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:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.util.Collections;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author lebegio
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        MyReader in = new MyReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        public void solve(int testNumber, MyReader in, PrintWriter out) {
            int n = in.nextInt();
            int k = in.nextInt();
            ArrayList<Pair> points = new ArrayList<Pair>();
            for (int i = 0; i < n; i++) {
                int x = in.nextInt();
                int y = in.nextInt();
                points.add(new Pair(x, y, i + 1, true));
                points.add(new Pair(y, x, i + 1, false));
            }
            Collections.sort(points, (o1, o2) -> {
                if (o1.x != o2.x) return Long.compare(o1.x, o2.x);

                if (o1.isStart != o2.isStart) {
                    return o1.isStart ? -1 : 1;
                }
                return 0;
            });
            long maxLen = 0;
            RedBlackBST<Pair, Integer> rbTree = new RedBlackBST<>();
            for (int i = 0; i < points.size(); i++) {
                Pair p = points.get(i);
                if (p.isStart) {
                    rbTree.put(p, 0);
                } else {
                    if (rbTree.size() >= k) {
                        maxLen = Math.max(maxLen, 1 + p.x - rbTree.select(k - 1).x);
                    }
                    rbTree.delete(new Pair(p.y, p.x, p.poz, true));
                }
            }

            out.println(maxLen);
            if (maxLen == 0) {
                for (int i = 0; i < k; i++)
                    out.print((i + 1) + " ");
            } else {
                RedBlackBST<Pair, Integer> tree = new RedBlackBST<>();
                for (int i = 0; i < points.size(); i++) {
                    Pair p = points.get(i);
                    if (p.isStart) {
                        tree.put(p, 0);
                    } else {
                        if (tree.size() >= k && maxLen == 1 + p.x - tree.select(k - 1).x) {
                            for (int j = 0; j < k; j++) {
                                out.print(tree.select(j).poz + " ");
                            }
                            return;
                        }
                        tree.delete(new Pair(p.y, p.x, p.poz, true));
                    }
                }
            }
        }

    }

    static class RedBlackBST<Key extends Comparable<Key>, Value> {
        private static final boolean RED = true;
        private static final boolean BLACK = false;
        private Node root;

        public RedBlackBST() {
        }

        private boolean isRed(Node x) {
            if (x == null) return false;
            return x.color == RED;
        }

        private int size(Node x) {
            if (x == null) return 0;
            return x.size;
        }

        public int size() {
            return size(root);
        }

        public boolean isEmpty() {
            return root == null;
        }

        public Value get(Key key) {
            if (key == null) throw new IllegalArgumentException("argument to get() is null");
            return get(root, key);
        }

        private Value get(Node x, Key key) {
            while (x != null) {
                int cmp = key.compareTo(x.key);
                if (cmp < 0) x = x.left;
                else if (cmp > 0) x = x.right;
                else return x.val;
            }
            return null;
        }

        public boolean contains(Key key) {
            return get(key) != null;
        }

        public void put(Key key, Value val) {
            if (key == null) throw new IllegalArgumentException("first argument to put() is null");
            if (val == null) {
                delete(key);
                return;
            }

            root = put(root, key, val);
            root.color = BLACK;
            // assert check();
        }

        private Node put(Node h, Key key, Value val) {
            if (h == null) return new Node(key, val, RED, 1);

            int cmp = key.compareTo(h.key);
            if (cmp < 0) h.left = put(h.left, key, val);
            else if (cmp > 0) h.right = put(h.right, key, val);
            else h.val = val;

            // fix-up any right-leaning links
            if (isRed(h.right) && !isRed(h.left)) h = rotateLeft(h);
            if (isRed(h.left) && isRed(h.left.left)) h = rotateRight(h);
            if (isRed(h.left) && isRed(h.right)) flipColors(h);
            h.size = size(h.left) + size(h.right) + 1;

            return h;
        }

        private Node deleteMin(Node h) {
            if (h.left == null)
                return null;

            if (!isRed(h.left) && !isRed(h.left.left))
                h = moveRedLeft(h);

            h.left = deleteMin(h.left);
            return balance(h);
        }

        public void delete(Key key) {
            if (key == null) throw new IllegalArgumentException("argument to delete() is null");
            if (!contains(key)) return;

