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.math.*;
import java.util.*;
import java.lang.*;

public class Main implements Runnable {
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1)
                throw new InputMismatchException();

            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }

                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        public int nextInt() {
            int c = read();

            while (isSpaceChar(c))
                c = read();

            int sgn = 1;

            if (c == '-') {
                sgn = -1;
                c = read();
            }

            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));

            return res * sgn;
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;

            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
            return res * sgn;
        }

        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            }
            while (!isSpaceChar(c));

            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return readString();
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }

    public static void main(String args[]) throws Exception {
        new Thread(null, new Main(), "Main", 1 << 26).start();
    }

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

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

    static long modPow(long a, long p, long m) {
        if (a == 1) return 1;
        long ans = 1;
        while (p > 0) {
            if (p % 2 == 1) ans = (ans * a) % m;
            a = (a * a) % m;
            p >>= 1;
        }
        return ans;
    }

    static long modInv(long a, long m) {
        return modPow(a, m - 2, m);
    }

    static long sol_x, sol_y, gcd_a_b;

    static void extendedEuclid(long a, long b) {
        if (b == 0) {
            gcd_a_b = a;
            sol_x = 1;
            sol_y = 0;
        } else {
            extendedEuclid(b, a % b);
            long temp = sol_x;
            sol_x = sol_y;
            sol_y = temp - (a / b) * sol_y;
        }
    }

    long modInverse(long a, long prime)
    {
        a = a % prime;
        for (int x=1; x<prime; x++)
            if ((a*x) % prime == 1)
                return x;

        return -1;
    }

    static class Bhavansort {
        Random random;

        Bhavansort(int a[]) {
            randomArray(a);
            sort(a);
        }

        Bhavansort(long a[]) {
            randomArray(a);
            sort(a);
        }

        static int[] sort(int a[]) {
            Arrays.sort(a);
            return a;
        }

        static long[] sort(long a[]) {
            Arrays.sort(a);
            return a;
        }

        void randomArray(long a[]) {
            int n = a.length;
            for (int i = 0; i < n; i++) {
                int p = random.nextInt(n) % n;
                long tm = a[i];
                a[i] = a[p];
                a[p] = tm;
            }
        }

        void randomArray(int a[]) {
            int n = a.length;
            for (int i = 0; i < n; i++) {
                int p = random.nextInt(n) % n;
                int tm = a[i];
                a[i] = a[p];
                a[p] = tm;
            }
        }
    }


    public void run() {
        InputReader sc = new InputReader(System.in);
        //Scanner sc=new Scanner(System.in);
        // Random rn=new Random();
        PrintWriter out = new PrintWriter(System.out);

        int n=sc.nextInt();
        int mod=sc.nextInt();
        int a[]=new int[n];
        for (int i = 0; i <n ; i++) {
            a[i]=sc.nextInt();
        }

        int l=0,r=mod,ans=mod;
        while (l<=r){
            int mid=(l+r)>>1;
            if(possible(mid,a,mod)){
                ans=mid;
                r=mid-1;
            }
            else{
                l=mid+1;
            }
        }
        out.println(ans);

        out.close();
    }

    boolean possible(int mid,int a[],int mod){
        int last=0;
        for (int i = 0; i <a.length ; i++) {
            if(last==a[i])continue;
            else if(last<a[i]){
                int temp=mod-a[i];
                temp+=last;
                if(temp<=mid){

                }
                else{
                    last=a[i];
                }
            }
            else{
                if(last-a[i]>mid)return false;
            }
        }
        return true;
    }



 }