Problem: The only difference between easy and hard versions is a number of elements in the array.

You are given an array a consisting of n integers. The value of the i-th element of the array is a_i.

You are also given a set of m segments. The j-th segment is [l_j; r_j], where 1 ≤ l_j ≤ r_j ≤ n.

You can choose some subset of the given set of segments and decrease values on each of the chosen segments by one (independently). For example, if the initial array a = [0, 0, 0, 0, 0] and the given segments are [1; 3] and [2; 4] then you can choose both of them and the array will become b = [-1, -2, -2, -1, 0].

You have to choose some subset of the given segments (each segment can be chosen at most once) in such a way that if you apply this subset of segments to the array a and obtain the array b then the value max_{i=1}^{n}b_i - min_{i=1}^{n}b_i will be maximum possible.

Note that you can choose the empty set.

If there are multiple answers, you can print any.

If you are Python programmer, consider using PyPy instead of Python when you submit your code.

Input

The first line of the input contains two integers n and m (1 ≤ n ≤ 10^5, 0 ≤ m ≤ 300) — the length of the array a and the number of segments, respectively.

The second line of the input contains n integers a_1, a_2, ..., a_n (-10^6 ≤ a_i ≤ 10^6), where a_i is the value of the i-th element of the array a.

The next m lines are contain two integers each. The j-th of them contains two integers l_j and r_j (1 ≤ l_j ≤ r_j ≤ n), where l_j and r_j are the ends of the j-th segment.

Output

In the first line of the output print one integer d — the maximum possible value max_{i=1}^{n}b_i - min_{i=1}^{n}b_i if b is the array obtained by applying some subset of the given segments to the array a.

In the second line of the output print one integer q (0 ≤ q ≤ m) — the number of segments you apply.

In the third line print q distinct integers c_1, c_2, ..., c_q in any order (1 ≤ c_k ≤ m) — indices of segments you apply to the array a in such a way that the value max_{i=1}^{n}b_i - min_{i=1}^{n}b_i of the obtained array b is maximum possible.

If there are multiple answers, you can print any.

Examples

Input


5 4
2 -2 3 1 2
1 3
4 5
2 5
1 3


Output


6
2
4 1 


Input


5 4
2 -2 3 1 4
3 5
3 4
2 4
2 5


Output


7
2
3 2 


Input


1 0
1000000


Output


0
0

Note

In the first example the obtained array b will be [0, -4, 1, 1, 2] so the answer is 6.

In the second example the obtained array b will be [2, -3, 1, -1, 4] so the answer is 7.

In the third example you cannot do anything so the answer is 0.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
//267630EY
public class Main1108E2
{
  static PrintWriter out=new PrintWriter(System.out);
  static class segMent
  {
    int[] t;
    int n;
    int[] lazy;
    boolean[] marked;
    public segMent(int[] a,int n)
    {
      this.n=n;
    
      lazy=new int[4*n];
      marked=new boolean[4*n];
      t=new int[4*n];
      build(1,0,a.length-1,a);
    }
    public void build(int v,int tl,int tr,int[] a)
    {
      if(tl==tr)
      {
        t[v]=a[tl];
      }
      else
      {
        
        int tm=(tl+tr)/2;
     
        build(2*v,tl,tm,a);
        build(2*v+1,tm+1,tr,a);
        t[v]=Math.min(t[2*v+1],t[2*v]);
      }
    }
    public void push(int v)
    {
      
      t[2*v]+=lazy[v];
      t[2*v+1]+=lazy[v];
      lazy[2*v]+=lazy[v];
      lazy[2*v+1]+=lazy[v];
      lazy[v]=0;
      
    }
          
    public void update(int v,int tl,int tr,int l,int r,int val)
    {
      if(l>r) return;
      else if(l==tl&&r==tr)
      {
        t[v]+=val;
        lazy[v]+=val;
       
      }
      else
      {
        push(v);
        int tm=(tl+tr)/2;
        
        update(2*v,tl,tm,l,Math.min(tm,r),val);
        update(2*v+1,tm+1,tr,Math.max(l,tm+1),r,val);
        t[v]=Math.min(t[2*v],t[2*v+1]);
      }
    }
    public int query(int v,int tl,int tr,int l,int r)
    {
      if(l>r) return 1000000000;
      else if(l<=tl&&r>=tr)
      {
        return t[v];
      }
      else
      {
        push(v);
        int tm=(tl+tr)/2;
        return Math.min(query(2*v,tl,tm,l,Math.min(tm,r)),query(2*v+1,tm+1,tr,Math.max(tm+1,l),r));
      }
    }
  }
  public static int max(int[] a)
  {
    int res=-10000000;
    for(int i=0;i<a.length;i++)
    {
      if(res<a[i])
        res=a[i];
    }
    return res;
  }
  public  static int min(int[] a)
  {
    int min=100000000;
    for(int i=0;i<a.length;i++)
    {
      if(min>a[i])
        min=a[i];
    }
    return min;
  }
  
