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.BufferedInputStream;
import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Main {
	public static void main(String[] args) throws FileNotFoundException, IOException {
		InputReader in = new InputReader(new BufferedInputStream(System.in));
		PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
		TaskB solver = new TaskB();
//		long t1 = System.currentTimeMillis();
		solver.solve(1, in, out);
		out.flush();
//		long t2 = System.currentTimeMillis();
//		System.err.println(t2 - t1);
		out.close();

	}
}

class Pos implements Comparable<Pos> {
	int x;
	int y;
	long val;

	public Pos(int x, int y, long val) {
		this.x = x;
		this.y = y;
		this.val = val;
	}

	public int compareTo(Pos p) {
		if (val == p.val) {
			if (x == p.x)
				return Integer.compare(y, p.y);
			return Integer.compare(x, p.x);
		}
		return Long.compare(val, p.val);
	}

}

class Pair implements Comparable<Pair> {
	int fir;
	int sec;

	Pair(int fir, int sec) {
		this.fir = fir;
		this.sec = sec;
	}

	public int compareTo(Pair p) {
		return Integer.compare(fir, p.fir);
	}
}

class TaskB {

	int INF = (int) 1e9 + 7;
	int id[];
	int sz[];
	long queue[];

	void solve(int testNumber, InputReader in, PrintWriter pw) {
		int n = in.nextInt();
		int m = in.nextInt();
		int a[] = new int[n];
		for (int i = 0; i < n; ++i)
			a[i] = in.nextInt();
		int l = -1;
		int r = m;
		while (l < r - 1) {
			int mid = (l + r) / 2;
			boolean ok = check(a, mid, m);
//			System.err.println(ok);
			if (ok) {
				r = mid;
			} else {
				l = mid;
			}
		}
		pw.println(r);
	}

	boolean check(int a[], int x, int m) {
		int n = a.length;
		int min = 0;
		for (int i = 0; i < n; ++i) {
			if (a[i] <= min) {
				if (a[i] + x < min)
					return false;
			} else {
				if (a[i] + x - m < min)
					min = a[i];
			}
		}
		return true;
	}

	int find(int x) {
		int p = x;
		if (p == id.length)
			return p;
		while (id[p] != p) {
			p = id[p];
		}
		while (id[x] != x) {
			int tmp = id[x];

			id[x] = p;
			x = tmp;
		}
		return p;

	}

	void union(int x, int y) {
		int u = find(x);
		int v = find(y);
		if (u == v)
			return;
		id[v] = u;
		sz[u] += sz[v];
	}

	long gcd(long a, long b) {
		if (b == 0)
			return a;
		return gcd(b, a % b);
	}
}

class InputReader {
	BufferedReader br;
	StringTokenizer st;

	public InputReader(InputStream in) {
		br = new BufferedReader(new InputStreamReader(in));
		st = null;
	}

	public String next() {
		while (st == null || !st.hasMoreTokens()) {
			try {
				st = new StringTokenizer(br.readLine());
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		return st.nextToken();
	}

	public int nextInt() {
		return Integer.parseInt(next());
	}

	public long nextLong() {
		return Long.parseLong(next());
	}

	public double nextDouble() {
		return Double.parseDouble(next());
	}
}