In a strategic computer game "Settlers II" one has to build defense structures to expand and protect the territory. Let's take one of these buildings. At the moment the defense structure accommodates exactly n soldiers. Within this task we can assume that the number of soldiers in the defense structure won't either increase or decrease.

Every soldier has a rank — some natural number from 1 to k. 1 stands for a private and k stands for a general. The higher the rank of the soldier is, the better he fights. Therefore, the player profits from having the soldiers of the highest possible rank.

To increase the ranks of soldiers they need to train. But the soldiers won't train for free, and each training session requires one golden coin. On each training session all the n soldiers are present.

At the end of each training session the soldiers' ranks increase as follows. First all the soldiers are divided into groups with the same rank, so that the least possible number of groups is formed. Then, within each of the groups where the soldiers below the rank k are present, exactly one soldier increases his rank by one.

You know the ranks of all n soldiers at the moment. Determine the number of golden coins that are needed to increase the ranks of all the soldiers to the rank k.

Input

The first line contains two integers n and k (1 ≤ n, k ≤ 100). They represent the number of soldiers and the number of different ranks correspondingly. The second line contains n numbers in the non-decreasing order. The i-th of them, ai, represents the rank of the i-th soldier in the defense building (1 ≤ i ≤ n, 1 ≤ ai ≤ k).

Output

Print a single integer — the number of golden coins needed to raise all the soldiers to the maximal rank.

Examples

Input

4 4
1 2 2 3


Output

4

Input

4 3
1 1 1 1


Output

5

Note

In the first example the ranks will be raised in the following manner:

1 2 2 3 →  2 2 3 4 →  2 3 4 4 →  3 4 4 4 →  4 4 4 4

Thus totals to 4 training sessions that require 4 golden coins.
import java.util.*;
import java.io.*;
import java.math.*;

public class Main implements Runnable {

    static int mod = 1000000007;
    static FastReader sc;
    static PrintWriter out;
    static boolean test_case_input = false;
    static final int MAX = 1000000001;
    static final int MIN = -1000000001;

    public static void solution(int test_case) throws IOException {
        // code
        int n = sc.nextInt();
        int k = sc.nextInt();
        Integer a[] = sc.intarr(n);
        int freq[] = new int[101];
        for(int i : a) {
            freq[i]++;
        }
//        debug("done");

        int gold = 0;
        while(freq[k] != n) {
            for(int i = k - 1; i >= 0; i--) {
                if(freq[i] == 0) continue;
                freq[i]--;
                freq[i + 1]++;
            }
//            debug(freq);
            gold++;
        }
        out.println(gold);
    }

    // log A base B
    public static int logint(int x, int base) {
        return (int) (Math.log(x) / Math.log(base));
    }

    public static int logint(long x, long base) {
        return (int) (Math.log(x) / Math.log(base));
    }

    public static int logint(double x, double base) {
        return (int) (Math.log(x) / Math.log(base));
    }

    public static double logdouble(int x, int base) {
        return (Math.log(x) / Math.log(base));
    }

    public static double logdouble(long x, long base) {
        return (Math.log(x) / Math.log(base));
    }

    public static double logdouble(double x, double base) {
        return (Math.log(x) / Math.log(base));
    }

    public static long loglong(int x, int base) {
        return (long) (Math.log(x) / Math.log(base));
    }

    public static long loglong(long x, long base) {
        return (long) (Math.log(x) / Math.log(base));
    }

    public static long loglong(double x, double base) {
        return (long) (Math.log(x) / Math.log(base));
    }

