p03370 AtCoder Beginner Contest 095 - Bitter Alchemy
Akaki, a patissier, can make N kinds of doughnut using only a certain powder called "Okashi no Moto" (literally "material of pastry", simply called Moto below) as ingredient. These doughnuts are called Doughnut 1, Doughnut 2, ..., Doughnut N. In order to make one Doughnut i (1 ≤ i ≤ N), she needs to consume m_i grams of Moto. She cannot make a non-integer number of doughnuts, such as 0.5 doughnuts.

Now, she has X grams of Moto. She decides to make as many doughnuts as possible for a party tonight. However, since the tastes of the guests differ, she will obey the following condition:

* For each of the N kinds of doughnuts, make at least one doughnut of that kind.



At most how many doughnuts can be made here? She does not necessarily need to consume all of her Moto. Also, under the constraints of this problem, it is always possible to obey the condition.

Constraints

* 2 ≤ N ≤ 100
* 1 ≤ m_i ≤ 1000
* m_1 + m_2 + ... + m_N ≤ X ≤ 10^5
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N X
m_1
m_2
:
m_N


Output

Print the maximum number of doughnuts that can be made under the condition.

Examples

Input

3 1000
120
100
140


Output

9


Input

4 360
90
90
90
90


Output

4


Input

5 3000
150
130
150
130
110


Output

26
```python
N,X = map(int, input().split())
M = [int(input()) for _ in range(N)]

X = X - sum(M)

print(N + X//min(M))
```