|시간 제한||메모리 제한||제출||정답||맞은 사람||정답 비율|
|1 초||256 MB||2||2||2||100.000%|
Little Y has recently been working at a currency exchange center. The currency exchange center only offers two types of vouchers to be exchanged: commemorative voucher A (henceforth known as voucher A) and commemorative voucher B (henceforth known as voucher B). All voucher-holding customers possess their very own account. The quantity of vouchers a customer has may be a real number.
Rising and falling daily with the waves of the market, the two types of vouchers each has their own values at any given time, and each unit of a voucher can be traded that day for some amount of cash. We note that on day K, the values of voucher A and voucher B are respectively AK and BK (dollars/unit voucher).
To make it more convenient for customers, the exchange center offers a very easy system to make transactions: the ratio exchange method. There are two different aspects to the ratio exchange method:
For example, let's assume for the next 3 three days the following changes in the values of AK, BK, and RateK:
Let's say that on one day, a customer has 100 dollars but no vouchers of any kind. The customer carry out the following transactions:
|Time||Transaction||Cash (Dollars)||Voucher A||Voucher B|
|Day 1||Buy – 100 dollars||0||50||50|
|Day 2||Sell – 50%||75||25||25|
|Day 2||Buy – 60 dollars||15||55||40|
|Day 3||Sell – 100%||205||0||0|
Note that there may be multiple transactions on a single day.
Little Y is a very economically-minded worker. After a relatively long time conducting operations and market estimates, he already knows within the future N days what the values of vouchers A and B, as well as rate will be. He wishes to calculate, if one starts with S dollars, what is the maximum amount of cash (in dollars) that can be obtained after N days.
The first line contains two positive integers N and S, representing the number of days that little Y's can foresee and the starting amount of cash respectively.
Within the next N lines, the K-th line contains three real numbers AK, BK, and RateK.
Output a single real number MaxProfit, indicating the maximum amount of cash in dollars that can be obtained after all operations on the N-th day has finished, accurate to 3 decimal places. Your answer will be considered correct if its absolute difference with the correct answer is no larger than 0.001.
3 100 1 1 1 1 2 2 2 2 3