 0; i < n; i++)
				pts[i] = new Point(i, in.nextInt(), in.nextInt());

			PriorityQueue<Integer> lefts = new PriorityQueue<>(Collections.reverseOrder());
			int ctr = 0;

			qs = new Q[2 * n];
/*			Arrays.sort(pts, new Comparator<Point>()
			{
				@Override public int compare(Point o1, Point o2)
				{
					return Integer.compare(o1.r, o2.r);
				}
			});*/

			for (int i = 0; i < n; i++)
			{
				qs[ctr++] = new Q(i, pts[i].l, 'l', pts[i].r);
				qs[ctr++] = new Q(i, pts[i].r, 'r', pts[i].l);
			}

			Arrays.sort(qs, new Comparator<Q>()
			{
				@Override public int compare(Q o1, Q o2)
				{
					if (o1.x == o2.x)
						return Character.compare(o1.type, o2.type);

					return Integer.compare(o1.x, o2.x);
				}
			});

			int ans, ml, mr;

			ans = ml = mr = 0;

			for (int i = 0; i < n << 1; i++)
			{
				if (qs[i].type == 'l')
					lefts.add(qs[i].x);
				else
				{
					if (lefts.size() >= k && qs[i].x - lefts.peek() + 1 > ans)
					{
						ans = qs[i].x - lefts.peek() + 1;
						ml = lefts.peek();
						mr = qs[i].x;
					}

					lefts.remove(qs[i].other);
				}
			}

			List<Integer> list = new ArrayList<>(k);

			for (int i = 0; i < n; i++)
			{
				if (pts[i].l <= ml && pts[i].r >= mr)
				{
					list.add(pts[i].id);

					if (list.size() == k)
						break;
				}
			}

//			System.out.println("ml : " + ml + ", mr : " + mr);

			if (list.size() < k)
			{
				out.println(0);

				for (int i = 1; i <= k; i++)
					out.print(i + " ");
			}
			else
			{
				out.println(ans);

				for (int x : list)
					out.print(x + 1 + " ");
			}
		}

		class Point
		{
			int id, l, r;

			public Point(int id, int l, int r)
			{
				this.id = id;
				this.l = l;
				this.r = r;
			}

			@Override public String toString()
			{
				return String.format("%d -> (%d, %d)", id, l, r);
//				return "(" + l + ", " + r + ")";
			}

		}

		class Q
		{
			int id, x, other;
			char type;

			public Q(int id, int x, char type, int other)
			{
				this.id = id;
				this.x = x;
				this.type = type;
				this.other = other;
			}

		}

/*		void solve2()
		{
			n = in.nextInt();
			k = in.nextInt();
			pts = new Point[n];

			for (int i = 0; i < n; i++)
				pts[i] = new Point(i, in.nextInt(), in.nextInt());

			shrink();
			bit = new int[max + 1];
			segmentTree = new Node[5 * max + 1];

			for (int i = 0; i < 5 * max; i++)
				segmentTree[i] = new Node(0);

			for (int i = 0; i < n; i++)
			{
				System.out.println("adding to [" + pts[i].sl + ", " + pts[i].sr);
				add(1, 0, max - 1, pts[i].sl, pts[i].sr, 1);
			}

			int ans = 0;
			int ml, mr;
			int currLeft;

			ml = mr = 0;

			System.out.println("query :");
			for (int i = 1; i < max; i++)
				System.out.println("i : " + i + ", query[i] : " + query(1, 0, max - 1, i, i));

			for (int i = 1; i < max; i++)
			{
				int currRight = currLeft = i;

//				if (query(1, 0, max - 1, i, i) < k)
//					continue;

				while (i < max && query(1, 0, max - 1, i, i) >= k)
				{
					currRight = i;
					i++;
				}

				Integer ll, rr;

				System.out.println("cL : " + currLeft + ", cr : " + currRight);
				ll = revMap.get(currLeft);
				rr = revMap.get(currRight);

				if (ll == null || rr == null)
					continue;

