Problem:
Problem D: Traveling by Stagecoach

Once upon a time, there was a traveler.

He plans to travel using stagecoaches (horse wagons).
His starting point and destination are fixed,
but he cannot determine his route.
Your job in this problem is to write a program
which determines the route for him.

There are several cities in the country,
and a road network connecting them.
If there is a road between two cities, one can travel by a stagecoach
from one of them to the other.
A coach ticket is needed for a coach ride.
The number of horses is specified in each of the tickets.
Of course, with more horses, the coach runs faster.

At the starting point, the traveler has a number of coach tickets.
By considering these tickets and the information on the road network,
you should find the best possible route that takes him to the destination
in the shortest time.
The usage of coach tickets should be taken into account.

The following conditions are assumed.

A coach ride takes the traveler from one city to another
directly connected by a road.
In other words, on each arrival to a city, he must change the coach.

Only one ticket can be used for a coach ride between two cities
directly connected by a road.

Each ticket can be used only once.

The time needed for a coach ride is the distance between two cities
divided by the number of horses.

The time needed for the coach change should be ignored.

Input

The input consists of multiple datasets, each in the following format.
The last dataset is followed by a line containing five zeros
(separated by a space).

n m p a b

t1 t2 ... tn

x1 y1 z1

x2 y2 z2

...

xp yp zp

Every input item in a dataset is a non-negative integer.
If a line contains two or more input items, they are separated by a space.

n is the number of coach tickets.
You can assume that the number of tickets is between 1 and 8.
m is the number of cities in the network.
You can assume that the number of cities is between 2 and 30.
p is the number of roads between cities, which may be zero.

a is the city index of the starting city.
b is the city index of the destination city.
a is not equal to b.
You can assume that all city indices in a dataset (including the above two)
are between 1 and m.

The second line of a dataset gives the details of coach tickets.
ti is the number of horses specified in the i-th
coach ticket (1<=i<=n).
You can assume that the number of horses is between 1 and 10.

The following p lines give the details of roads between cities.
The i-th road connects two cities with city indices
xi and yi,
and has a distance zi (1<=i<=p).
You can assume that the distance is between 1 and 100.

No two roads connect the same pair of cities.
A road never connects a city with itself.
Each road can be traveled in both directions.

Output

For each dataset in the input, one line should be output as specified below.
An output line should not contain extra characters such as spaces.

If the traveler can reach the destination, the time needed
for the best route (a route with the shortest time) should be printed.
The answer should not have an error greater than 0.001.
You may output any number of digits after the decimal point,
provided that the above accuracy condition is satisfied.

If the traveler cannot reach the destination,
the string "Impossible" should be printed.
One cannot reach the destination either when there are no routes
leading to the destination, or when the number of tickets is not sufficient.
Note that the first letter of "Impossible" is in uppercase,
while the other letters are in lowercase.

Sample Input

3 4 3 1 4
3 1 2
1 2 10
2 3 30
3 4 20
2 4 4 2 1
3 1
2 3 3
1 3 3
4 1 2
4 2 5
2 4 3 4 1
5 5
1 2 10
2 3 10
3 4 10
1 2 0 1 2
1
8 5 10 1 5
2 7 1 8 4 5 6 3
1 2 5
2 3 4
3 4 7
4 5 3
1 3 25
2 4 23
3 5 22
1 4 45
2 5 51
1 5 99
0 0 0 0 0

Output for the Sample Input

30.000
3.667
Impossible
Impossible
2.856

Solution in JAVA (judge verdict: Accepted)

import java.awt.geom.Point2D;
import java.io.IOException;
import java.io.InputStream;
import java.util.*;
import java.util.function.BiFunction;
import java.util.function.Function;
import java.util.function.Supplier;

public class Main {
  final static int INF = 1 << 28;
  final static long MOD = 1_000_000_007;
  final static double GOLDEN_RATIO = (1.0 + Math.sqrt(5)) / 2.0;
  Scanner sc = new Scanner(System.in);

  public static void main(String[] args) {
    new Main().run();
  }

  int n, m, p, a, b;
  double[][] dp;
  boolean[][] done;
  int[] t;
  ArrayList<LinkedList<Iku>> list;

