二分答案，贪心，先取一个点dfs，将所有点按照深度排序，然后从最深的点开始，向上走k步建立核心城市，再bfs标记已覆盖的城市

#include<queue>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int MAXN = 100005;

int n, k;
int fir[MAXN], nxt[MAXN << 1], to[MAXN << 1], cnt;
int dep[MAXN], fa[MAXN], rnk[MAXN], dis[MAXN];

inline int read(){
	int k = 0; char ch = getchar();
	while(ch < '0' || ch > '9') ch = getchar();
	while(ch >= '0' && ch <= '9'){k = k * 10 + ch - '0'; ch = getchar();}
	return k;
}

inline void add_edge(int a, int b){
	to[cnt] = b;
	nxt[cnt] = fir[a];
	fir[a] = cnt++;
}

void dfs(int u, int f, int d){
    dep[u] = d, fa[u] = f;
    for(int i = fir[u]; i != -1; i = nxt[i]){
        int v = to[i];
        if(v == f) continue;
        dfs(v, u, d + 1);
    }
}

int vis[MAXN];
queue <int> q;
void bfs(int u, int t){
    q.push(u);
    dis[u] = 0;
    while(!q.empty()){
        u = q.front(); q.pop();
        vis[u] = 0;
        for(int i = fir[u]; i != -1; i = nxt[i]){
            int v = to[i];
            if(dis[u] < t){
                dis[v] = dis[u] + 1;
                if(!vis[v]){
                	q.push(v);
                	vis[v] = 1;
				}
            }
        }
    }
}

bool check(int t){
	memset(dis, 0x3f, sizeof(dis));
	int ret = 0;
	for(int i = 1; i <= n; i++){
		int u = rnk[i];
		if(dis[u] != 0x3f3f3f3f) continue;
		for(int j = 1; j <= t; j++){
			if(u == 1) break;
			u = fa[u];
		}
		bfs(u, t);
		ret++;
	}
	if(ret <= k) return true;
	else return false;
}

inline bool cmp(int a, int b){
	return dep[a] > dep[b];
}

int main(){
	memset(fir, -1, sizeof(fir));
	n = read(), k = read();
	for(int i = 1; i < n; i++){
		int a = read(), b = read();
		add_edge(a, b);
		add_edge(b, a);
	}
	dfs(1, 0, 1);
	
	for(int i = 1; i <= n; i++) rnk[i] = i;
	sort(rnk + 1, rnk + n + 1, cmp);
	
	int l = 0, r = n;
	while(l < r){
		int mid = (l + r) / 2;
		if(check(mid)){
			r = mid;
		}
		else{
			l = mid + 1;
		}
	}
	printf("%d", l);
	return 0;
}