Bessla Motors

문제

Farmer John would like to promote his line of Bessla electric tractors by showcasing Bessla's network of charging stations. He has identified $NN$ ($2\le N\le 5\cdot {10}^{4}2\backslash le\; N\backslash le\; 5\backslash cdot\; 10^4$) points of interest labeled $1\dots N1\backslash dots\; N$, of which the first $CC$ () are charging stations and the remainder are travel destinations. These points of interest are interconnected by $MM$ ($1\le M\le {10}^{5}1\backslash le\; M\backslash le\; 10^5$) bidirectional roads, the $ii$-th of which connects distinct points $u_{i}u\_i$ and $v_{i}v\_i$ ($1\le u_i,v_i\le N1\backslash le\; u\_i,\; v\_i\backslash le\; N$) and has length ${\mathrm{\ell }}_i\backslash ell\_i$ miles ($1\le {\mathrm{\ell }}_i\le {10}^{9}1\backslash le\backslash ell\_i\backslash le\; 10^9$).

A Bessla can travel up to $2R2R$ miles ($1\le R\le {10}^{9}1\backslash le\; R\backslash le\; 10^9$) on a single charge, allowing it to reach any destination within $RR$ miles of a charging station. A destination is deemed well-connected if it is reachable from at least $KK$ ($1\le K\le 101\backslash le\; K\backslash le\; 10$) distinct charging stations. Your task is to assist Farmer John in identifying the set of well-connected travel destinations.

입력

The first line contains five space-separated integers $NN$, $MM$, $CC$, $RR$, and $KK$. Each of the following $MM$ lines contains three space-separated integers $u_{i}u\_i$, $v_{i}v\_i$, and ${\mathrm{\ell }}_i\backslash ell\_i$ such that $u_i\mathrm{\ne }{v}_{i}u\_i\backslash neq\; v\_i$.

The charging stations are labeled $1,2,\dots ,C1,\; 2,\; \backslash ldots,\; C$. The remaining points of interest are all travel destinations.

출력

First, output the number of well-connected travel destinations on a single line. Then, list all well-connected travel destinations in ascending order, each on a separate line.