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.util.*;
import java.io.*;
public class Main {
	static InputReader in = new InputReader(System.in);
	static int powers[] = new int[11];
	
	public static void main(String args[]) {
		int n = in.readInt(), k = in.readInt();
		Interval a[]=new Interval[n];
		for(int i=0;i<n;i++) a[i]=new Interval(in.readInt(),in.readInt(),i);
		Arrays.sort(a,new Comparator<Interval>() {
			public int compare(Interval i1,Interval i2) {
				if(i1.s<i2.s) return -1;
				if(i1.s==i2.s) {
					if(i1.f<i2.f) return -1;
					if(i1.f==i2.f) return 0;
					return 1;
				};
				return 1;
			}
		});
		
		TreeMap<Long, Long> t = new TreeMap<Long, Long>();
		PriorityQueue<Interval> pq = new PriorityQueue<Interval>(1, new Comparator<Interval>() {
			public int compare(Interval i1,Interval i2) {
				if(i1.f<i2.f) return -1;
				if(i1.f==i2.f) {
					if(i1.s<i2.s) return -1;
					if(i1.s==i2.s) return 0;
					return 1;
				};
				return 1;
			}
		});
		for(int i=0;i<k;i++) {
			if(t.containsKey(a[i].s)) {
				t.put(a[i].s,t.get(a[i].s)+1);
			}else t.put(a[i].s, (long)1);
			pq.add(a[i]);
		}
		long ans=0;
		int l=0;
		
		for(int i=0;i<n-k+1;i++) {
			Interval rem = pq.poll();
			if(t.higherEntry(rem.f)==null) {
				if((rem.f-t.lowerKey(rem.f+1)+1)>ans) {
					ans=rem.f-t.lowerKey(rem.f+1)+1;
					l=i;
				}
			}
			t.put(rem.s,t.get(rem.s)-1);
			if(t.get(rem.s)<=0) t.remove(rem.s);
			if(i+k<n) {
				if(t.containsKey(a[i+k].s)) {
					t.put(a[i+k].s,t.get(a[i+k].s)+1);
				}else t.put(a[i+k].s, (long)1);
				pq.add(a[i+k]);
			}
		}
		pq.clear();
		System.out.println(ans);
		for(int i=0;i<k;i++) {
			pq.add(a[i]);
		}
		for(int i=0;i<n-k+1;i++) {
			if(i==l) {
				while(!pq.isEmpty()) {
					System.out.print((pq.poll().in+1)+" ");
				}
				return;
			}else pq.poll();
			if(i+k<n) {
				pq.add(a[i+k]);
			}
		}
	}
	
	/*public static void main(String[] args) {
		int t = in.readInt();
		powers[0]=1;
		for(int i=1;i<11;i++) {
			powers[i]=powers[i-1]*3;
		}
		StringBuilder s = new StringBuilder("");
		while(t>0) {
			String s1 = in.next(), s2 = in.next();
			//solve(s1);
			//solve(s2);
			t--;
		}
		System.out.println(s);
	}
	/*static void solve(String s){
		int n = s.length();
		int dp[][][]=new int[20][60000][2];
		for(int i=0;i<10;i++) {
			if(i<=(s.charAt(n-1)-'0')) {
				dp[n-1][1<<i][1<<i][0]++;
			}else dp[n-1][1<<i][1<<i][1]++;
		}
		for(int i=n-2;i>=0;i--) {
			int j;
			for(j=0;j<(s.charAt(i)-'0');j++) {
				for(int k=0;k<1<<10;k++) {
					for(int l=0;l<1<<10;l++) {
						dp[i][k^(1<<j)][l|(1<<j)][0]+=
								dp[i+1][k][l][1]+dp[i+1][k][l][0];
					}
				}
			}
			for(int k=0;k<1<<10;k++) {
				for(int l=0;l<1<<10;l++) {
					dp[i][k^(1<<j)][l|(1<<j)][0]+=dp[i+1][k][l][0];
					dp[i][k^(1<<j)][l|(1<<j)][1]+=dp[i+1][k][l][1];
				}
			}
			j++;
			for(;j<10;j++) {
				for(int k=0;k<1<<10;k++) {
					for(int l=0;l<1<<10;l++) {
						dp[i][k^(1<<j)][l|(1<<j)][1]+=
								dp[i+1][k][l][1]+dp[i+1][k][l][0];
					}
				}
			}
		}
		int ans=0;
		for(int i=0;i<1<<10;i++) {
			for(int j=0;j<1<<10;j++) {
				boolean fl=false;
				int k=j,cn=0;
				while(k>0) {
					if(k>>cn>0) {
						if(cn%2==0 && ((i>>cn)&1)==0) fl=true;
						if(cn%2==1 && ((i>>cn)&1)==1) fl=true;
					}
					cn++;
					k>>=1;
				}
				if(!fl) ans+=dp[0][i][j][0];
			}
		}
		System.out.println(ans);
	}*/
}
class Interval{
	long s,f,in;
	Interval(int x,int y,int i){
		s=x;
		in =i;
		f=y;
	}
}
class Node extends ArrayList<Node>{
	boolean vis = false;
	long numEnded[] = new long[125];
	long numOpen[] = new long[125];
	int minV[] = new int[101];
	int nd;
	Node(int i) {
		nd=i;
	}
	void reset(){
		vis=false;
		numEnded = new long[125];
		numOpen = new long[125];
	}
	void dfs(int k) {
		vis = true;
		Arrays.fill(minV, 1000000);
		for(Node u : this) {
			if(!u.vis) {
				u.dfs(k);
				int temp[] = new int[101];
				Arrays.fill(temp, 1000000);
				for(int j=0;j<=k;j++) {
					for(int i=0;i<=k;i++) {
						if(i+j+1<=k) {
							temp[Math.max(i,j+1)] = 
									Math.min(temp[Math.max(i,j+1)],minV[i]+u.minV[j]);
						}
						temp[0] = Math.min(temp[0],minV[i]+u.minV[j]+1);