				System.out.println("\tll : " + ll + ", rr : " + rr + ", ans : " + ans);
				if (rr - ll + 1 > ans)
				{
					ans = rr - ll + 1;
					ml = ll;
					mr = rr;
				}
			}

			List<Integer> list = new ArrayList<>();

			for (int i = 0; i < n; i++)
			{
				if (pts[i].l <= ml && pts[i].r >= mr)
				{
					list.add(i);

					if (list.size() == k)
						break;
				}
			}

			if (list.size() < k)
			{
				out.println(0);

				for (int i = 1; i <= k; i++)
					out.print(i + " ");
			}
			else
			{
				out.println(ans);

				for (int x : list)
					out.print(x + 1 + " ");
			}
		}

		void shrink()
		{
			List<Integer> list = new ArrayList<>(n << 1);

			for (int i = 0; i < n; i++)
			{
				list.add(pts[i].l);
				list.add(pts[i].r);
			}

			Collections.sort(list);
			map = new HashMap<>();
			revMap = new HashMap<>();

			int ctr = 1;

			for (int xx : list)
			{
				if (!map.containsKey(xx))
					map.put(xx, ctr++);
			}

			max = ctr + 1;

			for (int i = 0; i < n; i++)
			{
				pts[i].sl = map.get(pts[i].l);
				pts[i].sr = map.get(pts[i].r);
				revMap.put(pts[i].sl, pts[i].l);
				revMap.put(pts[i].sr, pts[i].r);
			}
//			System.out.println("hh");
		}

		int query(int node, int treeStart, int treeEnd, int rangeStart, int rangeEnd)
		{
			Node tempNode = segmentTree[node];

			// i.e., lazy
			if (tempNode.update > 0)
			{
				tempNode.sum += tempNode.update;

				// not a leaf node
				if (treeStart != treeEnd)
				{
					int update = tempNode.update;

					segmentTree[2 * node].update = update;
					segmentTree[2 * node + 1].update = update;
				}

				tempNode.update = 0;
			}

			if (treeStart > treeEnd || treeStart > rangeEnd || treeEnd < rangeStart)
				return 0;

			if (treeStart >= rangeStart && treeEnd <= rangeEnd)
				return tempNode.sum;

			int mid, lSum, rSum;

			mid = (treeStart + treeEnd) / 2;
			lSum = query(2 * node, treeStart, mid, rangeStart, rangeEnd);
			rSum = query(2 * node + 1, mid + 1, treeEnd, rangeStart, rangeEnd);

			return lSum + rSum;
		}

		void add(int node, int treeStart, int treeEnd, int rangeStart, int rangeEnd, int addValue)
		{
			Node tempNode = segmentTree[node];

			if (tempNode.update > 0)
			{
				tempNode.sum += tempNode.update;

				if (treeStart != treeEnd)
				{
					segmentTree[2 * node].update += tempNode.update;
					segmentTree[2 * node + 1].update += tempNode.update;
				}

				tempNode.update = 0;
			}

			// if the update range is completely out of the range that this node
			// stores information of
			if (treeStart > treeEnd || treeStart > rangeEnd || treeEnd < rangeStart)
				return;

			// if the range this node holds is completely inside of the update range
			if (treeStart >= rangeStart && treeEnd <= rangeEnd)
			{
				tempNode.sum += addValue;

				// not a leaf node
				if (treeStart != treeEnd)
				{
					segmentTree[2 * node].update += addValue;
					segmentTree[2 * node + 1].update += addValue;
					System.out.println("setting lazy for ts : " + treeStart + ", te : " + treeEnd);
				}

				return;
			}

			int mid = (treeStart + treeEnd) / 2;

			add(2 * node, treeStart, mid, rangeStart, rangeEnd, addValue);
			add(2 * node + 1, mid + 1, treeEnd, rangeStart, rangeEnd, addValue);
			tempNode.sum = segmentTree[2 * node].sum + segmentTree[2 * node + 1].sum;
		}

