import java.awt.Point; import java.util.ArrayList; import java.util.BitSet; import java.util.HashSet; import java.util.PriorityQueue; public class Main { public static void main(String[] args) { new Main(); } public Main() { FastScanner fs = new FastScanner(); java.io.PrintWriter out = new java.io.PrintWriter(System.out); solve(fs, out); out.flush(); //if (fs.hasNext()) throw new AssertionError("read input"); } public void solve(FastScanner fs, java.io.PrintWriter out) { /* * まず、最短経路ははい * さて、2番目の候補は何か? * ・ どこかの電線を使わない(INF)として、その頂点のX側の端点からゴールまでを再計算する * 使わないもの決め打ちにO(N)、最短経路をO((M+N)logM)としてO(N(M+N)logM)とか * ただ、これはTLEが怖いのよね * さて、ではどうするべきか? * ゴールに近い方から最短経路を求めるとする * ただし、この時今まで使った辺は全てINFとする * すると、この候補は今まで通った頂点(既に計算済み)+新しい経路(INFの方で計算した)の合成と表せる * すると、次の候補は高々K-1個作られる(それ以外?どうせ答えじゃないから消しておk) * 後は再帰的にはい * 計算量はO(K(N+M)logM) * */ int N = fs.nextInt(), M = fs.nextInt(), K = fs.nextInt(); int X = fs.nextInt() - 1, Y = fs.nextInt() - 1; Point[] p = new Point[N]; for (int i = 0;i < N;++ i) p[i] = new Point(fs.nextInt(),fs.nextInt()); ArrayList> graph = new ArrayList>(); for (int i = 0;i < N;++ i) graph.add(new ArrayList<>()); for (int i = 0;i < M;++ i) { int P = fs.nextInt() - 1, Q = fs.nextInt() - 1; graph.get(P).add(Q); graph.get(Q).add(P); } PriorityQueue pq = new PriorityQueue((l, r) -> Double.compare(l.distance[Y], r.distance[Y])); { Path put = new Path(); put.distance = dijkstra(graph, X, Y, p, new Path()); { int now = Y; while(now != X) { int min = now; for (int i : graph.get(now)) if (min == now || put.distance[min] > put.distance[i]) min = i; put.path.add(now * 5000 + min); put.path.add(min * 5000 + now); now = min; } } pq.add(put); } final double[] INFS = new double[N]; java.util.Arrays.fill(INFS, 1e18); for (int i = 0;i < K;++ i) { final Path ans = pq.poll(); if (ans == null) { System.out.println(-1); continue; } System.out.println(ans.distance[Y]); double[] dist = dijkstra(graph, Y, X, p, ans); PriorityQueue next = new PriorityQueue<>((l, r) -> Double.compare(ans.distance[l] + dist[l], ans.distance[r] + dist[r])); for (int j = 0;j < N;++ j) { if (j == X || j == Y) continue; next.add(j); } for (int j = i;j < K && !next.isEmpty();++ j) { int tmp = next.poll(); Path put = new Path(); put.distance = java.util.Arrays.copyOf(INFS, N); { int now = tmp; while(now != X) { put.distance[now] = ans.distance[now]; int min = now; for (int k : graph.get(now)) if (ans.distance[min] > ans.distance[k]) min = k; put.path.add(now * 5000 + min); put.path.add(min * 5000 + now); now = min; } put.distance[X] = 0; } { int now = tmp; while(now != Y) { put.distance[now] = ans.distance[tmp] + dist[tmp] - dist[now]; int min = now; for (int k : graph.get(now)) if (dist[min] > dist[k]) min = k; put.path.add(now * 5000 + min); put.path.add(min * 5000 + now); now = min; } put.distance[Y] = ans.distance[tmp] + dist[tmp]; } pq.add(put); } } } double[] dijkstra(ArrayList> graph, int s, int t, Point[] p, Path ban) { double[] dist = new double[graph.size()]; java.util.Arrays.fill(dist, 1e18); dist[s] = 0; PriorityQueue pq = new PriorityQueue<>((l, r) -> Double.compare(l.dist, r.dist)); BitSet use = new BitSet(p.length); pq.add(new Dist(s, s, 0)); while(!pq.isEmpty()) { Dist tmp = pq.poll(); if (use.get(tmp.next)) continue; use.set(tmp.next); if (tmp.next == t) break; for (int i : graph.get(tmp.next)) { if (ban.path.contains(i * 5000 + tmp.next)) continue; double d = dist[tmp.next] + distance(p[tmp.next], p[i]); if (dist[i] + 0.0000001 > d) { dist[i] = d; pq.add(new Dist(tmp.next, i, d)); } } } return dist; } double distance(Point p1, Point p2) { return Math.sqrt(Math.pow(p1.x - p2.x, 2) + Math.pow(p1.y - p2.y, 2)); } class Path { double[] distance; HashSet path = new HashSet<>(); } class Dist { final int last, next; final double dist; Dist(int l, int n, double d) { last = l; next = n; dist = d; } } static class FastScanner { private final java.io.InputStream in = System.in; private final byte[] buffer = new byte[1024]; private int ptr = 0; private int buflen = 0; private boolean hasNextByte() { if (ptr < buflen) return true; ptr = 0; try { buflen = in.read(buffer); } catch (java.io.IOException e) { e.printStackTrace(); } return buflen > 0; } private byte readByte() { return hasNextByte() ? buffer[ptr++ ] : -1; } private static boolean isPrintableChar(byte c) { return 32 < c || c < 0; } private static boolean isNumber(int c) { return '0' <= c && c <= '9'; } public boolean hasNext() { while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++ ; return hasNextByte(); } public String next() { if (!hasNext()) throw new java.util.NoSuchElementException(); StringBuilder