fractional_knapsack

Problem Statement

The supermarket has N items, numbered from 1 to N. Item i has a weight of w_i and a value of v_i.

You decided to go to the supermarket with a knapsack that can hold up to a weight of S. Unlike other supermarkets, this is a special one. It allows all customers to split split their food in however way they want based on weight. So if someone splits an apple of weight 5 and value 3 to an apple of weight 2 and 3, the values of the split apples will be 3/5 * 2 and 3/5 * 3 respectively.

You do not care what type of item uou take, only the value. Calculate the maximum value of items you can take with your knapsack.

Constraints

• All values in input are integers, but output may be a long double
• 1 ≤ N ≤ 10⁶
• 1 ≤ w_i , v_i ≤ 10⁹
• 1 ≤ S ≤ 10¹⁵

Input

Input in given in the following way

N S

w₁ v₁

w₂ v₂

w₃ v₃

. .

. .

w_n v_n

Output

Print the highest possible sum of values of the items you can take. (10 decimal places)

Sample input 1

5 10

2 3

3 2

1 4

5 4

3 3

Sample output 1

13.2000000000

Sample testcase 1 explanation

You can take the 1st item fully, 3rd time fully, 4th item partially and the 5th item fully.