Toad Zitz has an array of integers, each integer is between 0 and m-1 inclusive. The integers are a_1, a_2, …, a_n.

In one operation Zitz can choose an integer k and k indices i_1, i_2, …, i_k such that 1 ≤ i_1 < i_2 < … < i_k ≤ n. He should then change a_{i_j} to ((a_{i_j}+1) mod m) for each chosen integer i_j. The integer m is fixed for all operations and indices.

Here x mod y denotes the remainder of the division of x by y.

Zitz wants to make his array non-decreasing with the minimum number of such operations. Find this minimum number of operations.

Input

The first line contains two integers n and m (1 ≤ n, m ≤ 300 000) — the number of integers in the array and the parameter m.

The next line contains n space-separated integers a_1, a_2, …, a_n (0 ≤ a_i < m) — the given array.

Output

Output one integer: the minimum number of described operations Zitz needs to make his array non-decreasing. If no operations required, print 0.

It is easy to see that with enough operations Zitz can always make his array non-decreasing.

Examples

Input


5 3
0 0 0 1 2


Output


0


Input


5 7
0 6 1 3 2


Output


1

Note

In the first example, the array is already non-decreasing, so the answer is 0.

In the second example, you can choose k=2, i_1 = 2, i_2 = 5, the array becomes [0,0,1,3,3]. It is non-decreasing, so the answer is 1.
/*
 * Remember a 6.72 student can know more than a 10.0 student.
 * Grades don't determine intelligence, they test obedience. 
 * I Never Give Up.
 * I will become Candidate Master.
 * I will defeat Saurabh Anand.
 * Skills are Cheap,Passion is Priceless.
 */
import java.util.*;
import java.util.Map.Entry;
import java.io.*;

import static java.lang.System.out;
import static java.util.Arrays.*;
import static java.lang.Math.*;
 
public class ContestMain{
	private static Reader in=new Reader();
	private static StringBuilder ans=new StringBuilder();
	private static long MOD=(long)1e9+7;
	private static final int N=(int) (1e6+7); // 1e5+7
    private static ArrayList<Integer> v[]=new ArrayList[N];
	private static boolean mark[]=new boolean[N];
//    private static BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	private static long powmod(long x,long n){
		if(n==0||x==0)
			return 1;
		else if(n%2==0)
			return(powmod((x*x)%MOD,n/2));
		else
			return (x*(powmod((x*x)%MOD,(n-1)/2)))%MOD;
	}
	private static void shuffle(long[] arr){
		for(int i=arr.length-1;i>=2;i--){
			int x=new Random().nextInt(i-1);
			long temp=arr[x];
			arr[x]=arr[i];
			arr[i]=temp;
		}
	}
	private static void shuffle(int[] arr){
		for(int i=arr.length-1;i>=2;i--){
			int x=new Random().nextInt(i-1);
			int temp=arr[x];
			arr[x]=arr[i];
			arr[i]=temp;
		}
	}
    private static long gcd(long a, long b){
        if(b==0)return a;
        return gcd(b,a%b);
    }
    private static int mod(int a,int b){
    	return (b+a%b)%b;
    }
//    private static boolean check(int x,int y){
//        if((x>=0&&x<n)&&(y>=0&&y<m)&&mat[x][y]!='X'&&!visited[x][y])return true;
//        return false;
//    }
    public static boolean check(int ar[],int maxOp,int m){
    	int prev=0,k;
    	for(int i=0;i<ar.length;i++){
    		if(ar[i]>=prev){
    			k=mod(prev-ar[i],m);
    			if(k>maxOp)prev=ar[i];
    		}
    		else{
    			k=prev-ar[i];
    			if(k>maxOp)return false;
    		}
    	}
    	return true;
    }
	public static void main(String[] args) throws IOException{
		int n=in.nextInt();
		int m=in.nextInt();
		int ar[]=new int[n];
		rep(ar,0,n-1);
		int l=0,r=m,mid;
		while(l+1!=r&&l<r){
			mid=(l+r)/2;
			if(check(ar,mid,m))r=mid;
			else l=mid;
		}
		if(check(ar,l,m))pn(l);
		else pn(r);
	}
	static class Pair<T> implements Comparable<Pair>{
		int l;
		int r;
		Pair(){
			l=0;
			r=0;
		}
		Pair(int k,int v){
			l=k;
			r=v;
		}
		@Override
		public int compareTo(Pair o){
			if(l!=o.l)return (int)(l-o.l);
			return (int)(r-o.r);
		}
		// Fenwick tree question comparator
//        @Override
//        public int compareTo(Pair o) {
//            if(o.r!=r)return (int) (r-o.r);
//            else return (int)(l-o.l);
//        }
	}
	//Reader Class
	static class Reader{
		BufferedReader br;
		StringTokenizer st;
		public Reader(){br=new BufferedReader(new InputStreamReader(System.in));}
		String next(){
			while(st==null||!st.hasMoreElements()){
				try{st=new StringTokenizer(br.readLine());
				}catch(IOException e){e.printStackTrace();}
			}
			return st.nextToken();
		}
		int nextInt(){return Integer.parseInt(next());}
		long nextLong(){return Long.parseLong(next());}
		double nextDouble(){return Double.parseDouble(next());}
		String nextLine(){
			String str="";
			try{
				str=br.readLine();
			}catch(IOException e){
				e.printStackTrace();
			}
			return str;
		}
	}
	//Looping methods
	static void rep(int ar[],int start,int end){
		for(int i=start;i<=end;i++)
			ar[i]=in.nextInt();
	}
	static void rep(long ar[],int start,int end){
		for(int i=start;i<=end;i++)
			ar[i]=in.nextLong();
	}
	static void rep(String ar[],int start,int end){
		for(int i=start;i<=end;i++)
			ar[i]=in.next();
	}
	//Printer Methods
	static void pn(Object o){out.print(o);}
	static void pln(Object o){out.println(o);}
	static void pln(){out.println();}
	static void pf(String format,Object o){out.printf(format,o);}
	//Appenders
	static void app(Object o){ans.append(o);}
}