H :: Road Planner

Time Limit: 10 Seconds    Memory Limit: 65536 KB

 An acyclic road network is composed of unidirectional road segments (edges), each connecting two intersections (vertices) out of a total of N intersections. The time necessary to travel on a road segment is always positive and it depends linearly on the number of cars C using the segment s:

a_S and b_s are two constants expressed as single precision floating point numbers, describing the properties of road segment s. The time necessary to cross an intersection is 0.
A number of cars must travel from vertex 0 to vertex N-1 in this road network. Each car chooses its route selfishly in order to reduce its own travel time; each car knows that all the other cars will also selfishly choose their route. You are asked to write a program that computes how many cars will travel on each of the possible paths from the source to the destination, and the time needed to travel on those paths.

Input

The input file contains several tests and is organized as follows. The first line contains the number of tests. The following lines contain the specification of the tests. Each test contains on the first line the number of vertices, the number of edges and the number of cars, separated by whitespaces. After that, each edge is given on a separate line and contains the following fields separated by spaces: source vertex, destination vertex, a_S and b_S.

Output

The output will contain one line for each test input, specifying the minimum time for any car to travel in the network, rounded down to the nearest integer.

Sample Input

2
4 4 4000
0 1 0.01 0
0 2 0 45.1
1 3 0 45.1
2 3 0.01 0
4 5 4000
0 1 0.01 0
0 2 0 45.1
1 3 0 45.1
1 2 0 0
2 3 0.01 0

Sample Output

65
80

Submit

Source: South Eastern European Regional Contest 2011