import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.FileWriter;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Comparator;
import java.util.PriorityQueue;
import java.util.StringTokenizer;
import java.util.logging.Level;
import java.util.logging.Logger;

class Pair extends Solution implements Comparator<Pair>{
    public int first;
    public int second;
  public Pair(Integer rt, Integer pr) { this.first = rt; this.second = pr; }
  public Pair(){
      first=-1;
      second=-1;
  }
  public static boolean same(Integer first, Integer second) {
    return first == null ? second == null : first.equals(second);
  }
  Integer getFirst() { return first; }
  Integer getSecond() { return second; }
  void setFirst(Integer o) { first = o; }
  void setSecond(Integer o) { second = o; }
  public boolean equals(Pair obj) {
    if( ! (obj instanceof Pair))
      return false;
    Pair p = (Pair)obj;
    return same(p.first, this.first) && same(p.second, this.second);
  }
  public String toString() {
    return "Pair{"+first+", "+second+"}";
  }
    public int compare(Pair o1, Pair o2) {
        return o2.second-o1.second;
    }
};
class Four extends Solution implements Comparator<Four>{
    public int first;
    public double second;
    public int third;
    public int four;
    public Four(int f, double s,int t,int fo){
        first = f;
        second = s;
        third = t;
        four = fo;
    }
    public Four(){
        first=-1;
        second=-1.0;
        third=-1;
        four = -1;
    }
    public int compare(Four o1, Four o2) {
        return (int)o1.second-(int)o2.second;
    }

};
public class Solution {
    public static ArrayList<ArrayList<ArrayList<Pair>>> matrix;
    public static int start;
    public static int finish;
    public static int num_of_cities;
    public static int num_of_roads;
    public static Pair nothing;
   public static void main(String arg[]) throws FileNotFoundException{
       matrix = new ArrayList< ArrayList< ArrayList< Pair >>>();
       nothing = new Pair(-1,-1);
       BufferedReader in = new BufferedReader(new FileReader("input.txt"));
       try{
       num_of_cities = Integer.parseInt(in.readLine());
       num_of_roads = Integer.parseInt(in.readLine());
       for(int i=0; i<num_of_cities ; i++)
       {
           ArrayList<ArrayList<Pair>> temp = new ArrayList<ArrayList<Pair>>();
           ArrayList<Pair> temp2 = new ArrayList<Pair>();
           temp2.add(nothing);
           for(int j=0;j<num_of_cities ; j++)
           {
              temp.add(temp2);
           }
           matrix.add(temp);
       }
       int road;
       int tocity;
       int fromcity;
       int coast;
       StringTokenizer str_tok;
       for(int i=0; i<num_of_roads; i++){
           str_tok = new StringTokenizer(in.readLine()," ");
           fromcity = Integer.parseInt(str_tok.nextToken());
           tocity = Integer.parseInt(str_tok.nextToken());
           road = Integer.parseInt(str_tok.nextToken());
           coast = Integer.parseInt(str_tok.nextToken());
           if(matrix.get(fromcity-1).get(tocity-1).get(0).second==-1){
                ArrayList<Pair> temp_arr = new ArrayList<Pair>();
                temp_arr.add(new Pair(road, coast));
                matrix.get(fromcity-1).set(tocity-1,temp_arr);
                matrix.get(tocity-1).set(fromcity-1,temp_arr);
           }
           else{
               matrix.get(fromcity-1).get(tocity-1).add(new Pair(road, coast));
               //matrix.get(tocity-1).get(fromcity-1).add(new Pair(road, coast));
           }
       }
       str_tok = new StringTokenizer(in.readLine()," ");
       start = Integer.parseInt(str_tok.nextToken());
       finish = Integer.parseInt(str_tok.nextToken());
            PrintWriter fout = new PrintWriter(new BufferedWriter(new FileWriter("output.txt")));
            Four answer = cheepest_way();
            if(answer.first==finish){
              fout.println("Yes");
              fout.printf("%.2f",answer.second);
            }
            else{
               fout.print("No");
            }
            fout.close();

      } catch (IOException ex) {
            Logger.getLogger(Solution.class.getName()).log(Level.SEVERE, null, ex);
       }
   }
   public static Four cheepest_way(){
      PriorityQueue<Four> queue = new PriorityQueue<Four>(1000000, new Four());
      Four temp = new Four(start, 0.0, -1,0);
      Pair temp2 = new Pair();
         for(int i=0;i<num_of_cities;i++){
             temp2=(matrix.get(temp.first-1).get(i).get(0));
             if(temp2.first!=-1){
                 for(int j=0;j<matrix.get(temp.first-1).get(i).size();j++){
                    temp2=(matrix.get(temp.first-1).get(i).get(j));
                    queue.add(new Four(i+1,(temp.second+(temp2.second+((double)temp2.second/10))),temp.first,j));
                 }
             }
         }
      while(!queue.isEmpty()){
          temp = queue.poll();
          if(temp.first==finish)
              return temp;

          for(int i=0;i<num_of_cities;i++){
              temp2=(matrix.get(temp.first-1).get(i).get(0));
              if(temp2.second!=-1){
                  for(int j=0;j<matrix.get(temp.first-1).get(i).size();j++){
                    temp2=(matrix.get(temp.first-1).get(i).get(j));
                    if(matrix.get(temp.first-1).get(temp.third-1).get(temp.four).first==temp2.first){
                        queue.add(new Four(i+1,temp.second+temp2.second,temp.first,j));
                    }
                    else{
                        queue.add(new Four(i+1,temp.second+
                                (temp2.second+(temp2.second/10)),temp.first,j));
                    }
                  }
              }
          }
          for(int j=0;j<matrix.get(temp.third-1).get(temp.first-1).size();j++){
          int g = matrix.get(temp.third-1).get(temp.first-1).get(j).first;
          matrix.get(temp.third-1).get(temp.first-1).set(j,
                  new Pair(g,-1));
          }
      }
      return temp;
   }
}