Description: You're given a simple, undirected, connected, weighted graph with $$$n$$$ nodes and $$$m$$$ edges. Nodes are numbered from $$$1$$$ to $$$n$$$. There are exactly $$$k$$$ centrals (recharge points), which are nodes $$$1, 2, \ldots, k$$$. We consider a robot moving into this graph, with a battery of capacity $$$c$$$, not fixed by the constructor yet. At any time, the battery contains an integer amount $$$x$$$ of energy between $$$0$$$ and $$$c$$$ inclusive. Traversing an edge of weight $$$w_i$$$ is possible only if $$$x \ge w_i$$$, and costs $$$w_i$$$ energy points ($$$x := x - w_i$$$). Moreover, when the robot reaches a central, its battery is entirely recharged ($$$x := c$$$). You're given $$$q$$$ independent missions, the $$$i$$$-th mission requires to move the robot from central $$$a_i$$$ to central $$$b_i$$$. For each mission, you should tell the minimum capacity required to acheive it. Input Format: The first line contains four integers $$$n$$$, $$$m$$$, $$$k$$$ and $$$q$$$ ($$$2 \le k \le n \le 10^5$$$ and $$$1 \le m, q \le 3 \cdot 10^5$$$). The $$$i$$$-th of the next $$$m$$$ lines contains three integers $$$u_i$$$, $$$v_i$$$ and $$$w_i$$$ ($$$1 \le u_i, v_i \le n$$$, $$$u_i \neq v_i$$$, $$$1 \le w_i \le 10^9$$$), that mean that there's an edge between nodes $$$u$$$ and $$$v$$$, with a weight $$$w_i$$$. It is guaranteed that the given graph is simple (there is no self-loop, and there is at most one edge between every pair of nodes) and connected. The $$$i$$$-th of the next $$$q$$$ lines contains two integers $$$a_i$$$ and $$$b_i$$$ ($$$1 \le a_i, b_i \le k$$$, $$$a_i \neq b_i$$$). Output Format: You have to output $$$q$$$ lines, where the $$$i$$$-th line contains a single integer : the minimum capacity required to acheive the $$$i$$$-th mission. Note: In the first example, the graph is the chain $$$10 - 9 - 2^C - 4 - 1^C - 5 - 7 - 3^C - 8 - 6$$$, where centrals are nodes $$$1$$$, $$$2$$$ and $$$3$$$. For the mission $$$(2, 3)$$$, there is only one simple path possible. Here is a simulation of this mission when the capacity is $$$12$$$. - The robot begins on the node $$$2$$$, with $$$c = 12$$$ energy points. - The robot uses an edge of weight $$$4$$$. - The robot reaches the node $$$4$$$, with $$$12 - 4 = 8$$$ energy points. - The robot uses an edge of weight $$$8$$$. - The robot reaches the node $$$1$$$ with $$$8 - 8 = 0$$$ energy points. - The robot is on a central, so its battery is recharged. He has now $$$c = 12$$$ energy points. - The robot uses an edge of weight $$$2$$$. - The robot is on the node $$$5$$$, with $$$12 - 2 = 10$$$ energy points. - The robot uses an edge of weight $$$3$$$. - The robot is on the node $$$7$$$, with $$$10 - 3 = 7$$$ energy points. - The robot uses an edge of weight $$$2$$$. - The robot is on the node $$$3$$$, with $$$7 - 2 = 5$$$ energy points. - The robot is on a central, so its battery is recharged. He has now $$$c = 12$$$ energy points. - End of the simulation. Note that if value of $$$c$$$ was lower than $$$12$$$, we would have less than $$$8$$$ energy points on node $$$4$$$, and we would be unable to use the edge $$$4 \leftrightarrow 1$$$ of weight $$$8$$$. Hence $$$12$$$ is the minimum capacity required to acheive the mission. — The graph of the second example is described here (centrals are red nodes): The robot can acheive the mission $$$(3, 1)$$$ with a battery of capacity $$$c = 38$$$, using the path $$$3 \rightarrow 9 \rightarrow 8 \rightarrow 7 \rightarrow 2 \rightarrow 7 \rightarrow 6 \rightarrow 5 \rightarrow 4 \rightarrow 1$$$ The robot can acheive the mission $$$(2, 3)$$$ with a battery of capacity $$$c = 15$$$, using the path $$$2 \rightarrow 7 \rightarrow 8 \rightarrow 9 \rightarrow 3$$$