#include<iostream>
#include<cmath>
#include<algorithm>
using namespace std;
const long double INF=1e17;
int T;
int N;
long double S;
struct NODE{
	long double p,b;
	long double pos_(long double t)
	{
		return p+(p<0?-1:1)*t*b;
	}
}A[508],C[508],D[508],E[508];
struct NODE2{
	int id;long double p,b;
}B[508];
long double f[508][508][2];
bool mcp(NODE2 x,NODE2 y)
{
	return x.p<y.p;
}
bool check(long double mid)
{
	for(int i=1;i<=N;i++)
	{
		B[i]={i,A[i].p+(A[i].p<=0?-1:1)*mid*A[i].b,A[i].b};
	}
	sort(B+1,B+N+1,mcp);
	int zo=N+1,totC=0;
	long double spd=-1;
	for(int i=1;i<=N;i++)
	{
		if(B[i].p>0)
		{
			zo=i;
			break;
		}
		if(spd<B[i].b) C[++totC]=A[B[i].id],spd=B[i].b;
	}
	spd=-1;
	int totD=0;
	for(int i=N;i>=zo;i--)
	{
		if(spd<B[i].b) D[++totD]=A[B[i].id],spd=B[i].b;
	}
	int M=0;
	for(int i=1;i<=totC;i++) E[++M]=C[i];
	for(int i=totD;i>=1;i--) E[++M]=D[i];
	for(int i=1;i<=M;i++) f[i][i][0]=f[i][i][1]=abs(E[i].p)/(S-E[i].b);
	for(int len=1;len<M;len++)
	{
		for(int l=1,r=l+len;r<=M;l++,r++)
		{
			f[l][r][0]=INF;
			long double t;
			f[l][r][0]=min(f[l][r][0],(t=f[l+1][r][0])+(E[l+1].pos_(t)-E[l].pos_(t))/(S-E[l].b));
			f[l][r][0]=min(f[l][r][0],(t=f[l+1][r][1])+(E[r].pos_(t)-E[l].pos_(t))/(S-E[l].b));
			
			f[l][r][1]=INF;
			f[l][r][1]=min(f[l][r][1],(t=f[l][r-1][1])+(E[r].pos_(t)-E[r-1].pos_(t))/(S-E[r].b));
			f[l][r][1]=min(f[l][r][1],(t=f[l][r-1][0])+(E[r].pos_(t)-E[l].pos_(t))/(S-E[r].b));
		}
	}
	return min(f[1][M][0],f[1][M][1])<=mid;
}
/*
2
4 3
3 6 9
3 2 1
2 2
1 -1
1 1
*/
void solve()
{
	cin>>S>>N;
	for(int i=1;i<=N;i++) cin>>A[i].p;
	for(int i=1;i<=N;i++) cin>>A[i].b;
	long double l=0,r=1e17,mid;
	while(r-l>1e-8)
	{
		mid=(l+r)/2.0;
		if(check(mid)) r=mid;
		else l=mid;
	}
	printf("%.6Lf\n",l);
}
signed main()
{
	cin>>T;
	while(T--)
	{
		solve();
//		init_();
	}
	return 0;
}
/*
1
1 1
1
0

2
4 3
3 6 9
3 2 1

2 2
1 -1
1 1
*/