					}
				}
				for(int i=0;i<=k;i++)
					minV[i]=Math.min(temp[i],minV[i]);
			}
		}
	}
	void countSubtrees(int k){
		vis = true;
		numOpen[0]++;
		for(Node u : this) {
			if(!u.vis) {
				u.countSubtrees(k);
				long sums[]=new long[70];
				long sum[]=new long[70];
				sum[0]=this.numOpen[0];
				sums[1]=u.numOpen[0];
				for(int i=1;i<=k;i++) {
					sums[i+1]+=sums[i]+u.numOpen[i];
					sum[i]+=sum[i-1]+numOpen[i];
				}
				for(int i=1;i<=k;i++) {
					numOpen[i]+=numOpen[i]*sums[Math.max(0,Math.min(k-i,i-1))];
				}
				for(int i=0;i<k;i++) {
					if(Math.min(k-i-1,i+1)>=0) {
						numOpen[i+1]+=u.numOpen[i]*sum[Math.min(k-i-1,i+1)];
					}
				}
			}
		}
	}
}
/*
public class Main {
	private static InputReader in = new InputReader(System.in);
	public static void main(String args[]) {
		StringBuilder s = new StringBuilder();
		int t = in.readInt();
		while(t>0) {
			
			t--;
		}
		System.out.println(s);
	}

	/*public static int solve(String s, int i,int j,
    		int dp[][],boolean visited[][]) {
    	if(i>j) return 0;
    	if(i==j) return dp[i][j]=1;
    	if(visited[i][j]) return dp[i][j];
    	visited[i][j]=true;
    	solve(s,i+1,j,dp,visited);
    	solve(s,i,j-1,dp,visited);
    	if(s.charAt(i)==s.charAt(j)) {
    		if(i+1==j)
    			return dp[i][j]=2;
    		else {
    			return dp[i][j]=dp[i+1][j]+dp[i][j-1]-dp[i+1][j-1]+1;
    		}
    	}else {
    		if(i+1==j) return dp[i][j]=1;
    		return dp[i][j]=dp[i+1][j]+dp[i][j-1]-dp[i+1][j-1];
    	}
    }*/
	/*
    public static void main(String args[]) {
    	int t = in.nextInt();
    	while(t>0) {
    		int m = in.nextInt(), n = in.nextInt();
    		long p = in.nextLong();
    		long dp[][][]=new long[11][300][300];

    		for(int i=1;i<=m;i++)
    			dp[1][i][i]=1;
    		for(int i=1;i<n;i++) {
    			for(int j=1;j<m;j++) {
    				for(int k=1;k<=j;k++) {
    					for(int l=k;l>=1;l--) {
    						if(j+l<=m)
    							dp[i+1][j+l][l]+=dp[i][j][k];
    					}
    				}
    			}
    		}
    		System.out.println(dp[n][m-1][2]);
    		for(int i=n;i>0;i--) {
    			for(int j=1;j<=m;j++) {
    				if(dp[i][m-j][j]>=p) {
    					//System.out.print(j+" ");
    					m-=j;
    					break;
    				}else {
    					p-=dp[i][m-j][j];
    					System.out.print(p+" ");
    				}
    			}
    		}
    		System.out.println();
    		t--;
    	}

    }*/

class sh implements Comparable<sh>{
	int h,w,i;
	sh(int a,int b,int c){
		w=a;
		h=b;
		i=c;
	}
	@Override
	public int compareTo(sh o) {
		if(w==o.w) return h-o.h;
		return w-o.w;
	}

}

class InputReader {

	private InputStream stream;
	private byte[] buf = new byte[1024];
	private int curChar;
	private int numChars;
	private SpaceCharFilter filter;

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

	public byte 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 readInt() {
		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 - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	public String readString() {
		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) {
		if (filter != null)
			return filter.isSpaceChar(c);
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}

	public String next() {
		return readString();
	}

	public interface SpaceCharFilter {
		public boolean isSpaceChar(int ch);
	}
}

class IOUtils {

	public static int[] readIntArray(InputReader in, int size) {
		int[] array = new int[size];
		for (int i = 0; i < size; i++)
			array[i] = in.readInt();
		return array;
	}
}