		static class Node
		{
			int sum;
			int update; // if lazy, this will be != 0, else, 0

			public Node(int sum)
			{
				this.sum = sum;
				this.update = 0;
			}

		}

		void add(int l, int r)
	{
		put(r, 1);
		put(l - 1, -1);
	}

		void put(int ind, int val)
		{
			if (ind == 0)
				return;

			while (ind <= max)
			{
				bit[ind] += val;
				ind += ind & -ind;
			}
		}

		int query(int l, int r)
		{
			return ask(r) - ask(l - 1);
		}

		int ask(int ind)
		{
			if (ind == 0)
				return 0;

			int ans = 0;

			while (ind > 0)
			{
				ans += bit[ind];
				ind -= ind & -ind;
			}

			return ans;
		}

		class Point
		{
			int id, l, r, sl, sr;

			public Point(int id, int l, int r)
			{
				this.id = id;
				this.l = l;
				this.r = r;
			}

		}*/

		public Solver(InputReader in, PrintWriter out)
		{
			this.in = in;
			this.out = out;
		}

	}

	static class InputReader
	{
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

		public InputReader(InputStream stream)
		{
			this.stream = stream;
		}

		public 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++];
		}

		public 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 & 15;

				c = read();
			} while (!isSpaceChar(c));

			return res * sgn;
		}

		public int[] nextIntArray(int arraySize)
		{
			int array[] = new int[arraySize];

			for (int i = 0; i < arraySize; i++)
				array[i] = nextInt();

			return array;
		}

		public long nextLong()
		{
			int c = read();

			while (isSpaceChar(c))
				c = read();

			int sign = 1;

			if (c == '-')
			{
				sign = -1;

				c = read();
			}

			long result = 0;

			do
			{
				if (c < '0' || c > '9')
					throw new InputMismatchException();

				result *= 10;
				result += c & 15;

				c = read();
			} while (!isSpaceChar(c));

			return result * sign;
		}

		public long[] nextLongArray(int arraySize)
		{
			long array[] = new long[arraySize];

			for (int i = 0; i < arraySize; i++)
				array[i] = nextLong();

			return array;
		}

		public float nextFloat()
		{
			float result, div;
			byte c;

			result = 0;
			div = 1;
			c = (byte) read();

			while (c <= ' ')
				c = (byte) read();

			boolean isNegative = (c == '-');

			if (isNegative)
				c = (byte) read();

			do
			{
				result = result * 10 + c - '0';
			} while ((c = (byte) read()) >= '0' && c <= '9');

			if (c == '.')
				while ((c = (byte) read()) >= '0' && c <= '9')
					result += (c - '0') / (div *= 10);

			if (isNegative)
				return -result;

			return result;
		}

		public double nextDouble()
		{
			double ret = 0, div = 1;
			byte c = (byte) read();

			while (c <= ' ')
				c = (byte) read();

			boolean neg = (c == '-');

			if (neg)
				c = (byte) read();

			do
			{
				ret = ret * 10 + c - '0';
			} while ((c = (byte) read()) >= '0' && c <= '9');

			if (c == '.')
				while ((c = (byte) read()) >= '0' && c <= '9')
					ret += (c - '0') / (div *= 10);

			if (neg)
				return -ret;

			return ret;
		}

		public String next()
		{
			int c = read();

			while (isSpaceChar(c))
				c = read();

			StringBuilder res = new StringBuilder();

			do
			{
				res.appendCodePoint(c);

				c = read();
			} while (!isSpaceChar(c));

			return res.toString();
		}

		public boolean isSpaceChar(int c)
		{
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		public String nextLine()
		{
			int c = read();

			StringBuilder result = new StringBuilder();

			do
			{
				result.appendCodePoint(c);

				c = read();
			} while (!isNewLine(c));

			return result.toString();
		}

		public boolean isNewLine(int c)
		{
			return c == '\n';
		}

		public void close()
		{
			try
			{
				stream.close();
			}
			catch (IOException e)
			{
				e.printStackTrace();
			}
		}

	}

}