            // if both children of root are black, set root to red
            if (!isRed(root.left) && !isRed(root.right))
                root.color = RED;

            root = delete(root, key);
            if (!isEmpty()) root.color = BLACK;
            // assert check();
        }

        private Node delete(Node h, Key key) {
            // assert get(h, key) != null;

            if (key.compareTo(h.key) < 0) {
                if (!isRed(h.left) && !isRed(h.left.left))
                    h = moveRedLeft(h);
                h.left = delete(h.left, key);
            } else {
                if (isRed(h.left))
                    h = rotateRight(h);
                if (key.compareTo(h.key) == 0 && (h.right == null))
                    return null;
                if (!isRed(h.right) && !isRed(h.right.left))
                    h = moveRedRight(h);
                if (key.compareTo(h.key) == 0) {
                    Node x = min(h.right);
                    h.key = x.key;
                    h.val = x.val;
                    // h.val = get(h.right, min(h.right).key);
                    // h.key = min(h.right).key;
                    h.right = deleteMin(h.right);
                } else h.right = delete(h.right, key);
            }
            return balance(h);
        }

        private Node rotateRight(Node h) {
            // assert (h != null) && isRed(h.left);
            Node x = h.left;
            h.left = x.right;
            x.right = h;
            x.color = x.right.color;
            x.right.color = RED;
            x.size = h.size;
            h.size = size(h.left) + size(h.right) + 1;
            return x;
        }

        private Node rotateLeft(Node h) {
            // assert (h != null) && isRed(h.right);
            Node x = h.right;
            h.right = x.left;
            x.left = h;
            x.color = x.left.color;
            x.left.color = RED;
            x.size = h.size;
            h.size = size(h.left) + size(h.right) + 1;
            return x;
        }

        private void flipColors(Node h) {
            // h must have opposite color of its two children
            // assert (h != null) && (h.left != null) && (h.right != null);
            // assert (!isRed(h) &&  isRed(h.left) &&  isRed(h.right))
            //    || (isRed(h)  && !isRed(h.left) && !isRed(h.right));
            h.color = !h.color;
            h.left.color = !h.left.color;
            h.right.color = !h.right.color;
        }

        private Node moveRedLeft(Node h) {
            // assert (h != null);
            // assert isRed(h) && !isRed(h.left) && !isRed(h.left.left);

            flipColors(h);
            if (isRed(h.right.left)) {
                h.right = rotateRight(h.right);
                h = rotateLeft(h);
                flipColors(h);
            }
            return h;
        }

        private Node moveRedRight(Node h) {
            // assert (h != null);
            // assert isRed(h) && !isRed(h.right) && !isRed(h.right.left);
            flipColors(h);
            if (isRed(h.left.left)) {
                h = rotateRight(h);
                flipColors(h);
            }
            return h;
        }

        private Node balance(Node h) {
            // assert (h != null);

            if (isRed(h.right)) h = rotateLeft(h);
            if (isRed(h.left) && isRed(h.left.left)) h = rotateRight(h);
            if (isRed(h.left) && isRed(h.right)) flipColors(h);

            h.size = size(h.left) + size(h.right) + 1;
            return h;
        }

        private Node min(Node x) {
            // assert x != null;
            if (x.left == null) return x;
            else return min(x.left);
        }

        public Key select(int k) {
            if (k < 0 || k >= size()) throw new IllegalArgumentException();
            Node x = select(root, k);
            return x.key;
        }

        private Node select(Node x, int k) {
            // assert x != null;
            // assert k >= 0 && k < size(x);
            int t = size(x.left);
            if (t > k) return select(x.left, k);
            else if (t < k) return select(x.right, k - t - 1);
            else return x;
        }

        private class Node {
            private Key key;
            private Value val;
            private Node left;
            private Node right;
            private boolean color;
            private int size;

            public Node(Key key, Value val, boolean color, int size) {
                this.key = key;
                this.val = val;
                this.color = color;
                this.size = size;
            }

        }

    }

    static class Pair implements Comparable<Pair> {
        public int poz = 0;
        public long x = 0;
        public long y = 0;
        public boolean isStart = true;

        public Pair(long xx, long yy) {
            this.x = xx;
            this.y = yy;
        }

        public Pair(long xx, long yy, int poz) {
            this.x = xx;
            this.y = yy;
            this.poz = poz;
        }

        public Pair(long xx, long yy, int poz, boolean isStart) {
            this.x = xx;
            this.y = yy;
            this.poz = poz;
            this.isStart = isStart;
        }


        public int compareTo(Pair o) {
            if (x != o.x) return Long.compare(x, o.x);
            return poz - o.poz;
        }

    }

    static class MyReader {
        private BufferedReader buffReader;
        private StringTokenizer strTokenizer;
        private static final int SIZE = 32768;

        public MyReader(InputStream inputStream) {
            buffReader = new BufferedReader(new InputStreamReader(inputStream), SIZE);
        }

        public String next() {
            if (strTokenizer == null || !strTokenizer.hasMoreTokens()) {
                try {
                    strTokenizer = new StringTokenizer(buffReader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return strTokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}