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.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

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

  static class TaskD {
    int n;
    int m;
    TaskD.Range[] ranges;
    int resIdx;

    public void solve(int testNumber, QuickScanner in, QuickWriter out) {
      n = in.nextInt();
      m = in.nextInt();
      ranges = new TaskD.Range[n];
      for (int i = 0; i < n; ++i) {
        int lower = in.nextInt();
        int upper = in.nextInt();
        ranges[i] = new TaskD.Range(lower, upper, i);
      }
      Arrays.sort(ranges);
      int res = calc();
      out.println(res);
      if (res == 0) {
        for (int i = 0; i < m; ++i) {
          if (i > 0) out.print(' ');
          out.print(i + 1);
        }
      } else {
        out.print(ranges[resIdx].idx + 1);
        for (int i = 0, rem = m - 1; i < resIdx && rem > 0; ++i)
          if (ranges[resIdx].lower + res - 1 <= ranges[i].upper) {
            out.print(' ');
            out.print(ranges[i].idx + 1);
          }
      }
      out.println();
    }

    int calc() {
      int res;
      if (m == 1) {
        resIdx = 0;
        res = ranges[0].length();
        for (int i = 1; i < n; ++i)
          if (res < ranges[i].length()) {
            res = ranges[i].length();
            resIdx = i;
          }
        return res;
      }
      res = 0;
      IntPriorityQueue queue = new IntPriorityQueue(m - 1);
      for (int i = 0; i < m - 1; ++i) {
        queue.add(ranges[i].upper);
      }
      for (int i = m - 1; i < n; ++i) {
        int curRes = Math.min(queue.peek(), ranges[i].upper) - ranges[i].lower + 1;
        if (res < curRes) {
          res = curRes;
          resIdx = i;
        }
        if (queue.peek() < ranges[i].upper) {
          queue.poll();
          queue.add(ranges[i].upper);
        }
      }
      return res;
    }

    static class Range implements Comparable<TaskD.Range> {
      final int lower;
      final int upper;
      final int idx;

      Range(int lower, int upper, int idx) {
        this.lower = lower;
        this.upper = upper;
        this.idx = idx;
      }

      int length() {
        return upper - lower + 1;
      }


      public int compareTo(TaskD.Range o) {
        return lower - o.lower;
      }


      public String toString() {
        return String.format("[%d,%d]:%d", lower, upper, idx);
      }

    }

  }

  static interface IntComparator {
    int compare(int o1, int o2);

  }

  static class QuickWriter {
    private final PrintWriter writer;

    public QuickWriter(OutputStream outputStream) {
      this.writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public QuickWriter(Writer writer) {
      this.writer = new PrintWriter(writer);
    }

    public void print(Object... objects) {
      for (int i = 0; i < objects.length; ++i) {
        if (i > 0) {
          writer.print(' ');
        }
        writer.print(objects[i]);
      }
    }

    public void println(Object... objects) {
      print(objects);
      writer.print('\n');
    }

    public void close() {
      writer.close();
    }

  }

  static class IntPriorityQueue extends IntArrayList {
    private final IntComparator comparator;

    public IntPriorityQueue(int capacity) {
      this(capacity, (x, y) -> x - y);
    }

    public IntPriorityQueue(int capacity, IntComparator comparator) {
      super(capacity);
      this.comparator = comparator;
      clear();
    }


    public void add(int value) {
      super.add(value);
      int i = size - 1;
      while (i > 0) {
        int parent = (i - 1) >> 1;
        int parentValue = values[parent];
        if (comparator.compare(value, parentValue) >= 0) break;
        values[i] = parentValue;
        i = parent;
      }
      values[i] = value;
    }

    public int peek() {
      if (size == 0) throw new ArrayIndexOutOfBoundsException();
      return values[0];
    }

    public int poll() {
      if (size == 0) throw new ArrayIndexOutOfBoundsException();
      int res = values[0];
      int value = values[--size];
      int half = size >> 1;
      int i = 0;
      while (i < half) {
        int child = (i << 1) | 1;
        int childValue = values[child];
        int right = child + 1;
        if (right < size && comparator.compare(childValue, values[right]) > 0) {
          child = right;
          childValue = values[child];
        }
        if (comparator.compare(value, childValue) <= 0) break;
        values[i] = childValue;
        i = child;
      }
      values[i] = value;
      return res;
    }


    public String toString() {
      StringBuilder sb = new StringBuilder("[");
      for (int i = 0; i < size; ++i) {
        if (i > 0) sb.append(',').append(' ');
        sb.append(values[i]);
      }
      return sb.append(']').toString();
    }

  }

  static class IntArrayUtils {
    public static String toString(int[] values, int fromIdx, int toIdx) {
      StringBuilder sb = new StringBuilder("[");
      for (int i = fromIdx; i < toIdx; ++i) {
        if (i != fromIdx) sb.append(", ");
        sb.append(values[i]);
      }
      return sb.append("]").toString();
    }

  }

  static interface IntCollection {
  }

  static class QuickScanner {
    private static final int BUFFER_SIZE = 1024;
    private InputStream stream;
    private byte[] buffer;
    private int currentPosition;
    private int numberOfChars;

    public QuickScanner(InputStream stream) {
      this.stream = stream;
      this.buffer = new byte[BUFFER_SIZE];
      this.currentPosition = 0;
      this.numberOfChars = 0;
    }

    public int nextInt() {
      int c = nextNonSpaceChar();
      boolean positive = true;
      if (c == '-') {
        positive = false;
        c = nextChar();
      }
      int res = 0;
      do {
        if (c < '0' || '9' < c) throw new RuntimeException();
        res = res * 10 + c - '0';
        c = nextChar();
      } while (!isSpaceChar(c));
      return positive ? res : -res;
    }

    public int nextNonSpaceChar() {
      int res = nextChar();
      for (; isSpaceChar(res) || res < 0; res = nextChar()) ;
      return res;
    }

    public int nextChar() {
      if (numberOfChars == -1) {
        throw new RuntimeException();
      }
      if (currentPosition >= numberOfChars) {
        currentPosition = 0;
        try {
          numberOfChars = stream.read(buffer);
        } catch (Exception e) {
          throw new RuntimeException(e);
        }
        if (numberOfChars <= 0) {
          return -1;
        }
      }
      return buffer[currentPosition++];
    }

    public boolean isSpaceChar(int c) {
      return c == ' ' || c == '\t' || isEndOfLineChar(c);
    }

    public boolean isEndOfLineChar(int c) {
      return c == '\n' || c == '\r' || c < 0;
    }

  }

  static class IntArrayList implements IntCollection {
    private static final int[] EMPTY = {};
    public int[] values;
    public int size;

    public IntArrayList() {
      values = EMPTY;
      clear();
    }

    public IntArrayList(int capacity) {
      values = new int[Integer.highestOneBit(capacity) << 1];
      clear();
    }


    public void clear() {
      size = 0;
    }


    public void add(int value) {
      ensureCapacity(size + 1);
      values[size++] = value;
    }


    public String toString() {
      return IntArrayUtils.toString(values, 0, size);
    }

    public void ensureCapacity(int capacity) {
      if (capacity <= values.length) return;
      int[] newValues = new int[Integer.highestOneBit(capacity) << 1];
      for (int i = 0; i < size; ++i) {
        newValues[i] = values[i];
      }
      values = newValues;
    }

  }
}