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.util.*;
import java.io.*;
public class a {
  static long mod = 1000000007;
public static void main(String[] args) throws IOException
{
  input.init(System.in);
  PrintWriter out = new PrintWriter(new PrintStream(System.out));
  //input.init(new FileInputStream(new File("input.txt")));
  //PrintWriter out = new PrintWriter(new File("output.txt"));
  int n = input.nextInt(), m = input.nextInt();
  int[] data = new int[n];
  for(int i = 0; i<n; i++) data[i] = input.nextInt();
  int max = 0;
  for(int i = 0; i<n; i++)
    for(int j = i+1; j<n; j++)
      max = Math.max(max, data[j]*(m/data[i]) - (m/data[i])*data[i]);
  out.println(m+max);


  out.close();
}
static long pow(long a, long p)
{
  if(p==0) return 1;
  if((p&1) == 0)
  {
    long sqrt = pow(a, p/2);
    return (sqrt*sqrt)%mod;
  }
  else
    return (a*pow(a,p-1))%mod;
}
static class input {
  static BufferedReader reader;
  static StringTokenizer tokenizer;

  /** call this method to initialize reader for InputStream */
  static void init(InputStream input) {
      reader = new BufferedReader(
                   new InputStreamReader(input) );
      tokenizer = new StringTokenizer("");
  }

  /** get next word */
  static String next() throws IOException {
      while ( ! tokenizer.hasMoreTokens() ) {
          //TODO add check for eof if necessary
          tokenizer = new StringTokenizer(
                 reader.readLine() );
      }
      return tokenizer.nextToken();
  }

  static int nextInt() throws IOException {
      return Integer.parseInt( next() );
  }
  static long nextLong() throws IOException {
    return Long.parseLong( next() );
}

  static double nextDouble() throws IOException {
      return Double.parseDouble( next() );
  }
  static String nextLine() throws IOException {
    return reader.readLine();
  }
}
}