#include <cstdio>
#include <algorithm>
#include <cmath>
#include <cstdlib>
#include <cstring>
#include <queue>
#include <iostream>
using namespace std;
#define N 2505
#define eps 5e-4
#define max(a,b) ((a)<(b)?(b):(a))
double f[N][N],ans;
int a[N],b[N],dep[N],head[N],cnt,k,n,siz[N];
struct node
{int to,next;
}e[N<<1];
void add(int x,int y)
{e[cnt].to=y;e[cnt].next=head[x];head[x]=cnt++;return ;
}
void dfs(int x,int from)
{dep[x]=dep[from]+1;siz[x]=1;if(x)f[x][1]=-ans*a[x]+b[x];for(int i=head[x];i!=-1;i=e[i].next){int to1=e[i].to;if(to1!=from){dfs(to1,x);int o=min(k,siz[x]+siz[to1]),u=min(k,siz[to1]);for(int j=o;j>=1;j--){for(int l=max(j-siz[x],1);l<=u;l++){if(l>j)break;f[x][j]=max(f[x][j],f[x][j-l]+f[to1][l]);}}siz[x]+=siz[to1];}}
}
bool check(double x)
{for(int i=0;i<=n;i++)for(int j=0;j<=k;j++)f[i][j]=-1e9;dep[0]=f[0][0]=0;ans=x;dfs(0,0);if(f[0][k]>0)return 1;return 0;
}
int main()
{// freopen("sales.in","r",stdin);// freopen("sales.out","w",stdout);memset(head,-1,sizeof(head));scanf("%d%d",&k,&n);for(int i=1;i<=n;i++){int x;scanf("%d%d%d",&a[i],&b[i],&x);add(x,i);}double l=0,r=10000;while(l<r-eps){double mid=(l+r)/2;if(check(mid))l=mid;else r=mid;}printf("%.3lf\n",l);return 0;
}

#include <cstdio>
#include <algorithm>
#include <cmath>
#include <cstdlib>
#include <cstring>
#include <queue>
#include <iostream>
using namespace std;
#define N 2505
#define eps 5e-4
#define max(a,b) ((a)<(b)?(b):(a))
double f[N][N],ans;
int a[N],b[N],head[N],cnt,k,n,idx[N],x,siz[N],tims;
struct node
{int to,next;
}e[N<<1];
void add(int x,int y)
{e[cnt].to=y;e[cnt].next=head[x];head[x]=cnt++;return ;
}
void dfs(int x,int from)
{idx[++tims]=x;siz[x]=1;for(int i=head[x];i!=-1;i=e[i].next){int to1=e[i].to;if(to1!=from){dfs(to1,x);siz[x]+=siz[to1];}}
}
bool check(double x)
{for(int i=1;i<=n+2;i++){for(int j=0;j<=k;j++){f[i][j]=-1e9;}}f[n+2][0]=0;for(int i=n+1;i>=1;i--){int t=idx[i];int u=min(k,n+2-i);if(i!=1){for(int j=u;j>=1;j--){f[i][j]=f[i+1][j-1]-x*a[t]+b[t];}}else{for(int j=k;j>=1;j--){f[i][j]=f[i+1][j];}}for(int j=u;j>=0;j--){f[i][j]=max(f[i][j],f[i+siz[t]][j]);}}if(f[1][k]>0)return 1;return 0;
}
int main()
{// freopen("sales.in","r",stdin);// freopen("sales.out","w",stdout);memset(head,-1,sizeof(head));scanf("%d%d",&k,&n);for(int i=1;i<=n;i++){int x;scanf("%d%d%d",&a[i],&b[i],&x);add(x,i);}dfs(0,0);double l=0,r=10000;while(l<r-eps){double mid=(l+r)/2;if(check(mid))l=mid;else r=mid;}printf("%.3lf\n",l);return 0;
}