赛道修建

#include <bits/stdc++.h>
#define mid ((l+r)>>1)
#define ll long long
#define maxn 50010
using namespace std;
struct Edge{
    int to,next,val;
    Edge(int a=0,int b=0,int c=0){
        to=a,next=b,val=c;
    }
}l[maxn<<1];
int head[maxn],cnt,n,m;
vector<int> son[maxn];
ll f[maxn];
int subans[maxn];
void Add(int a,int b,int c){
    l[++cnt]=Edge(b,head[a],c);
    head[a]=cnt;
}
int check(int u,int pos,int tot,ll x){
    int res=0,l=0;
    for (register int r=tot-1;r;--r){
        r-=r==pos;
        while (l<r&&son[u][l]+son[u][r]<x) ++l;
        l+=l==pos;
        if (l>=r) break;
        ++res;++l;
    }
    return res;
}
void Dfs(int u,int fa,ll x){
    f[u]=subans[u]=0;
    son[u].clear();
    for (register int i=head[u];i;i=l[i].next){
        int v=l[i].to;
        if (v==fa) continue;
        Dfs(v,u,x);
        f[v]+=l[i].val;
        if (f[v]>=x) subans[u]++;
        else son[u].push_back(f[v]);
    }
    int tot=son[u].size();
    sort(son[u].begin(),son[u].end());
    int l=0,r=tot,sub=0,res;
    for (register int r=tot-1;r;--r){
        while (l<r&&son[u][l]+son[u][r]<x) ++l;
        if (l>=r) break;
        ++sub;++l;
    }
    subans[u]+=sub;
    if (sub*2==tot) return;
    l=0,r=tot-1;
    while(l<=r){
        int tem=check(u,mid,tot,x);
        if (tem==sub) res=mid,l=mid+1;
        else r=mid-1;
    }
    f[u]=son[u][res];
}
bool check(ll x){
    int tem=0;
    Dfs(1,0,x);
    for (register int i=1;i<=n;++i)
        tem+=subans[i];
    return tem>=m;
}
int main(){
    ll l=0,r=0,ans,c;
    scanf("%d%d",&n,&m);
    for (register int i=1,a,b;i<n;++i)
        scanf("%d%d%lld",&a,&b,&c),
        Add(a,b,c),Add(b,a,c),r+=c;
    r/=(ll)m;
    while(l<=r){
        if (check(mid)) ans=mid,l=mid+1;
        else r=mid-1;
    }
    printf("%lld\n",ans);
    return 0;
}