Time Limit: 1000MS	Memory Limit: 30000K
Total Submissions: 28989	Accepted: 10834

Description

Several currency exchange points are working 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 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 R_AB, C_AB, R_BA and C_BA - 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 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 - 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<=S<=N<=100, 1<=M<=100, V is real number, 0<=V<=10³.
For each point exchange rates and commissions are real, given with at most two digits after the decimal point, 10^-2<=rate<=10², 0<=commission<=10².
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 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

YES

解題思路：這道題可以用bellman演算法，不過要稍微變通一下，把檢查有無負環改成檢測有無正環，而且只要檢測出來就行了，
不用求具體的路徑

#include <cstring>
#include <cstdio>

const int MAXN = 105;
const int INF = 0x3f3f3f3f;
struct Edge{
int from;
int to;
double rab, cab;
};
Edge edge[MAXN * MAXN];
int edgeNum;
int m, n, s;
double v;

bool isYes()
{
double dis[MAXN];
memset(dis, 0, sizeof(dis));//檢測正環，所以初始化為0
dis[s] = v;
bool isUp = false;
for (int i = 0; i < edgeNum + 1; i++) {
isUp = false;
for (int j = 0; j < edgeNum; j++) {
if (dis[edge[j].to] < (dis[edge[j].from] - edge[j].cab) * edge[j].rab) {
dis[edge[j].to] = (dis[edge[j].from] - edge[j].cab) * edge[j].rab;
isUp = true;
if (i == edgeNum) { //如果無正環，i最多迴圈edgeNum次，也就是遍歷一次所有的邊
return true;
}
}
}
if (!isUp) {
return false;
}
}
}

int main()
{
scanf("%d%d%d%lf", &n, &m, &s, &v);
edgeNum = 0;
int fromS, toS;
double rabS, cabS, rbaS, cbaS;
for (int i = 0; i < m; i++) {
scanf("%d%d%lf%lf%lf%lf", &fromS, &toS, &rabS, &cabS, &rbaS, &cbaS);
edge[edgeNum].from = fromS;
edge[edgeNum].to = toS;
edge[edgeNum].rab = rabS;
edge[edgeNum].cab = cabS;
edgeNum++;
edge[edgeNum].from = toS;
edge[edgeNum].to = fromS;
edge[edgeNum].rab = rbaS;
edge[edgeNum].cab = cbaS;
edgeNum++;
}
if (isYes()) {
printf("YES\n");
}
else {
printf("NO\n");
}
return 0;
}