One day Vasya got hold of information on the Martian dollar course in bourles for the next n days. The buying prices and the selling prices for one dollar on day i are the same and are equal to ai. Vasya has b bourles. He can buy a certain number of dollars and then sell it no more than once in n days. According to Martian laws, one can buy only an integer number of dollars. Which maximal sum of money in bourles can Vasya get by the end of day n?

Input

The first line contains two integers n and b (1 ≤ n, b ≤ 2000) — the number of days and the initial number of money in bourles. The next line contains n integers ai (1 ≤ ai ≤ 2000) — the prices of Martian dollars.

Output

Print the single number — which maximal sum of money in bourles can Vasya get by the end of day n.

Examples

Input

2 4
3 7


Output

8


Input

4 10
4 3 2 1


Output

10


Input

4 10
4 2 3 1


Output

15
import java.io.*;
import java.util.*;

public class B {

	void run() throws IOException {
		int n = ni(), b = ni();
		int[] a = na(n);
		int max = b;
		for (int i = 0; i < n; i++) {
			int d = b / a[i];
			int p = b % a[i];
			for (int j = i + 1; j < n; j++) {
				if (p + d * a[j] > max)
					max = p + d * a[j];
			}

		}
		pw.println(max);
	}

	int[] na(int a_len) throws IOException {
		int[] _a = new int[a_len];
		for (int i = 0; i < a_len; i++)
			_a[i] = ni();
		return _a;
	}

	int[][] nm(int a_len, int a_hei) throws IOException {
		int[][] _a = new int[a_len][a_hei];
		for (int i = 0; i < a_len; i++)
			for (int j = 0; j < a_hei; j++)
				_a[i][j] = ni();
		return _a;
	}

	String next() throws IOException {
		while (st == null || !st.hasMoreTokens())
			st = new StringTokenizer(br.readLine());
		return st.nextToken();
	}

	int ni() throws IOException {
		return Integer.parseInt(next());
	}

	String nl() throws IOException {
		return br.readLine();
	}

	void tr(String debug) {
		if (!OJ)
			pw.println(" " + debug);
	}

	static PrintWriter pw;
	static BufferedReader br;
	static StringTokenizer st;
	static boolean OJ;

	public static void main(String[] args) throws IOException {
		long timeout = System.currentTimeMillis();
		OJ = System.getProperty("ONLINE_JUDGE") != null;
		pw = new PrintWriter(System.out);
		br = new BufferedReader(OJ ? new InputStreamReader(System.in) : new FileReader(new File("B.txt")));

		while (br.ready())
			new B().run();
		if (!OJ) {
			pw.println();
			pw.println(System.currentTimeMillis() - timeout);
		}
		br.close();
		pw.close();
	}

}
