P10758 [CTSC2011] Road Monitoring.

The road safety department recently plans to deploy a road monitoring system from City A to City B, to improve its ability to respond to emergencies. The road network from City A to City B can be described as an undirected graph $G=(V, E)$, where $V$ is the set of nodes in the road network, and $E$ is the set of bidirectional roads connecting the nodes. All nodes are numbered from $1$ to $n$, where $n$ is the number of nodes. City A is located at node $s$, and City B is located at node $t$. The department plans to install monitoring devices on some roads, in order to reduce the overall **response difficulty** of the road network. When an emergency happens, the department needs to assign personnel to be on duty on some roads, so that **any path from node $s$ to node $t$ passes through at least one monitored road** (a road with a monitoring device installed, or a road with personnel on duty). Therefore, the **response difficulty** is defined as the minimum number of roads that need personnel to be assigned, so that any path from $s$ to $t$ passes through at least one monitored road. Due to different natural environments, the cost of installing monitoring devices on different roads may also differ. Specifically, for an edge $e$, the installation cost is $W(e)$. Since the budget is limited, they want to find a plan such that the response difficulty of the road network does not exceed $k$. Please help them find a deployment plan that is as economical as possible.

This is an output-only problem. There are $10$ input files `road*.in` in your directory. The first line of each input file contains three integers $n$, $m$, and $k$, representing the number of nodes, the number of roads, and the upper limit of the response difficulty. The second line contains two integers $s$ and $t$, representing the node indices of City A and City B. The next $m$ lines each contain three positive integers $a_i$, $b_i$, and $w_i$, describing a road connecting node $a_i$ and node $b_i$, with an installation cost of $w_i$ for the monitoring device.

For each input file, provide the corresponding output file `road*.out` in the directory. The first line of the output file contains a value $s$, indicating that in the contestant’s plan, monitoring devices will be installed on $s$ roads. The next $s$ lines each contain an integer $p_i$, indicating that a monitoring device is installed on the $p_i$-th road in the input file (edges are numbered starting from $1$).

For each test case, if you do not output anything or your output is invalid, you will get $0$ points. For each test case, we have five scoring parameters $m_1$, $m_2$, $m_3$, $m_4$, and $m_5$. Suppose the total cost of the contestant’s plan is $c$. - If $c