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.util.Scanner;

public class C1169 {
	static int[] Array;
	static int UseForMod;
	public static void main(String[] args) {
		Scanner Xv=new Scanner(System.in);
		
		int NumberOfElements=Xv.nextInt();
		UseForMod=Xv.nextInt();
		Array=new int[NumberOfElements];
		
		int j=0;
		while(j!=NumberOfElements) {
			Array[j]=Xv.nextInt();
			j++;
		}
		
		int left=0;
		int right=UseForMod;
		boolean flag=true;
		while(left<=right) {
			int mid=(left+right)/2;
			flag=Solver(mid);
			//System.out.println(mid+" "+flag);
		
			if(flag==true) {
				
				right=mid-1;
			}
			else {
				
				left=mid+1;
			}
		}
		//System.out.println(left+" "+right);
		if(left>right) System.out.println(left);
		else System.out.println(right);
	
		
	}
	
	
	public static boolean Solver(int X) {
		
		int prev=0;
/*				Array[0];
		for(int i=1;i<Array.length;i++) {
			if(prev>Array[i]) prev= Array[i];
			if(prev==0) break;
		}*/
		//System.out.println("PREV IS "+prev);
		int j=0;
		while(j<Array.length) {
			if(prev<=Array[j]) {
				if(prev==Array[j]) prev=Array[j];
				else if(prev<Array[j]) {
					int steps=UseForMod-Array[j]+prev;
					if((steps>X)) prev=Array[j];
				}
			}
			else {
				int steps=prev-Array[j];
				if(steps>X) {
					//System.out.println(prev+" "+Array[j]+" false here! Because X is "+X);
					return false;
				}
			}
			j++;
		}
		return true;
		
	}

	
	
}