    // Debug
    public static void debug(String msg, Object value) {
        File output = new File("output.txt");
        if (!output.exists()) return;
        String type = value.getClass().getSimpleName();
        if (type.equals("int[]")) out.println(msg + " => " + Arrays.toString((int[]) value));
        else if (type.equals("double[]")) out.println(msg + " => " + Arrays.toString((double[]) value));
        else if (type.equals("float[]")) out.println(msg + " => " + Arrays.toString((float[]) value));
        else if (type.equals("long[]")) out.println(msg + " => " + Arrays.toString((long[]) value));
        else if (type.equals("char[]")) out.println(msg + " => " + Arrays.toString((char[]) value));
        else if (type.equals("String[]")) out.println(msg + " => " + Arrays.toString((String[]) value));
        else if (type.equals("int[][]")) {
            out.println(msg + "=>");
            for (int i[] : (int[][]) value)
                out.println(" . " + Arrays.toString(i).replace(' ', '\t'));
        } else if (type.equals("double[][]")) {
            out.println(msg + "=>");
            for (double i[] : (double[][]) value)
                out.println(" . " + Arrays.toString(i).replace(' ', '\t'));
        } else if (type.equals("float[][]")) {
            out.println(msg + "=>");
            for (float i[] : (float[][]) value)
                out.println(" . " + Arrays.toString(i).replace(' ', '\t'));
        } else if (type.equals("long[][]")) {
            out.println(msg + "=>");
            for (long i[] : (long[][]) value)
                out.println(" . " + Arrays.toString(i).replace(' ', '\t'));
        } else if (type.equals("char[][]")) {
            out.println(msg + "=>");
            for (char i[] : (char[][]) value)
                out.println(" . " + Arrays.toString(i).replace(' ', '\t'));
        } else if (type.equals("String[][]")) {
            out.println(msg + "=>");
            for (String i[] : (String[][]) value)
                out.println(" . " + Arrays.toString(i).replace(' ', '\t'));
        } else out.println(msg + " => " + value);
    }

    public static void debug(Object value) {
        File output = new File("output.txt");
        if (!output.exists()) return;
        String type = value.getClass().getSimpleName();
        if (type.equals("int[]")) out.println(" => " + Arrays.toString((int[]) value));
        else if (type.equals("double[]")) out.println(" => " + Arrays.toString((double[]) value));
        else if (type.equals("float[]")) out.println(" => " + Arrays.toString((float[]) value));
        else if (type.equals("long[]")) out.println(" => " + Arrays.toString((long[]) value));
        else if (type.equals("char[]")) out.println(" => " + Arrays.toString((char[]) value));
        else if (type.equals("String[]")) out.println(" => " + Arrays.toString((String[]) value));
        else if (type.equals("int[][]")) {
            out.println("=>");
            for (int i[] : (int[][]) value)
                out.println(" . " + Arrays.toString(i).replace(' ', '\t'));
        } else if (type.equals("double[][]")) {
            out.println("=>");
            for (double i[] : (double[][]) value)
                out.println(" . " + Arrays.toString(i).replace(' ', '\t'));
        } else if (type.equals("float[][]")) {
            out.println("=>");
            for (float i[] : (float[][]) value)
                out.println(" . " + Arrays.toString(i).replace(' ', '\t'));
        } else if (type.equals("long[][]")) {
            out.println("=>");
            for (long i[] : (long[][]) value)
                out.println(" . " + Arrays.toString(i).replace(' ', '\t'));
        } else if (type.equals("char[][]")) {
            out.println("=>");
            for (char i[] : (char[][]) value)
                out.println(" . " + Arrays.toString(i).replace(' ', '\t'));
        } else if (type.equals("String[][]")) {
            out.println("=>");
            for (String i[] : (String[][]) value)
                out.println(" . " + Arrays.toString(i).replace(' ', '\t'));
        } else out.println(" => " + value);
    }

    // Graph Functions
    public static void addUndirectedEdge(ArrayList<ArrayList<Integer>> adj, int u, int v) {
        adj.get(u).add(v);
        adj.get(v).add(u);
    }

    public static void addDirectedEdge(ArrayList<ArrayList<Integer>> adj, int u, int v) {
        adj.get(u).add(v);
    }

    public static <T> void addUndirectedEdge(ArrayList<ArrayList<Point>> adj, int u, int v, T weight) {
        adj.get(u).add(new Point(v, weight));
        adj.get(v).add(new Point(u, weight));
    }

    public static <T> void addDirectedEdge(ArrayList<ArrayList<Point>> adj, int u, int v, T weight) {
        adj.get(u).add(new Point(v, weight));
    }

    public static <T> void toString(String msg, ArrayList<ArrayList<T>> adj) {
        out.println(msg + ":");
        int count = 0;
        for (ArrayList<T> i : adj) {
            out.print("\t" + count++ + ": ");
            for (T j : i) {
                out.print(j + " ");
            }
            out.println();
        }
    }