  void run() {
    for (; ; ) {
      n = ni();
      m = ni();
      p = ni();
      a = ni();
      b = ni();
      if (n == 0) {
        break;
      }
      t = new int[n];
      for (int i = 0; i < n; ++i) {
        t[i] = ni();
      }
      list = new ArrayList<>();
      for (int i = 0; i <= m; ++i) {
        list.add(new LinkedList<>());
      }
      for (int i = 0; i < p; ++i) {
        int x = ni();
        int y = ni();
        int z = ni();
        Iku left = new Iku();
        left.dist = y;
        left.kyori = z;
        list.get(x).add(left);
        Iku right = new Iku();
        right.dist = x;
        right.kyori = z;
        list.get(y).add(right);
      }
      dp = new double[m + 1][1 << n];
      for (int i = 0; i <= m; ++i) {
        Arrays.fill(dp[i], Double.MAX_VALUE);
      }
      done = new boolean[m + 1][1 << n];
      PriorityQueue<Node> queue = new PriorityQueue<>(
          Comparator.comparingDouble(a -> a.time)
      );
      Node atom = new Node();
      atom.now = a;
      atom.bits = 0;
      atom.time = 0;
      queue.add(atom);
      while (queue.size() > 0) {
        Node node = queue.poll();
        if (done[node.now][node.bits]) {
          continue;
        }
        done[node.now][node.bits] = true;
        dp[node.now][node.bits] = node.time;
        for (Iku ite : list.get(node.now)) {
          for (int i = 0; i < n; ++i) {
            if (((node.bits >> i) & 1) == 1) {
              continue;
            }
            Node next = new Node();
            next.now = ite.dist;
            next.bits = node.bits | (1 << i);
            next.time = node.time + (double) ite.kyori / t[i];
            queue.add(next);
          }
        }
      }
      double min = Double.MAX_VALUE;
      boolean ok = false;
      for (int i = 0; i < 1 << n; ++i) {
        if (done[b][i]) {
          ok |= true;
          min = Math.min(min, dp[b][i]);
        }
      }
      if (ok) {
        System.out.println(min);
      } else {
        System.out.println("Impossible");
      }
    }
  }

  class Node {
    int now;
    int bits;
    double time;
  }

  class Iku {
    int dist;
    int kyori;
  }

  int ni() {
    return Integer.parseInt(sc.next());
  }

  void debug(Object... os) {
    System.err.println(Arrays.deepToString(os));
  }

  /**
   * ??????????????????????????????
   *
   * @return a ??¨ b ????????§??¬?´???°
   */
  long gcd(long a, long b) {
    if (b == 0) {
      return a;
    }
    return gcd(b, a % b);
  }

  /**
   * ????????????????????????????????????
   *
   * @return mx + ny = gcd(m, n)??¨???????????????(x, y)?????????
   */
  Pair<Long, Long> gcd_ex(long m, long n) {
    long[][] mat = _gcd_ex(m, n);
    return new Pair<>(mat[0][0], mat[0][1]);
  }

  long[][] _gcd_ex(long m, long n) {
    if (n == 0) {
      return new long[][]{{1, 0}, {0, 1}};
    }
    long k = m / n;
    long[][] K = new long[][]{{0, 1}, {1, -k}};
    long[][] r = _gcd_ex(n, m % n);
    long[][] dst = new long[2][2];
    for (int y = 0; y < 2; ++y)
      for (int x = 0; x < 2; ++x)
        for (int i = 0; i < 2; ++i)
          dst[y][x] += r[y][i] * K[i][x];
    return dst;
  }

  /**
   * ??°?????????2???????????¨??????????????????????£?
   *
   * @return a^r (mod 1,000,000,007)
   */
  long pow(long a, long r) {
    long sum = 1;
    while (r > 0) {
      if ((r & 1) == 1) {
        sum *= a;
        sum %= MOD;
      }
      a *= a;
      a %= MOD;
      r >>= 1;
    }
    return sum;
  }

