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.*;

public class Solution {

    public static void main(String[] args) {
        int n;
        int t;
        Scanner scan = new Scanner(System.in);
        n = scan.nextInt();
        t = scan.nextInt();
        int dup = Math.min(n, t);
        int[] nums = new int[n * n];
        int[] dp = new int[n * n];
        int[] cnt = new int[301];
        int occurCnt = 0;
        for (int i=0; i<n; i++) {
            nums[i] = scan.nextInt();
            occurCnt = Math.max(occurCnt, ++cnt[nums[i]]);
        }
        for (int i=n; i<n*dup; i++) {
            nums[i] = nums[i-n];
        }

        int last = 0;
        for (int i=0; i<n*dup; i++) {
            dp[i] = 1;
            for (int j=0; j<i; j++) {
                if (nums[i] >= nums[j]) {
                    dp[i] = Math.max(dp[i], dp[j] + 1);
                }
            }
        }

        int maxCnt = 0;
        for (int i=0; i<n*dup; i++) {
            maxCnt = Math.max(dp[i], maxCnt);
        }
        int mul = Math.max(t-n, 0);
        System.out.println(maxCnt + mul * occurCnt);
    }
}
