Bitter Alchemy

Source: AtCoder

Version: Phuoc Hung OJ Extended

Problem Statement

There are $N$ doughnut types. Making one doughnut of type $i$ consumes $m_i$ grams of ingredient. You have $X$ grams and must make at least one doughnut of every type. Find the maximum total number of doughnuts that can be made.

Input

The first line contains integers $N, X$. Each of the next $N$ lines contains $m_i$.

Output

Print one integer: the maximum number of doughnuts.

Subtasks

General constraints:

• $2 \le N \le 100$.

• $1 \le m_i \le 1000$.

• $\sum m_i \le X \le 10^5$.

• Subtask 1 (20 points): $N \le 10$, $X \le 1000$

• Subtask 2 (30 points): $N \le 50$, $X \le 10^4$

• Subtask 3 (50 points): No additional constraints.

Examples

Input

3 1000
120
100
140

Output

9

Explanation

Making one of each type consumes $360$ grams, leaving $640$ grams. The cheapest type costs $100$ grams, so six more can be made. The total is $3+6=9$.