  /**
   * ???????????????
   * O(n)
   *
   * @return {}_nC_r
   */
  long C(int n, int r) {
    long sum = 1;
    for (int i = n; 0 < i; --i) {
      sum *= i;
      sum %= MOD;
    }
    long s = 1;
    for (int i = r; 0 < i; --i) {
      s *= i;
      s %= MOD;
    }
    sum *= pow(s, MOD - 2);
    sum %= MOD;

    long t = 1;
    for (int i = n - r; 0 < i; --i) {
      t *= i;
      t %= MOD;
    }
    sum *= pow(t, MOD - 2);
    sum %= MOD;

    return sum;
  }

  /**
   * ??????????????¢?´¢
   *
   * @param left  ??????
   * @param right ??????
   * @param f     ??¢?´¢????????¢??°
   * @param comp  ??????????????¢??°?????¢?´¢????????¨?????????Comparator.comparingDouble(Double::doubleValue)
   *              ??????????????¢??°?????¢?´¢????????¨?????????Comparator.comparingDouble(Double::doubleValue).reversed()
   * @return ?\?????????§?¨?x
   */
  double goldenSectionSearch(double left, double right, Function<Double, Double> f, Comparator<Double> comp) {
    double c1 = divideInternally(left, right, 1, GOLDEN_RATIO);
    double c2 = divideInternally(left, right, GOLDEN_RATIO, 1);
    double d1 = f.apply(c1);
    double d2 = f.apply(c2);
    while (right - left > 1e-9) {
      if (comp.compare(d1, d2) > 0) {
        right = c2;
        c2 = c1;
        d2 = d1;
        c1 = divideInternally(left, right, 1, GOLDEN_RATIO);
        d1 = f.apply(c1);
      } else {
        left = c1;
        c1 = c2;
        d1 = d2;
        c2 = divideInternally(left, right, GOLDEN_RATIO, 1);
        d2 = f.apply(c2);
      }
    }
    return right;
  }

  /**
   * [a,b]???m:n???????????????????????????
   */
  double divideInternally(double a, double b, double m, double n) {
    return (n * a + m * b) / (m + n);
  }

  /**
   * http://alexbowe.com/popcount-permutations/
   * bit????????£???????????°????°?????????????????????????????????¨???????????????
   * ex)
   * <pre>
   * for (int i = 0; i < 25; ++i) {
   *   int bits = (1 << i) - 1;
   *   long m = C(25, num);
   *   for (j = 0; j < m; ++j) {
   *     ...(25???????????????i???bit????????£?????????)
   *     if (bits != 0)
   *       bits = next_perm(bits);
   *   }
   * }
   * </pre>
   *
   * @param v ?????¨???bit???
   * @return ?¬????bit???
   */
  int next_perm(int v) {
    int t = (v | (v - 1)) + 1;
    return t | ((((t & -t) / (v & -v)) >> 1) - 1);
  }

  /**
   * from http://gihyo.jp/dev/serial/01/geometry part 6
   */
  static class Line {
    double a;
    double b;
    double c;

    /**
     * ?????¬??¢??????????????????????????´??????????????????
     *
     * @param a x????????°
     * @param b y????????°
     * @param c ?????°???
     */
    Line(double a, double b, double c) {
      this.a = a;
      this.b = b;
      this.c = c;
    }

    /**
     * 2???(x1, y1), (x2, y2)???????????´??????????????????
     *
     * @param x1 1?????????x??§?¨?
     * @param y1 1?????????y??§?¨?
     * @param x2 2?????????x??§?¨?
     * @param y2 2?????????y??§?¨?
     * @return ??´???
     */
    static Line fromPoints(double x1, double y1, double x2, double y2) {
      double dx = x2 - x1;
      double dy = y2 - y1;
      return new Line(dy, -dx, dx * y1 - dy * x1);
    }

    /**
     * ?????????????????´?????¨??????????????????
     *
     * @param l ??´???
     * @return ?????????2??´?????????????????´??????null
     */
    Point2D getIntersectionPoint(Line l) {
      double d = a * l.b - l.a * b;
      if (d == 0.0) {
        return null;
      }
      double x = (b * l.c - l.b * c) / d;
      double y = (l.a * c - a * l.c) / d;
      return new Point2D.Double(x, y);
    }

    @Override
    public String toString() {
      return "a = " + a + ", b = " + b + ", c = " + c;
    }
  }

  /**
   * from http://gihyo.jp/dev/serial/01/geometry part 6
   */
  static public class LineSegment {
    double x1;
    double y1;
    double x2;
    double y2;

    LineSegment(double x1, double y1, double x2, double y2) {
      this.x1 = x1;
      this.y1 = y1;
      this.x2 = x2;
      this.y2 = y2;
    }