    public static void addUndirectedEdge(Map<Integer, ArrayList<Integer>> adj, int u, int v) {
        if (adj.containsKey(u)) {
            ArrayList<Integer> temp = adj.get(u);
            temp.add(v);
            adj.put(u, temp);
        } else {
            ArrayList<Integer> temp = new ArrayList<>();
            temp.add(v);
            adj.put(u, temp);
        }
        if (adj.containsKey(v)) {
            ArrayList<Integer> temp = adj.get(v);
            temp.add(u);
            adj.put(v, temp);
        } else {
            ArrayList<Integer> temp = new ArrayList<>();
            temp.add(u);
            adj.put(v, temp);
        }
    }

    public static void addDirectedEdge(Map<Integer, ArrayList<Integer>> adj, int u, int v) {
        if (adj.containsKey(u)) {
            ArrayList<Integer> temp = adj.get(u);
            temp.add(v);
            adj.put(u, temp);
        } else {
            ArrayList<Integer> temp = new ArrayList<>();
            temp.add(v);
            adj.put(u, temp);
        }
    }

    public static <T> void addUndirectedEdge(Map<Integer, ArrayList<Point>> adj, int u, int v, T weight) {
        if (adj.containsKey(u)) {
            ArrayList<Point> temp = adj.get(u);
            temp.add(new Point(v, weight));
            adj.put(u, temp);
        } else {
            ArrayList<Point> temp = new ArrayList<>();
            temp.add(new Point(v, weight));
            adj.put(u, temp);
        }
        if (adj.containsKey(v)) {
            ArrayList<Point> temp = adj.get(v);
            temp.add(new Point(u, weight));
            adj.put(v, temp);
        } else {
            ArrayList<Point> temp = new ArrayList<>();
            temp.add(new Point(u, weight));
            adj.put(v, temp);
        }
    }

    public static <T> void addDirectedEdge(Map<Integer, ArrayList<Point>> adj, int u, int v, T weight) {
        if (adj.containsKey(u)) {
            ArrayList<Point> temp = adj.get(u);
            temp.add(new Point(v, weight));
            adj.put(u, temp);
        } else {
            ArrayList<Point> temp = new ArrayList<>();
            temp.add(new Point(v, weight));
            adj.put(u, temp);
        }
    }

    public static <T> void toString(String msg, Map<T, ArrayList<T>> adj) {
        out.println(msg + ":");
        for (Map.Entry<T, ArrayList<T>> entry : adj.entrySet()) {
            out.println("\t" + entry.getKey() + ": " + entry.getValue());
        }
    }

    // GCD
    public static int __gcd(int a, int b) {
        BigInteger n1 = BigInteger.valueOf(a);
        BigInteger n2 = BigInteger.valueOf(b);
        BigInteger gcd = n1.gcd(n2);
        return gcd.intValue();
    }

    public static long __gcd(long a, long b) {
        BigInteger n1 = BigInteger.valueOf(a);
        BigInteger n2 = BigInteger.valueOf(b);
        BigInteger gcd = n1.gcd(n2);
        return gcd.longValue();
    }

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

    @Override
    public void run() {
        long start = 0, end = 0;
        try {
            File output = new File("output.txt");
            sc = new FastReader();
            if (output.exists()) {
                out = new PrintWriter(new FileOutputStream("output.txt"));
                start = System.nanoTime();
            } else {
                out = new PrintWriter(System.out);
            }

            int test_cases = 1;
            if (test_case_input) test_cases = sc.nextInt();
            for (int i = 1; i <= test_cases; i++) {
                solution(i);
            }
            if (output.exists()) {
                end = System.nanoTime();
                out.println("Execution time: " + (end - start) / 1000000 + " ms");
            }
            out.flush();
            out.close();
        } catch (Exception e) {
            out.println("Exception: " + e);
            out.println("At Line no. : " + e.getStackTrace()[0].getLineNumber());
            out.flush();
            out.close();
            return;
        }
    }

