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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.NoSuchElementException;
import java.util.Random;

public class D {
  private void solve(FastScanner in, PrintWriter out) {
    int N = in.nextInt();
    int K = in.nextInt();

    long[] l = new long[N];
    long[] r = new long[N];
    long min = 0;
    for (int i = 0; i < N; i++) {
      l[i] = in.nextInt();
      r[i] = in.nextInt();
      min = Math.min(min, l[i]);
    }
    for (int i = 0; i < N; i++) {
      l[i] -= min;
      r[i] -= min;
      l[i] = l[i] * 2 * N + i;
      r[i] = r[i] * 2 * N + i + N;
    }

    long[][] events = new long[2 * N][2];
    for (int i = 0; i < N; i++) {
      events[2 * i][0] = l[i];
      events[2 * i][1] = i;
      events[2 * i + 1][0] = r[i];
      events[2 * i + 1][1] = -i - 1;
    }
    Arrays.sort(events, (o1, o2) -> {
      if (o1[0] == o2[0]) return Long.compare(o1[1], o2[1]);
      return Long.compare(o1[0], o2[0]);
    });

    Treap treap = new Treap();
    long from = -1;
    long max = 0;
    long[] range = null;
    int coupons = 0;
    for (long[] e : events) {
      int i = (int) e[1];
      if (i >= 0) {
        coupons++;
        treap.insert(l[i]);
        if (coupons == K) {
          from = l[i] / (2 * N);
        }
      } else {
        i = -(i + 1);
        long tr = r[i] / (2 * N);
        long tl = l[i] / (2 * N);
        if (tl <= from && coupons >= K) {
          long curRange = tr - from + 1;
          if (max < curRange) {
            max = curRange;
            range = new long[]{from, tr};
          }
          treap.erase(l[i]);
          if (coupons > K) {
            long kth = treap.rank(K - 1);
            from = kth / (2 * N);
          }
        } else {
          treap.erase(l[i]);
        }
        coupons--;
      }
    }
    out.println(max);
    if (max == 0) {
      for (int i = 0; i < K; i++) {
        out.print((i + 1) + " ");
      }
      out.println();
      return;
    }

    for (int i = 0; i < N; i++) {
      long L = l[i] / (2 * N);
      long R = r[i] / (2 * N);
      if (L <= range[0] && range[1] <= R) {
        out.print((i + 1) + " ");
        K--;
        if (K == 0) break;
      }
    }
    out.println();
  }

  public class Treap {
    Random random = new Random();

    private class Node {
      Node left, right;
      long key;
      int priority;
      int count;

      Node(long key) {
        this.key = key;
        priority = random.nextInt();
        left = null;
        right = null;
        count = 1;
      }
    }

    private Node root = null;

    public void clear() {
      root = null;
    }

    public boolean isEmpty() {
      return count(root) == 0;
    }

    private int count(Node n) {
      return n == null ? 0 : n.count;
    }

    private void update(Node c) {
      c.count = 1 + count(c.left) + count(c.right);
    }

    private Node leftRotate(Node c) {
      Node r = c.right;
      c.right = r.left;
      r.left = c;
      update(c);
      return r;
    }

    private Node rightRotate(Node c) {
      Node l = c.left;
      c.left = l.right;
      l.right = c;
      update(c);
      return l;
    }

    private Node insert(Node c, long key) {
      if (c == null) return new Node(key);
      if (c.key < key) {
        c.right = insert(c.right, key);
        if (c.right.priority < c.priority) c = leftRotate(c);
      } else {
        c.left = insert(c.left, key);
        if (c.left.priority < c.priority) c = rightRotate(c);
      }
      update(c);
      return c;
    }

    private Node getMinNode(Node c) {
      while (c.left != null) c = c.left;
      return c;
    }

    private Node erase(Node c, long key) {
      if (key == c.key) {
        if (c.left == null) return c.right;
        if (c.right == null) return c.left;

