#include<stdio.h>
#include<math.h>
#include<vector>
#include<limits.h>
#include<float.h>
#include<utility>
using namespace std;
#define E 0.0000000001
#define EE 0.00000001

void bf( int N, const vector< vector< pair<int, pair<int,int> > > > &e, double ce, double ct, int src, 
 vector< double > &d, vector<int> &prev, vector<int> &prev_nth )
{
	d.resize( N );
	prev.resize( N );
	prev_nth.resize( N );
	for( int i = 0; i < N; i ++ ){
		d[i] = DBL_MAX;
		prev[i] = -1;
		prev_nth[i] = -1;
	}
	d[src] = 0;
	for( int k = 1; k < N; k ++ ){
		int flag = 0;
		for( int i = 0; i < N; i ++ ){
			for( int j = 0; j < e[i].size(); j ++ ){
				int J    = e[i][j].first;
				if( J < 0 )
					continue;
				double D = d[i] + e[i][j].second.first * ce + e[i][j].second.second * ct;
				if( d[J] - E > D ){
					d[J] = D;
					prev[J] = i;
					prev_nth[J] = j;
					flag = 1;
				}
			}
		}
		if( !flag )
			break;
	}
}

int main( void )
{
	FILE *in = fopen( "rakunarok.in", "r" );
	if( in == NULL )
		return 0;

	int TT;
	fscanf( in,"%d", &TT );
	for( int C = 0; C < TT; C ++ ){
		int n, m;
		fscanf( in, "%d%d", &n, &m );
		int s, t;
		fscanf( in, "%d%d", &s, &t );
		vector< vector< pair<int, pair<int,int> > > > e( n );
		double T = 0, Etotal = 0;
		for( int i = 0; i < m; i ++ ){
			int a, b, ee, t;
			fscanf( in, "%d%d%d%d", &a, &b, &ee, &t );
			e[a].push_back( pair<int, pair<int,int> >(b, pair<int,int>(ee,t) ) );
			e[b].push_back( pair<int, pair<int,int> >(a, pair<int,int>(ee,t) ) );
			T += t;
			Etotal += ee;
		}

		vector<double> dt( n ), de( n ), dr( n );
		vector<int> prev, prev_nth;
		bf( n, e, 0, 1, t, dt, prev, prev_nth );
		bf( n, e, 1, 0, t, de, prev, prev_nth );
//		printf( "a\n" );
		double vm = de[s] / T;
		double vM = Etotal / dt[s];
		vM = max(vM, vm + EE * 2);

		for( int i = 0; i < n; i ++ ){
			for( int j = 0; j < e[i].size(); j ++ ){
				int J    = e[i][j].first;
				if( dt[i] <= dt[J] ){
					e[i][j].first = -1;
				}
			}
		}

		while( vm + EE < vM ){
//			printf( "%.20lf - %.20lf\n", vm, vM );
			double r = (vm + vM) * 0.5;
			bf( n, e, -1, r, s, dr, prev, prev_nth );
			if( dr[t] > 0 )
				vM = r;
			else
				vm = r;
		}

		bf( n, e, -1, (vm + vM) * 0.5, s, dr, prev, prev_nth );
		double re = 0, rt = 0;
		for( int i = t; i >= 0 && prev[i] >= 0; i = prev[i] ){
//			printf( "%d %d %d\n", i, prev[i], prev_nth[i] );
			re += e[prev[i]][prev_nth[i]].second.first;
			rt += e[prev[i]][prev_nth[i]].second.second;
		}

		printf( "%.4lf\n", re / rt );
	}
	fclose( in );
	return 0;
}