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.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.InputMismatchException;

/**
 * @author Egor Kulikov (egor@egork.net)
 */
public class TaskB {
	@SuppressWarnings({"FieldCanBeLocal", "UnusedDeclaration"})
	private InputReader in;
	private PrintWriter out;

	private void solve() {
		int soldierCount = in.readInt();
		int rankCount = in.readInt();
		int[] ranks = new int[rankCount];
		for (int i = 0; i < soldierCount; i++)
			ranks[in.readInt() - 1]++;
		int moneyRequired = 0;
		while (true) {
			boolean updated = false;
			for (int i = rankCount - 2; i >= 0; i--) {
				if (ranks[i] != 0) {
					ranks[i]--;
					ranks[i + 1]++;
					updated = true;
				}
			}
			if (!updated)
				break;
			moneyRequired++;
		}
		out.println(moneyRequired);
	}

	public static void main(String[] args) {
		new TaskB().run();
	}

	private TaskB() {
		@SuppressWarnings({"UnusedDeclaration"})
		String id = getClass().getName().toLowerCase();
		//noinspection EmptyTryBlock
		try {
//			System.setIn(new FileInputStream(id + ".in"));
//			System.setOut(new PrintStream(new FileOutputStream(id + ".out")));
//			System.setIn(new FileInputStream("input.txt"));
//			System.setOut(new PrintStream(new FileOutputStream("output.txt")));
		} catch (Exception e) {
			throw new RuntimeException(e);
		}
		in = new InputReader(System.in);
		out = new PrintWriter(System.out);
	}

	private void run() {
		//noinspection InfiniteLoopStatement
//		while (true)
//		int testCount = in.readInt();
//		for (int i = 0; i < testCount; i++)
		solve();
		exit();
	}

	@SuppressWarnings({"UnusedDeclaration"})
	private void exit() {
		out.close();
		System.exit(0);
	}

	@SuppressWarnings({"UnusedDeclaration"})
	private static class InputReader {
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar, numChars;

		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 int readInt() {
			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 readLong() {
			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 String readString() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuffer res = new StringBuffer();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		private boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private String readLine0() {
			StringBuffer buf = new StringBuffer();
			int c = read();
			while (c != '\n' && c != -1) {
				if (c != '\r')
					buf.appendCodePoint(c);
				c = read();
			}
			return buf.toString();
		}

		public String readLine() {
			String s = readLine0();
			while (s.trim().length() == 0)
				s = readLine0();
			return s;
		}

		public String readLine(boolean ignoreEmptyLines) {
			if (ignoreEmptyLines)
				return readLine();
			else
				return readLine0();
		}

		public BigInteger readBigInteger() {
			try {
				return new BigInteger(readString());
			} catch (NumberFormatException e) {
				throw new InputMismatchException();
			}
		}

		public char readCharacter() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			return (char) c;
		}

		public double readDouble() {
			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, readInt());
				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, readInt());
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					m /= 10;
					res += (c - '0') * m;
					c = read();
				}
			}
			return res * sgn;
		}

		public int[] readIntArray(int size) {
			int[] array = new int[size];
			for (int i = 0; i < size; i++)
				array[i] = readInt();
			return array;
		}

		public long[] readLongArray(int size) {
			long[] array = new long[size];
			for (int i = 0; i < size; i++)
				array[i] = readLong();
			return array;
		}

		public double[] readDoubleArray(int size) {
			double[] array = new double[size];
			for (int i = 0; i < size; i++)
				array[i] = readDouble();
			return array;
		}

		public String[] readStringArray(int size) {
			String[] array = new String[size];
			for (int i = 0; i < size; i++)
				array[i] = readString();
			return array;
		}

		public char[][] readTable(int rowCount, int columnCount) {
			char[][] table = new char[rowCount][columnCount];
			for (int i = 0; i < rowCount; i++) {
				for (int j = 0; j < columnCount; j++)
					table[i][j] = readCharacter();
			}
			return table;
		}

		public void readIntArrays(int[]... arrays) {
			for (int i = 0; i < arrays[0].length; i++) {
				for (int j = 0; j < arrays.length; j++)
					arrays[j][i] = readInt();
			}
		}
	}
}