    Line toLine() {
      return Line.fromPoints(x1, y1, x2, y2);
    }

    boolean intersects(Line l) {
      double t1 = l.a * x1 + l.b * y1 + l.c;
      double t2 = l.a * x2 + l.b * y2 + l.c;
      return t1 * t2 <= 0;
    }

    boolean intersects(LineSegment s) {
      return bothSides(s) && s.bothSides(this);
    }

    // s???????????????????????´????????????????????????????????????
    private boolean bothSides(LineSegment s) {
      double ccw1 = GeomUtils.ccw(x1, y1, s.x1, s.y1, x2, y2);
      double ccw2 = GeomUtils.ccw(x1, y1, s.x2, s.y2, x2, y2);
      if (ccw1 == 0 && ccw2 == 0) { // s??¨?????????????????´?????????????????´???
        // s???????????????1???????????????????????????????????????????????°???s??????????????¨??±?????¨?????????????????§
        // true?????????
        return internal(s.x1, s.y1) || internal(s.x2, s.y2);
      } else { // ????????\????????´???
        // CCW???????¬?????????°????????´??????true?????????
        return ccw1 * ccw2 <= 0;
      }
    }

    // (x, y)?????????????????????????????????????????????????????????
    private boolean internal(double x, double y) {
      // (x, y)????????????????????????????????????????????????????????\?????§????????°????????¨?????????
      return GeomUtils.dot(x1 - x, y1 - y, x2 - x, y2 - y) <= 0;
    }

    public Point2D getIntersectionPoint(Line l) {
      if (!intersects(l)) {
        return null; // ?????????????????´??????null?????????
      }
      return l.getIntersectionPoint(toLine());
    }

    public Point2D getIntersectionPoint(LineSegment s) {
      if (!intersects(s)) {
        return null; // ?????????????????´??????null?????????
      }
      return s.toLine().getIntersectionPoint(toLine());
    }

    @Override
    public String toString() {
      return "(" + x1 + ", " + y1 + ") - (" + x2 + ", " + y2 + ")";
    }
  }

  /**
   * from http://gihyo.jp/dev/serial/01/geometry part 6
   */
  static class GeomUtils {
    static double cross(double x1, double y1, double x2, double y2) {
      return x1 * y2 - x2 * y1;
    }

    static double dot(double x1, double y1, double x2, double y2) {
      return x1 * x2 + y1 * y2;
    }

    // (x1, y1) -> (x2, y2) -> (x3, y3) ??¨?????????????????????????¨????????????´????????£?????????
    // ????¨????????????´???????????????????????´???????????´?????????????????????
    static double ccw(double x1, double y1, double x2, double y2,
                      double x3, double y3) {
      return cross(x2 - x1, y2 - y1, x3 - x2, y3 - y2);
    }

    static double ccw(Point2D p1, Point2D p2, Point2D p3) {
      return ccw(p1.getX(), p1.getY(), p2.getX(), p2.getY(), p3.getX(), p3.getY());
    }
  }

  /**
   * http://qiita.com/p_shiki37/items/65c18f88f4d24b2c528b
   */
  static class FastScanner {
    private final InputStream in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;

    public FastScanner(InputStream in) {
      this.in = in;
    }

    private static boolean isPrintableChar(int c) {
      return 33 <= c && c <= 126;
    }

    private boolean hasNextByte() {
      if (ptr < buflen) {
        return true;
      } else {
        ptr = 0;
        try {
          buflen = in.read(buffer);
        } catch (IOException e) {
          e.printStackTrace();
        }
        if (buflen <= 0) {
          return false;
        }
      }
      return true;
    }

    private int readByte() {
      if (hasNextByte()) return buffer[ptr++];
      else return -1;
    }

    private void skipUnprintable() {
      while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
    }

    public boolean hasNext() {
      skipUnprintable();
      return hasNextByte();
    }

    public String next() {
      if (!hasNext()) throw new NoSuchElementException();
      StringBuilder sb = new StringBuilder();
      int b = readByte();
      while (isPrintableChar(b)) {
        sb.appendCodePoint(b);
        b = readByte();
      }
      return sb.toString();
    }

    public long nextLong() {
      if (!hasNext()) throw new NoSuchElementException();
      long n = 0;
      boolean minus = false;
      int b = readByte();
      if (b == '-') {
        minus = true;
        b = readByte();
      }
      if (b < '0' || '9' < b) {
        throw new NumberFormatException();
      }
      while (true) {
        if ('0' <= b && b <= '9') {
          n *= 10;
          n += b - '0';
        } else if (b == -1 || !isPrintableChar(b)) {
          return minus ? -n : n;
        } else {
          throw new NumberFormatException();
        }
        b = readByte();
      }
    }
  }

  static class Pair<F extends Comparable<F>, S extends Comparable<S>> implements Comparable<Pair<F, S>> {
    F f;
    S s;

