/********************************************************************
@file     Main.cpp
@date     2019-5-9 10:06:33
@author   Zoro_Tiger
@brief    问题 1078: Repairing a Road
          https://www.dotcpp.com/oj/problem1078.html
@detail   https://www.cnblogs.com/oyking/p/3278741.html
********************************************************************/
#include <cmath>
#include <cstdio>

#define EPS 1E-6
#define MAX_VALUE 1E+6
#define VERTEX_MAX_SIZE 100

double Cost[VERTEX_MAX_SIZE][VERTEX_MAX_SIZE];
double Coef[VERTEX_MAX_SIZE][VERTEX_MAX_SIZE];

inline void Min(double& lValue, const double& rValue) { if (lValue > rValue) lValue = rValue; }

int main(int argc, const char* argv[])
{
    int verCnt, edgeCnt;
    while (scanf("%d %d", &verCnt, &edgeCnt) != EOF)
    {
        //结束用例
        if (verCnt == 0 && edgeCnt == 0)
            break;

        //初始化
        for (int i = 0; i < verCnt; ++i)
        {
            for (int j = 0; j < verCnt; ++j)
            {
                Coef[i][j] = 0.0f;
                Cost[i][j] = MAX_VALUE;
            }
            Cost[i][i] = 0.0f;
        }

        //读取数据
        int verIndex1, verIndex2;
        double cost, coef;
        for (int i = 0; i < edgeCnt; ++i)
        {
            scanf("%d %d %lf %lf", &verIndex1, &verIndex2, &cost, &coef);
            Cost[verIndex1 - 1][verIndex2 - 1] = Cost[verIndex2 - 1][verIndex1 - 1] = cost;
            Coef[verIndex1 - 1][verIndex2 - 1] = Coef[verIndex2 - 1][verIndex1 - 1] = coef;
        }

        //Floyd
        for (int i = 0; i < verCnt; ++i)
            for (int j = 0; j < verCnt; ++j)
                for (int k = 0; k < verCnt; ++k)
                    Min(Cost[j][k], Cost[j][i] + Cost[i][k]);

        //计算花费
        double final_cost = Cost[0][verCnt - 1];
        for (int i = 0; i < verCnt; ++i)
            for (int j = 0; j < verCnt; ++j)
            {
                if (Coef[i][j] > EPS)
                {
                    double lValue = Cost[0][i], rValue = final_cost, mValue, checkValue;
                    if (lValue < rValue)
                    {
                        while (rValue - lValue > EPS)
                        {
                            mValue = (lValue + rValue) / 2.0f;
                            checkValue = 1 - log(Coef[i][j]) * Cost[i][j] * pow(Coef[i][j], 0 - mValue);
                            if (checkValue > EPS)
                                rValue = mValue;
                            else
                                lValue = mValue;
                        }
                        Min(final_cost, lValue + Cost[j][verCnt - 1] + Cost[i][j] * pow(Coef[i][j], 0 - lValue));
                    }
                }
            }
        printf("%.3f\n", final_cost);
    }
    return 0;
}