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

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N X m_1 m_2 : m_N

outputFormat

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

样例

3 1000
120
100
140

9