    // Edge Class
    static class Edge implements Comparable<Edge> {
        Object u;
        Object v;
        Object wt;

        public Edge(Object origin, Object destination, Object weight) {
            u = origin;
            v = destination;
            wt = weight;
        }

        public String toString() {
            String ans = u + " -> " + v + " : " + wt;
            return ans;
        }

        public int getIntOrigin() {
            return (int) u;
        }

        public int getIntDestination() {
            return (int) v;
        }

        public int getIntWeight() {
            return (int) wt;
        }

        public long getLongOrigin() {
            return (long) u;
        }

        public long getLongDestination() {
            return (long) v;
        }

        public long getLongWeight() {
            return (long) wt;
        }

        @Override
        public int compareTo(Edge edge) {
            if ((edge.u).getClass() == Long.class) return (((Long) this.wt).compareTo((Long) edge.wt));
            else return (((Integer) this.wt).compareTo((Integer) edge.wt));
        }
    }

    // Point Class
    static class Point implements Comparable<Point> {
        Object x;
        Object y;

        public Point(Object a, Object b) {
            x = a;
            y = b;
        }

        public int getIntX() {
            return (int) x;
        }

        public int getIntY() {
            return (int) y;
        }

        public long getLongX() {
            return (long) x;
        }

        public long getLongY() {
            return (long) y;
        }

        public int compareTo(Point obj) {
            if (obj.x.equals(this.x)) {
                if ((obj.y).getClass() == Long.class) return ((Long) this.y).compareTo((Long) obj.y);
                else return ((Integer) this.y).compareTo((Integer) obj.y);
            } else {
                if ((obj.x).getClass() == Long.class) return ((Long) this.x).compareTo((Long) obj.x);
                else return ((Integer) this.x).compareTo((Integer) obj.x);
            }
        }

        public String toString() {
            String ans = "(" + x + ", " + y + ")";
            return ans;
        }

        @Override
        public int hashCode() {
            int hash = 7;
            hash = 71 * hash + (int) this.x;
            hash = 71 * hash + (int) this.y;
            return hash;
        }

        @Override
        public boolean equals(Object obj) {
            if (obj == null) return false;
            Point point = (Point) obj;
            if (point.x.equals(this.x) && point.y.equals(this.y)) return true;
            else return false;
        }
    }

    // Fast IO
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() throws FileNotFoundException {
            File in = new File("input.txt");
            if (in.exists()) {
                br = new BufferedReader(new InputStreamReader(new FileInputStream("input.txt")));
            } else {
                br = new BufferedReader(new InputStreamReader(System.in));
            }
        }

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

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

        float nextFloat() {
            return Float.parseFloat(next());
        }

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

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

        Integer[] intarr(int n) {
            Integer a[] = new Integer[n];
            for (int i = 0; i < n; i++) {
                a[i] = Integer.parseInt(next());
            }
            return a;
        }

        Long[] longarr(int n) {
            Long a[] = new Long[n];
            for (int i = 0; i < n; i++) {
                a[i] = Long.parseLong(next());
            }
            return a;
        }

        float[] floatarr(int n) {
            float a[] = new float[n];
            for (int i = 0; i < n; i++) {
                a[i] = Float.parseFloat(next());
            }
            return a;
        }

        Double[] doublearr(int n) {
            Double a[] = new Double[n];
            for (int i = 0; i < n; i++) {
                a[i] = Double.parseDouble(next());
            }
            return a;
        }


        Integer[][] intmatrix(int row, int col) {
            Integer a[][] = new Integer[row][col];
            for (int i = 0; i < row; i++) {
                for (int j = 0; j < col; j++) {
                    a[i][j] = Integer.parseInt(next());
                }
            }
            return a;
        }

        Long[][] longmatrix(int row, int col) {
            Long a[][] = new Long[row][col];
            for (int i = 0; i < row; i++) {
                for (int j = 0; j < col; j++) {
                    a[i][j] = Long.parseLong(next());
                }
            }
            return a;
        }

        Float[][] floatmatrix(int row, int col) {
            Float a[][] = new Float[row][col];
            for (int i = 0; i < row; i++) {
                for (int j = 0; j < col; j++) {
                    a[i][j] = Float.parseFloat(next());
                }
            }
            return a;
        }

        Double[][] doublematrix(int row, int col) {
            Double a[][] = new Double[row][col];
            for (int i = 0; i < row; i++) {
                for (int j = 0; j < col; j++) {
                    a[i][j] = Double.parseDouble(next());
                }
            }
            return a;
        }

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