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.util.HashMap;
import java.util.Map;
import java.util.Scanner;

public class D {
    public static void main(String[] args) {
        Scanner cin = new Scanner(System.in);

        int n = cin.nextInt();
        int t = cin.nextInt();
        int[] a = new int[n];

        Map<Integer, Integer> map = new HashMap<>();
        long ma = 1;

        for (int i = 0; i < n; i++) {
            a[i] = cin.nextInt();

            Integer value = map.get(a[i]);
            if (value == null) {
                value = 0;
            }
            value++;
            if (value > ma) ma = value;
            map.put(a[i], value);
        }

        int len = Math.min(n * n, n * t);

        int[] dp = new int[len];

        long ans = 1;
        for (int i = 0; i < len; i++) {
            dp[i] = 1;
            for (int j = Math.max(0, i - n); j < i; j++) {
                int x = i % n;
                int y = j % n;
                if (a[x] >= a[y] && dp[i] < dp[j] + 1) {
                    dp[i] = dp[j] + 1;
                }
            }
            if (dp[i] > ans) ans = dp[i];
        }


        if (t > n) {
            ans += (t - n) * ma;
        }

        System.out.println(ans);

        cin.close();
    }
}