        Node minNode = getMinNode(c.right);
        c.key = minNode.key;
        c.right = erase(c.right, minNode.key);
      } else {
        if (c.key < key) c.right = erase(c.right, key);
        else c.left = erase(c.left, key);
      }
      update(c);
      return c;
    }

    public void insert(long key) {
      if (contains(key)) return;
      root = insert(root, key);
    }

    public void erase(long key) {
      root = erase(root, key);
    }

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

    public boolean contains(long key) {
      return find(root, key) >= 0;
    }

    public int find(long key) {
      return find(root, key);
    }

    private int find(Node c, long key) {
      if (c == null) return -1;
      if (c.key == key) return count(c.left);
      if (key < c.key) return find(c.left, key);
      int pos = find(c.right, key);
      if (pos < 0) return pos;
      return count(c.left) + 1 + pos;
    }

    private Node rank(Node c, int rank) {
      while (c != null) {
        int leftCount = count(c.left);
        if (leftCount == rank) return c;
        if (leftCount < rank) {
          rank -= leftCount + 1;
          c = c.right;
        } else {
          c = c.left;
        }
      }
      return null;
    }

    public long rank(int rank) {
      if (root == null)
        throw new NullPointerException();
      Node r = rank(root, rank);
      if (r == null)
        throw new NullPointerException();
      return r.key;
    }

  }

  public static void main(String[] args) {
    FastScanner in = new FastScanner();
    PrintWriter out = new PrintWriter(System.out);
    new D().solve(in, out);
    out.close();
  }

  private static class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int bufferLength = 0;

    private boolean hasNextByte() {
      if (ptr < bufferLength) {
        return true;
      } else {
        ptr = 0;
        try {
          bufferLength = in.read(buffer);
        } catch (IOException e) {
          e.printStackTrace();
        }
        if (bufferLength <= 0) {
          return false;
        }
      }
      return true;
    }

    private int readByte() {
      if (hasNextByte()) return buffer[ptr++];
      else return -1;
    }

    private static boolean isPrintableChar(int c) {
      return 33 <= c && c <= 126;
    }

    private void skipUnprintable() {
      while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
    }

    boolean hasNext() {
      skipUnprintable();
      return hasNextByte();
    }

    public String next() {
      if (!hasNext()) throw new NoSuchElementException();
      StringBuilder sb = new StringBuilder();
      int b = readByte();
      while (isPrintableChar(b)) {
        sb.appendCodePoint(b);
        b = readByte();
      }
      return sb.toString();
    }

    long nextLong() {
      if (!hasNext()) throw new NoSuchElementException();
      long n = 0;
      boolean minus = false;
      int b = readByte();
      if (b == '-') {
        minus = true;
        b = readByte();
      }
      if (b < '0' || '9' < b) {
        throw new NumberFormatException();
      }
      while (true) {
        if ('0' <= b && b <= '9') {
          n *= 10;
          n += b - '0';
        } else if (b == -1 || !isPrintableChar(b)) {
          return minus ? -n : n;
        } else {
          throw new NumberFormatException();
        }
        b = readByte();
      }
    }

    double nextDouble() {
      return Double.parseDouble(next());
    }

    double[] nextDoubleArray(int n) {
      double[] array = new double[n];
      for (int i = 0; i < n; i++) {
        array[i] = nextDouble();
      }
      return array;
    }

    double[][] nextDoubleMap(int n, int m) {
      double[][] map = new double[n][];
      for (int i = 0; i < n; i++) {
        map[i] = nextDoubleArray(m);
      }
      return map;
    }

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

    public int[] nextIntArray(int n) {
      int[] array = new int[n];
      for (int i = 0; i < n; i++) array[i] = nextInt();
      return array;
    }

    public long[] nextLongArray(int n) {
      long[] array = new long[n];
      for (int i = 0; i < n; i++) array[i] = nextLong();
      return array;
    }

    public String[] nextStringArray(int n) {
      String[] array = new String[n];
      for (int i = 0; i < n; i++) array[i] = next();
      return array;
    }

    public char[][] nextCharMap(int n) {
      char[][] array = new char[n][];
      for (int i = 0; i < n; i++) array[i] = next().toCharArray();
      return array;
    }

    public int[][] nextIntMap(int n, int m) {
      int[][] map = new int[n][];
      for (int i = 0; i < n; i++) {
        map[i] = nextIntArray(m);
      }
      return map;
    }
  }
}