当前没有测试数据。

题目描述

Your are given an undirect connected graph.Every edge has a cost to pass.You should choose a path from S to T and you need to pay for all the edges in your path. However, you can choose at most k edges in the graph and change their costs to zero in the beginning. Please answer the minimal total cost you need to pay.

输入格式

The first line contains five integers n,m,S,T,K.

For each of the following m lines, there are three integers a,b,l, meaning there is an edge that costs l between a and b.

n is the number of nodes and m is the number of edges.

输出格式

An integer meaning the minimal total cost.

样例

样例输入 1

3 2 1 3 1
1 2 1
2 3 2

样例输出 1

1

数据范围与提示

1≤n,m≤10^3,1≤S,T,a,b≤n,0≤k≤m,1≤l≤10^6. Multiple edges and self loops are allowed.