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.*;
import java.nio.CharBuffer;
import java.util.NoSuchElementException;

public class P1169C {

    public static void main(String[] args) {
        SimpleScanner scanner = new SimpleScanner(System.in);
        PrintWriter writer = new PrintWriter(System.out);

        int n = scanner.nextInt();
        int m = scanner.nextInt();
        int[] x = new int[n];
        for (int i = 0; i < n; ++i)
            x[i] = scanner.nextInt();
        int l = 0, r = m - 1;
        while (l < r) {
            int mid = (l + r) >> 1;
            if (!test(x, mid, m)) {
                l = mid + 1;
            } else
                r = mid;
        }
        writer.println(l);
        writer.close();
    }

    private static boolean test(int[] x, int k, int m) {
        int n = x.length;
        int pre = 0;
        for (int value : x) {
            if (value + k < m) {
                if (value + k < pre)
                    return false;
                pre = Math.max(value, pre);
            } else {
                if (pre < value && pre > (value + k) % m)
                    pre = value;
            }
        }
        return true;
    }

    private static boolean testOne(int[][] pair, int base, int x) {
        int m = pair.length;
        for (int i = base; i < m; ++i) {
            if (pair[i][0] != x && pair[i][1] != x) {
                return testTwo(pair, i, x, pair[i][0]) || testTwo(pair, i, x, pair[i][1]);
            }
        }
        return true;
    }

    private static boolean testTwo(int[][] pair, int base, int x, int y) {
        int m = pair.length;
        for (int i = base; i < m; ++i) {
            if (pair[i][0] != x && pair[i][0] != y && pair[i][1] != x && pair[i][1] != y) {
                return false;
            }
        }
        return true;
    }

    private static class SimpleScanner {

        private static final int BUFFER_SIZE = 10240;

        private Readable in;
        private CharBuffer buffer;
        private boolean eof;

        SimpleScanner(InputStream in) {
            this.in = new BufferedReader(new InputStreamReader(in));
            buffer = CharBuffer.allocate(BUFFER_SIZE);
            buffer.limit(0);
            eof = false;
        }


        private char read() {
            if (!buffer.hasRemaining()) {
                buffer.clear();
                int n;
                try {
                    n = in.read(buffer);
                } catch (IOException e) {
                    n = -1;
                }
                if (n <= 0) {
                    eof = true;
                    return '\0';
                }
                buffer.flip();
            }
            return buffer.get();
        }

        void checkEof() {
            if (eof)
                throw new NoSuchElementException();
        }

        char nextChar() {
            checkEof();
            char b = read();
            checkEof();
            return b;
        }

        String next() {
            char b;
            do {
                b = read();
                checkEof();
            } while (Character.isWhitespace(b));
            StringBuilder sb = new StringBuilder();
            do {
                sb.append(b);
                b = read();
            } while (!eof && !Character.isWhitespace(b));
            return sb.toString();
        }

        int nextInt() {
            return Integer.valueOf(next());
        }

        long nextLong() {
            return Long.valueOf(next());
        }

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