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外汇市场交易最主要的8种货币

3 2 1 20.0 1 2 1.00 外汇市场交易最主要的8种货币 1.00 1.00 1.00 2 3 1.10 1.外汇市场交易最主要的8种货币 00 1.10 1.00

Problem Description

Several currency exchange points are working 外汇市场交易最主要的8种货币 in our city. Let us suppose that each point specializes in two particular currencies and performs exchange operations only with these currencies. There can be several points specializing in the same pair of currencies. Each point has its own exchange rates, exchange rate of A to B is the quantity of B you get for 1A. Also each exchange point has some commission, the sum you have to pay for your exchange operation. Commission is always collected in source currency.
For example, if you want to exchange 100 US Dollars into Russian Rubles at the exchange 外汇市场交易最主要的8种货币 point, where the exchange rate is 29.75, and the commission is 0.39 you will get (100 - 0.39) * 29.75 = 2963.3975RUR.
You surely know that there are N different currencies you can deal with in our city. Let us assign unique integer number from 1 to N to each currency. Then each exchange point can be described with 6 numbers: integer A and B - numbers of currencies it exchanges, and real RAB, CAB, RBA and CBA - exchange rates 外汇市场交易最主要的8种货币 and commissions when exchanging A to B and B to A respectively.
Nick has some money in currency S and wonders if he can somehow, after some exchange operations, increase his capital. Of course, he wants to have his money in currency S in the end. Help him to answer this difficult question. Nick must always have non-negative sum of money while making his operations.

Input

The first line of the input contains four numbers: N - the number of currencies, M - the number of exchange points, S - the number of currency Nick has and V 外汇市场交易最主要的8种货币 - the quantity of currency units he has. The following M lines contain 6 numbers each - the description of the corresponding exchange point - in specified above order. Numbers are separated by one or more spaces. 1

For each point exchange rates and commissions are real, given with at most two digits after the decimal point, 10-2

Let us call some sequence of the exchange operations simple if no exchange point is used more than once in this sequence. You may assume that ratio of the numeric values of the sums at the end and at the beginning of any simple sequence of the exchange operations will be less than 104.

Output

If Nick can increase his wealth, 外汇市场交易最主要的8种货币 外汇市场交易最主要的8种货币 output YES, in other case output NO to the output file.

Sample Input

3 2 1 20.0

1 2 1.00 1.00 1.00 1.00

2 3 1.10 1.00 1.10 1.00

Sample Output

题意: 给出 n 种货币,以及 m 对货币之间的兑换率,现在手上有 S 货币,问能否通过不断的 对换来增加之间 S 货币的总量

思路:实质是给出一个 n 个点 m 条边的无向图,要从 S 外汇市场交易最主要的8种货币 出发,寻找图上是否存在一个递增的环,Ford 求的是最短路,而这里要找最长路,因此需要更改松弛情况,且当结点入队次数大于 n 时,那么图中存在递增环。

Simple Sidebar

The starting state of the menu will appear collapsed on smaller screens, and will appear non-collapsed on larger screens. When toggled using the button below, the menu will change.

Make sure to keep all page content within the #page-content-wrapper . The 外汇市场交易最主要的8种货币 top navbar is optional, and just for demonstration. Just create 外汇市场交易最主要的8种货币 an element with the #sidebarToggle ID which will toggle the menu when clicked.

Problem Description

Several currency exchange points are working in our city. Let us suppose that each point specializes in two 外汇市场交易最主要的8种货币 particular currencies and performs exchange operations only with these currencies. There can be several points specializing in the same pair of currencies. Each point has its own exchange rates, exchange rate of A to B is the quantity of B you get for 1A. Also each exchange point has some commission, the sum you have to pay for your exchange operation. Commission is always collected in source currency.
For example, if you want to exchange 100 US Dollars into Russian Rubles at the exchange point, where 外汇市场交易最主要的8种货币 the exchange rate is 29.75, and the commission is 0.39 you will get (100 - 0.39) * 29.外汇市场交易最主要的8种货币 75 = 2963.3975RUR.
You surely know that there are N different currencies you can deal with in our city. Let us assign unique integer number from 1 to N to each currency. Then each exchange point can be described with 6 numbers: integer A and B - numbers of currencies it exchanges, and 外汇市场交易最主要的8种货币 real RAB, CAB, RBA and CBA - exchange rates and commissions when exchanging A to B and B to A respectively.
Nick has some money in currency S and wonders if he 外汇市场交易最主要的8种货币 can somehow, after some exchange operations, increase his capital. Of course, he wants to have his money in currency S in the end. Help him to answer this difficult question. Nick must always 外汇市场交易最主要的8种货币 have non-negative sum of money while making his operations.

Input

The first line of the input contains four numbers: N - the number of currencies, M - the number of exchange points, S 外汇市场交易最主要的8种货币 - the number of currency Nick has and V - the quantity of currency units he has. The following M lines contain 6 numbers each - the description of the corresponding exchange point - in specified above order. Numbers are separated by one or more spaces. 1

For each point exchange rates and commissions are real, given with at most two digits after the decimal point, 10-2

Let us call some sequence of the exchange operations simple if no exchange point is used more than once in this sequence. You may assume that ratio of the numeric values of the sums at the end and at the beginning of any simple sequence of the exchange operations will be less than 104.

Output

If Nick can increase his wealth, output 外汇市场交易最主要的8种货币 YES, in other case output NO to the output file.

Sample Input

3 2 1 20.0

1 2 1.00 1.00 1.00 1.00

2 3 1.10 1.00 1.10 1.00

Sample Output

题意: 给出 n 种货币,以及 m 对货币之间的兑换率,现在手上有 S 货币,问能否通过不断的 对换来增加之间 S 货币的总量

思路:实质是给出一个 n 个点 m 条边的无向图,要从 S 出发,寻找图上是否存在一个递增的环,Ford 求的是最短路,而这里要找最长路,因此需要更改松弛情况,且当结点入队次数大于 n 时,那么图中存在递增环。

Simple Sidebar

The starting state of the menu will appear collapsed on smaller screens, and will appear non-collapsed on larger screens. When toggled using the button below, the menu will change.

Make 外汇市场交易最主要的8种货币 sure to keep all page content within the #page-content-wrapper . The top 外汇市场交易最主要的8种货币 navbar is optional, and just for demonstration. Just create an element with the #sidebarToggle ID which will toggle the menu when clicked.