    Pair() {
    }

    Pair(F f, S s) {
      this.f = f;
      this.s = s;
    }

    Pair(Pair<F, S> p) {
      f = p.f;
      s = p.s;
    }

    @Override
    public int compareTo(Pair<F, S> p) {
      if (f.compareTo(p.f) != 0) {
        return f.compareTo(p.f);
      }
      return s.compareTo(p.s);
    }

    @Override
    public int hashCode() {
      return f.hashCode() ^ s.hashCode();
    }

    @Override
    public boolean equals(Object o) {
      if (this == o) {
        return true;
      }
      if (o == null || this.f == null || this.s == null) {
        return false;
      }
      if (this.getClass() != o.getClass()) {
        return false;
      }
      Pair p = (Pair) o;
      return this.f.equals(p.f) && this.s.equals(p.s);
    }

    @Override
    public String toString() {
      return "{" + f.toString() + ", " + s.toString() + "}";
    }
  }

  class BIT<T> {
    int n;
    ArrayList<T> bit;
    BiFunction<T, T, T> bif;

    /**
     * 1-indexed ???Binary Indexed Tree????§??????????
     *
     * @param n   ??????
     * @param bif ?????¨???????????¢??°
     * @param sup ?????????
     */
    BIT(int n, BiFunction<T, T, T> bif, Supplier<T> sup) {
      this.n = n;
      bit = new ArrayList<>(n + 1);
      for (int i = 0; i < n + 1; ++i) {
        bit.add(sup.get());
      }
      this.bif = bif;
    }

    /**
     * i??????????????????v??§??´??°??????
     *
     * @param i index
     * @param v ??°?????????
     */
    void set(int i, T v) {
      for (int x = i; x <= n; x += x & -x) {
        bit.set(x, bif.apply(bit.get(x), v));
      }
    }

    /**
     * ?????¨??????
     *
     * @param defaultValue ?????????
     * @param i            index
     * @return [1, i]?????§f????????¨????????????
     */
    T reduce(T defaultValue, int i) {
      T ret = defaultValue;
      for (int x = i; x > 0; x -= x & -x) {
        ret = bif.apply(ret, bit.get(x));
      }
      return ret;
    }
  }

  class SegmentTree<T> {
    int n;
    ArrayList<T> dat;
    BiFunction<T, T, T> bif;
    Supplier<T> sup;

    /**
     * 0-indexed ???Segment Tree????§??????????
     *
     * @param n_  ????±???????
     * @param bif ?????¨???????????¢??°
     * @param sup ?????????
     */
    SegmentTree(int n_, BiFunction<T, T, T> bif, Supplier<T> sup) {
      n = 1;
      while (n < n_) n *= 2;

      dat = new ArrayList<>(2 * n - 1);
      for (int i = 0; i < 2 * n - 1; ++i) {
        dat.add(sup.get());
      }
      this.bif = bif;
      this.sup = sup;
    }

    /**
     * k??????????????????v??§??´??°??????
     *
     * @param k index
     * @param v ??°?????????
     */
    void set(int k, T v) {
      k += n - 1;
      dat.set(k, v);
      while (k > 0) {
        k = (k - 1) / 2;
        dat.set(k, bif.apply(dat.get(k * 2 + 1), dat.get(k * 2 + 2)));
      }
    }

    /**
     * ?????¨??????
     *
     * @param l ?????????
     * @param r ?????????
     * @return [l, r)??§?????????bif????????¨?????????????????????
     */
    T reduce(int l, int r) {
      return _reduce(l, r, 0, 0, n);
    }

    T _reduce(int a, int b, int k, int l, int r) {
      if (r <= a || b <= l) return sup.get();
      if (a <= l && r <= b) return dat.get(k);
      T vl = _reduce(a, b, k * 2 + 1, l, (l + r) / 2);
      T vr = _reduce(a, b, k * 2 + 2, (l + r) / 2, r);
      return bif.apply(vl, vr);
    }
  }
}