  public static void main(String[] args) throws IOException
  {
    Scanner sc=new Scanner(System.in);
    //long startTime=System.nanoTime();
    int n=sc.nextInt();
    int m=sc.nextInt();
    int[] a=sc.nextIntArray(n);
    int[] l=new int[m];
    int[] r=new int[m];
    for(int i=0;i<m;i++)
    {
      l[i]=sc.nextInt();
      r[i]=sc.nextInt();
      l[i]-=1;
      r[i]-=1;
    }
    int ans=max(a)-min(a);   
    
    Vector<Integer> sol=new Vector<Integer>();
    Vector<Integer>[] pos=(Vector<Integer>[]) new Vector[n+1];
    Vector<Integer>[] neg=(Vector<Integer>[]) new Vector[n+1];
    
    for(int i=0;i<=n;i++)
    {
      
      pos[i]=new Vector<Integer>();
      neg[i]=new Vector<Integer>();
    }
    
    for(int j=0;j<m;j++)
    {
      
      pos[r[j]+1].add(j);
      neg[l[j]].add(j);
    }
      
    int ansin=0;
    segMent tr=new segMent(a,n);
    for(int i=0;i<m;i++)
      tr.update(1,0,a.length-1,l[i],r[i],-1);
    
    for(int i=0;i<n;i++)
    {
      for(int j=0;j<pos[i].size();j++)
      {
        int k=pos[i].elementAt(j);
        tr.update(1,0,a.length-1,l[k],r[k],-1);
      }
      for(int j=0;j<neg[i].size();j++)
      {
        int k=neg[i].elementAt(j);
        tr.update(1,0,a.length-1,l[k],r[k],+1);
      }
          
      int minNew=tr.query(1,0,a.length-1,0,a.length-1);
      
      if(a[i]-minNew>=ans)
      {
        
        ans=a[i]-minNew;
        ansin=i;
        
        
      }
    }
   
    for(int i=0;i<m;i++)
    {
      if(!(l[i]<=ansin&&r[i]>=ansin))
        sol.add(i);
    }
    
    out.println(ans);
    out.println(sol.size());
    for(int i:sol)
      out.print((i+1)+" ");
    out.flush();
    //long endTime=System.nanoTime();
    //out.println((endTime-startTime)+"ns");
    //out.flush();
      
 
  }
  static class Scanner
  {
    BufferedReader br;
    StringTokenizer tk=new StringTokenizer("");
    public Scanner(InputStream is) 
        {
      br=new BufferedReader(new InputStreamReader(is));
    }
        public int nextInt() throws IOException
        {
          if(tk.hasMoreTokens())
                return Integer.parseInt(tk.nextToken());
          tk=new StringTokenizer(br.readLine());
          return nextInt();
        }
        public long nextLong() throws IOException
        {
            if(tk.hasMoreTokens())
              return Long.parseLong(tk.nextToken());
            tk=new StringTokenizer(br.readLine());
            return nextLong();
        }
        public String next() throws IOException
        {
          if(tk.hasMoreTokens())
            return (tk.nextToken());
            tk=new StringTokenizer(br.readLine());
            return next();
        }
        public String nextLine() throws IOException
        {
          tk=new StringTokenizer("");
          return br.readLine();
        }
        public double nextDouble() throws IOException
        {
            if(tk.hasMoreTokens())
              return Double.parseDouble(tk.nextToken());
            tk=new StringTokenizer(br.readLine());
            return nextDouble();
        }
        public char nextChar() throws IOException
        {
            if(tk.hasMoreTokens())
              return (tk.nextToken().charAt(0));
            tk=new StringTokenizer(br.readLine());
            return nextChar();
        }
        public int[] nextIntArray(int n) throws IOException
        {
            int a[]=new int[n];
            for(int i=0;i<n;i++)
              a[i]=nextInt();
            return a;
        }
        public long[] nextLongArray(int n) throws IOException
        {
          long a[]=new long[n];
            for(int i=0;i<n;i++)
              a[i]=nextLong();
            return a;
        }
        public int[] nextIntArrayOneBased(int n) throws IOException
        {
          int a[]=new int[n+1];
            for(int i=1;i<=n;i++)
              a[i]=nextInt();
            return a;
        }
        public long[] nextLongArrayOneBased(int n) throws IOException
        {
          long a[]=new long[n+1];
          for(int i=1;i<=n;i++)
                a[i]=nextLong();
          return a;
        }
  }
}