Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

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B. Martian Dollar

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputOne 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 *a*_{i}. 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 *a*_{i} (1 ≤ *a*_{i} ≤ 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

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