KOICOST - Cost

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You are given an undirected graph with N vertices and M edges, where the weights are unique. 

There is a function Cost(u, v), which is defined as follows:

While there is a path between vertex u and v, delete the edge with the smallest weight. Cost(u,v) is the sum of the weights of the edges that were deleted in this process.

graph

For example, from the graph above (same as the sample input), Cost(2,6) is 2+3+4+5+6 = 20.

Given an undirected graph, your task is to calculate the sum of Cost(u,v) for all vertices u and v, where u < v. Since the answer can get large, output the answer modulo 10^9.

Input

The first line of the input consists of two integers, N and M. (1 <= N <= 100,000, 0 <= M <= 100,000)

The next M lines consists of three integers, u, v, and w. This means that there is an edge between vertex u and v with weight w. (1 <= u, v <= N, 1 <= w <= 100,000)

Output

Output the sum specified in the problem statement.

Example

Input:
6 7
1 2 10
2 3 2
4 3 5
6 3 15
3 5 4
4 5 3
2 6 6 Output: 256

hide comments
abhi_8: 2023-07-27 11:05:50

Remember that it is 10^9 and not 10^9 + 7 for modulus

ivanmilinovic: 2023-06-30 11:31:10

Good task.

Last edit: 2023-07-01 10:00:39
ankhang277: 2021-08-03 15:27:24

Wr in someway that i strongly believe my code was right

jeaf_dean: 2021-06-05 15:57:30

"While there is a path between vertex u and v, delete the edge with the smallest weight" doesn't imply weight in a given path.
wasted much time in getting this.

greenindia: 2021-03-06 18:19:25

i think its the best question on dsu

lamda_cdm_10: 2021-02-26 17:07:10

Beautiful problem on DSU . Enjoy solving it !!

iamfarraz: 2020-11-02 22:18:06

why sigabrt : (((

anish1712: 2020-06-28 22:59:07

I removed SIGSEGV by adding
if(!m) return cout << 0, 0;

It passed too!

Last edit: 2020-06-28 22:59:42
luvkumbi: 2020-03-13 09:28:52

getting SIGSEGV ....any help?.....perfectly runs on my ide

nadstratosfer: 2020-03-01 22:12:29

From TLE in C to AC in pure Python =) Great problem, came upon more ideas just improving my code here than I usually get solving several tasks.


Added by:Lawl
Date:2011-06-01
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:2011 KOI Regional