sb = new StringBuilder(); byte b; while (isPrintableChar(b = readByte())) sb.appendCodePoint(b); return sb.toString(); } public final long nextLong() { if (!hasNext()) throw new java.util.NoSuchElementException(); long n = 0; try { byte b = readByte(); if (b == '-') { while(isNumber(b = readByte())) n = n * 10 + '0' - b; return n; } else if (!isNumber(b)) throw new NumberFormatException(); do n = n * 10 + b - '0'; while (isNumber(b = readByte())); } catch (java.util.NoSuchElementException e) { } return n; } public final int nextInt() { if (!hasNext()) throw new java.util.NoSuchElementException(); int n = 0; try { byte b = readByte(); if (b == '-') { while(isNumber(b = readByte())) n = n * 10 + '0' - b; return n; } else if (!isNumber(b)) throw new NumberFormatException(); do n = n * 10 + b - '0'; while (isNumber(b = readByte())); } catch (java.util.NoSuchElementException e) { } return n; } public double nextDouble() { return Double.parseDouble(next()); } } public static class Arrays { public static void sort(final int[] array) { int l, min = 0xFFFFFFFF, max = 0; for (l = 0;l < array.length;++ l) { int i = array[l]; min &= i; max |= i; if ((i & 0x80000000) == 0) break; } for (int r = l + 1;r < array.length;++ r) { int i = array[r]; min &= i; max |= i; if ((i & 0x80000000) != 0) { array[r] = array[l]; array[l ++] = i; } } int use = min ^ max, bit = Integer.highestOneBit(use & 0x7FFFFFFF); if (bit == 0) return; sort(array, 0, l, use, bit); sort(array, l, array.length, use, bit); } private static void sort(final int[] array, final int left, final int right, final int use, int digit) { if (right - left <= 96) { for (int i = left + 1;i < right;++ i) { int tmp = array[i], tmp2, j; for (j = i;j > left && (tmp2 = array[j - 1]) > tmp;-- j) array[j] = tmp2; array[j] = tmp; } return; } int l = left; while(l < right && (array[l] & digit) == 0) ++ l; for (int r = l + 1;r < right;++ r) { int i = array[r]; if ((i & digit) == 0) { array[r] = array[l]; array[l ++] = i; } } if ((digit = Integer.highestOneBit(use & digit - 1)) == 0) return; sort(array, left, l, use, digit); sort(array, l, right, use, digit); } public static void sort(final long[] array) { int l; long min = 0xFFFFFFFFFFFFFFFFL, max = 0; for (l = 0;l < array.length;++ l) { long i = array[l]; min &= i; max |= i; if ((i & 0x8000000000000000L) == 0) break; } for (int r = l + 1;r < array.length;++ r) { long i = array[r]; min &= i; max |= i; if ((i & 0x8000000000000000L) != 0) { array[r] = array[l]; array[l ++] = i; } } long use = min ^ max, bit = Long.highestOneBit(use & 0x7FFFFFFFFFFFFFFFL); if (bit == 0) return; sort(array, 0, l, use, bit); sort(array, l, array.length, use, bit); } private static void sort(final long[] array, final int left, final int right, final long use, long digit) { if (right - left <= 96) { for (int i = left + 1, j;i < right;++ i) { long tmp = array[i], tmp2; for (j = i;j > left && (tmp2 = array[j - 1]) > tmp;-- j) array[j] = tmp2; array[j] = tmp; } return; } int l = left; while(l < right && (array[l] & digit) == 0) ++ l; for (int r = l + 1;r < right;++ r) { long i = array[r]; if ((i & digit) == 0) { array[r] = array[l]; array[l ++] = i; } } if ((digit = Long.highestOneBit(use & digit - 1)) == 0) return; sort(array, left, l, use, digit); sort(array, l, right, use, digit); } } public static class IntMath { public static int gcd(int a, int b) { while (a != 0) if ((b %= a) != 0) a %= b; else return a; return b; } public static int gcd(int... array) { int ret = array[0]; for (int i = 1;i < array.length;++ i) ret = gcd(ret, array[i]); return ret; } public static long gcd(long a, long b) { while (a != 0) if ((b %= a) != 0) a %= b; else return a; return b; } public static long gcd(long... array) { long ret = array[0]; for (int i = 1;i < array.length;++ i) ret = gcd(ret, array[i]); return ret; } public static long lcm(long a, long b) { return a / gcd(a, b) * b; } public static int pow(int a, int b) { int ans = 1; for (int mul = a;b > 0;b >>= 1, mul *= mul) if ((b & 1) != 0) ans *= mul; return ans; } public static long powLong(int a, int b) { long ans = 1; for (int mul = a;b > 0;b >>= 1, mul *= mul) if ((b & 1) != 0) ans *= mul; return ans; } public static int pow(int a, int b, int mod) { if (b < 0) b = b % (mod - 1) + mod - 1; long ans = 1; for (long mul = a;b > 0;b >>= 1, mul = mul * mul % mod) if ((b & 1) != 0) ans = ans * mul % mod; return (int)ans; } public static int floorsqrt(long n) { return (int)Math.sqrt(n + 0.1); } public static int ceilsqrt(long n) { return n <= 1 ? (int)n : (int)Math.sqrt(n - 0.1) + 1; } } }