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.
import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Collections;
import java.util.Comparator;
import java.util.Deque;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Random;
import java.util.Set;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

public class q5 {
	static int[] arr;
	static boolean check(int mid,int m) {
		boolean v=true;
		int zc=0;
		int n=arr.length;
		for(int i=0;i<n;i++) {
			if(zc==0) {
				if((m-arr[i])%m<=mid)arr[i]=0;
				else zc=1;
			}
			else {
				if(arr[i]>=arr[i-1]) {
					if((m-arr[i]+arr[i-1])%m<=mid) {
						arr[i]=arr[i-1];
					}
				}
				else {
					int low=0;
					int high=i-1;
					int pos=-1;
					while(low<=high) {
						int miid=(low+high)/2;
						if(arr[miid]<=arr[i]) low=miid+1;
						else {
							pos=miid;high=miid-1;
						}
					}
					if((m-arr[pos]+arr[i])%m<=mid) {
						for(int j=pos;j<=i-1;j++)arr[j]=arr[i];
					}
					else {
						if(arr[i-1]-arr[i]<=mid) {
							arr[i]=arr[i-1];
						}
						else v=false;
					}
				}
			}
		}
		return v;
	}
	public static void main(String[] args) throws IOException {
		
		Reader.init(System.in);
		PrintWriter out=new PrintWriter(System.out);
		StringBuffer output=new StringBuffer("");
		int n=Reader.nextInt(),m=Reader.nextInt();
		arr=new int[n];
		int[] arr2=new int[n];
		for(int i=0;i<n;i++) {arr[i]=Reader.nextInt();arr2[i]=arr[i];}
		int a1=0;
		int ans=m-1;
		int low=0;
		int high=m-1;
		while(low<=high) {
			int mid=(low+high)/2;
			if(check(mid,m)) {
				ans=mid;
				high=mid-1;
			}
			else low=mid+1;
			for(int i=0;i<n;i++)arr[i]=arr2[i];
		}
		out.println(ans);
		out.flush();
	}
}



class NoD{
	int a,b;
	String s;
	double c,d;
	NoD(int aa,int bb){
		a=aa;b=bb;
		s=a+" "+b;
		
	}
	NoD(double cc, double dd){
		c=cc;d=dd;
	}
//	NoD(int aa,int bb,int cc){
//		a=aa;b=bb;c=cc;
//	}
//	NoD(long m,long l,long r,long t){
//		ms=m;ls=l;rs=r;ts=t;
//	}
	@Override
	public boolean equals(Object o) {
		if(o!=null && o.getClass()==getClass()) {
			NoD c= (NoD) o;
			return c.a==a && c.b==b;
		}
		return false;
	}
	@Override
	public int hashCode() {
		return s.hashCode();
	}
}
class DisJoint {
	int[] arr;
	int[] parent;
	int[] rank;
	DisJoint(int n){
		arr=new int[n+1];
		parent=new int[n+1];
		rank=new int[n+1];
		for(int i=1;i<=n;i++) {
			arr[i]=i;
			parent[i]=i;
			rank[i]=0;
		}
	}

	int find(int value) {
		int par=parent[value];
		if(par==value)
			return par;
		parent[value]=find(par);
		return parent[value];
	}
	
	void union(int data1,int data2) {
		int parent1=find(data1);
		int parent2=find(data2);
		if(parent1!=parent2) {
			if(rank[parent1]>=rank[parent2]) {
				parent[parent2]=parent1;
				if(rank[parent1]==rank[parent2])
					rank[parent1]++;
			}
			else {
				parent[parent1]=parent2;
			}
		}
		
	}
	

}

class Seg{
	long[] st;
	long[] arr;
	long[] lazy;
	Seg(int n){
		st=new long[4*n];
		//lazy=new long[4*n];
		
	}
	void build(int index,int low,int high) {
		if(low==high) {
			st[index]=arr[low];
		}
		else {
			int middle=(low+high)/2;
			build(2*index+1,low,middle);
			build(2*index+2,middle+1,high);
			st[index]=Math.min(st[2*index+1], st[2*index+2]);
		}
	}
	
	long query(int index,int low,int high, int ql,int qh) {
//		if(lazy[index]!=0) {
//			st[index]+=lazy[index];
//			if(low<high) {
//				lazy[2*index+1]+=lazy[index];
//				lazy[2*index+2]+=lazy[index];
//				
//			}
//			lazy[index]=0;
//		}
		
		if(ql<=low && high<=qh) {
			return st[index];
		}
		else if(!(ql>high || qh<low)) {
			int middle=(low+high)/2;
			long left=query(2*index+1,low,middle,ql,qh);
			long right=query(2*index+2,middle+1,high,ql,qh);
			//st[index]=st[2*index+1]+ st[2*index+2];
			return left+right;
			
		}
		return 0;
	}
	
	
	void u1(int index, int low,int high, int pos) {
//		if(lazy[index]!=0) {
//			st[index]+=lazy[index];
//			if(low<high) {
//				lazy[2*index+1]+=lazy[index];
//				lazy[2*index+2]+=lazy[index];
//				
//			}
//			lazy[index]=0;
//		}
		if(low==high) {
			st[index]++;
		}
		else {
			int middle=(low+high)/2;
			if(pos<=middle) u1(2*index+1,low,middle,pos);
			else u1(2*index+2,middle+1,high,pos);
			st[index]=st[2*index+1]+ st[2*index+2];
		}
	}
	
	
}
class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;
    /** call this method to initialize reader for InputStream */
    static void init(InputStream input) {
        reader = new BufferedReader(
                     new InputStreamReader(input) );
        tokenizer = new StringTokenizer("");
    }
    /** get next word */
    static String nextLine() throws IOException{
    	return reader.readLine();
    }
    static String next() throws IOException {
        while ( ! tokenizer.hasMoreTokens() ) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                   reader.readLine() );
        }
        return tokenizer.nextToken();
    }
    static int nextInt() throws IOException {
        return Integer.parseInt( next() );
    }
    static long nextLong() throws IOException {
        return Long.parseLong( next() );
    }
    static double nextDouble() throws IOException {
        return Double.parseDouble( next() );
    }
}