17340번 - Cash Exchange 스페셜 저지다국어

문제

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 A_K and B_K (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:

1. Selling vouchers: the customer provides a real number OP in the range [0, 100] as the selling ratio. This means that OP% of voucher A and OP% of voucher B are exchanged for cash with the rate at that point in time.
2. Buying vouchers: the customer pays IP dollars, and the exchange center takes this money to exchange it for vouchers. Furthermore, the ratio between the amount of voucher A and voucher B on day K just happens to be Rate_K.

For example, let's assume for the next 3 three days the following changes in the values of A_K, B_K, and Rate_K:

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:

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.

입력

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 A_K, B_K, and Rate_K.

출력

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.

제한

• N ≤ 100 000
• 0 < A_K ≤ 10;
• 0 < B_K ≤ 10;
• 0 < Rate_K ≤ 100;
• MaxProfit ≤ 10⁹.

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