MROADS - Roads Repair


English Vietnamese

The traffic network in a country consists of N cities (labeled with integers 1 to N) and N-1 roads connecting the cities. There is a unique path between each pair of different cities.


Because of the many years of lazy maintenance the roads are pretty damaged and for each road two numbers A and B are known – the integer A represents the current time (in seconds) needed to travel along the road, and the integer B represents the smallest possible time (in seconds) needed to travel along this road if we repair all the damage.


We want to invest a certain amount of money into road repair. For a particular road, the result will be proportional to the amount of invested money. For each euro invested in some road, the time needed to travel along that road will be reduced by one second (the amount of money invested in some road has to be an integer). The travel time cannot be reduced beyond the smallest possible time B described above.


We are given a certain amount of money. We want to distribute this money along different roads in such a way that the time needed to travel from the city 1 to the most distant city (after all the repairs) is as small as possible.


Write a program that will find this smallest time.

Input

The first line of input contains two integers N and K, 2 ≤ N ≤ 100 000, 0 ≤ K ≤ 1 000 000, the number of cities and the total amount of money (in euros).


Each of the next N-1 lines contains four integers X, Y, A and B, 0 ≤ B ≤ A ≤ 10 000. It means that there is a road between cities X and Y, with the numbers A and B representing the current time and the minimum time as described above.

Output

The first and only line of output should contain a single integer – the minimum time from the task description.

Sample

input 
 
3 200
1 2 200 100
2 3 450 250
 
output
 
450

input
 
5 11
1 2 10 5
1 3 3 2
1 4 9 6
3 5 7 3
 
output
 
6

input
 
11 12
1 2 7 5
1 3 20 15
2 4 10 8
2 5 5 3
2 6 6 2
4 7 3 0
4 8 7 2
5 9 8 4
5 10 9 8
5 11 6 5
 
output
 
17


hide comments
mhamed_resli: 2018-01-30 18:43:56

AC after 6 TLE . nice problem!

Tomek Jurkiewicz: 2017-01-20 13:05:44

@Jelle van den Hooff: solution is O(n lg(k))

coding_express: 2013-05-28 11:06:05

please explain test case no 3
please......

Sigma Kappa: 2011-05-29 12:47:53

@kush sharma: the answer is indeed "17".

Last edit: 2011-05-29 15:04:32
Kush Sharma: 2011-03-19 17:19:51

can u explain the third test case..?
the longest path is 1->2->5->10
and the o/p should be 16

Last edit: 2011-03-19 17:38:35
amaroq: 2009-06-08 08:20:33

'Most distant city' refers to the city to which it takes the most time to get to, rather than deepest in the tree. I found this a bit confusing at first.

Jelle van den Hooff: 2009-06-07 19:24:40

Time limit seems to be rather strict for my O(K lg(n)) (I even think it's more like n lg(n))

Last edit: 2009-06-07 18:31:04

Added by:~!(*(@*!@^&
Date:2009-06-06
Time limit:0.100s-0.112s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:COI 06