You are given an array of positive integers a1, a2, ..., an × T of length n × T. We know that for any i > n it is true that ai = ai - n. Find the length of the longest non-decreasing sequence of the given array.

Input

The first line contains two space-separated integers: n, T (1 ≤ n ≤ 100, 1 ≤ T ≤ 107). The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 300).

Output

Print a single number — the length of a sought sequence.

Examples

Input

4 3
3 1 4 2


Output

5

Note

The array given in the sample looks like that: 3, 1, 4, 2, 3, 1, 4, 2, 3, 1, 4, 2. The elements in bold form the largest non-decreasing subsequence. 
import java.io.IOException;
import java.io.InputStream;
import java.util.InputMismatchException;

public class dupdated {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		FastReader in = new FastReader(inputStream);
		int n = in.nextInt();
		int t = in.nextInt();
		int temp = n*Math.min(t, n);
		int[] sequence = new int[n];
		int[] cost = new int[temp];
		int mox0 = 0;
		for (int i = 0; i < n; i++) {
			sequence[i] = in.nextInt();
			if (sequence[i] > mox0)
				mox0 = sequence[i];
		}
		int result = 0;
		for (int i = 0; i < temp; i++) {
			int max = 0;
			for (int j = 0; j < i; j++) {
				if (sequence[i % n] >= sequence[j % n] && cost[j] >= max)
					max = cost[j];
			}
			cost[i] = max + 1;
			result = Math.max(result, cost[i]);
		}
		int[] frequency = new int[mox0];
		for (int i = 0; i < n; i++) {
			frequency[sequence[i]-1]++;
		}
		int localmax = 0;
		for (int i = 0; i < mox0; i++) {
			if (frequency[i] > localmax) {
				localmax = frequency[i];
			}
		}
		System.out.println(result + localmax * Math.max(0, t-n));
	}
}

class FastReader {
	private InputStream stream;
	private byte[] buf = new byte[1024];
	private int curChar;
	private int numChars;
	private SpaceCharFilter filter;

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

	public static boolean isWhitespace(int c) {
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}

	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 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 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 isWhitespace(c);
	}

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

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

	public Long readLong() {
		return Long.parseLong(readString());
	}

	public Double readDouble() {
		return Double.parseDouble(readString());
	}
}