#include <cstdio>
#include <cstring>
#include <array>
#include <iostream>
using namespace std;
const int N = 2001;

int n, k, u[N], v[N], w[N], head[N], nxt[N << 1], to[N << 1], val[N << 1], eid = 2;
bool del[N];
void addedge(int u, int v, int w) {
    to[eid] = v;
    val[eid] = w;
    nxt[eid] = head[u];
    head[u] = eid++;
}

struct info{
    int u;
    long long val;
    info(){}
    info(int u, long long val) : u(u), val(val){}
};

typedef array<info, 3> tupl;

int fa[N];
long long ansup[N], ansdn[N];
void getfa(int i){
    // printf("fa[%d] = %d\n", i, to[fa[i]]);
    for (int e = head[i]; e; e = nxt[e])
        if(e != fa[i]) {
            fa[to[e]] = e ^ 1;
            getfa(to[e]);
        }
}

tupl uptu[N], dntu[N], upson[N];

void merge(tupl &tu, info inf) {
    if(inf.val >= tu[0].val) {
        tu[2] = tu[1];
        tu[1] = tu[0];
        tu[0] = inf;
    }
    else if(inf.val >= tu[1].val) {
        tu[2] = tu[1];
        tu[1] = inf;
    }
    else if(inf.val >= tu[2].val)
        tu[2] = inf;
}

void up(int i) {
    ansup[i] = 0;
    uptu[i] = tupl();
    upson[i] = tupl();
    for (int e = head[i]; e; e = nxt[e])
        if(e != fa[i] && !del[e >> 1]) {
            up(to[e]);
            ansup[i] = max(ansup[i], ansup[to[e]]);
            info inf = uptu[to[e]][0];
            inf.u = to[e];
            inf.val += val[e];
            merge(uptu[i], inf);
            merge(upson[i], info(to[e], ansup[to[e]]));
        }
    ansup[i] = max(ansup[i], uptu[i][0].val + uptu[i][1].val);
    // printf("ansup[%d] = %d\n", i, ansup[i]);
}

void down(int i) {
    ansdn[i] = 0;
    dntu[i] = uptu[i];
    if(fa[i] && !del[fa[i] >> 1]) {
        int f = to[fa[i]];
        info inf = dntu[f][0].u != i ? dntu[f][0] : dntu[f][1];
        inf.val += val[fa[i]];
        merge(dntu[i], inf);
        ansdn[i] = max(ansdn[f], upson[f][0].u != i ? upson[f][0].val : upson[f][1].val);
        if(dntu[f][0].u == i)
            ansdn[i] = max(ansdn[i], dntu[f][1].val + dntu[f][2].val);
        else if(dntu[f][1].u == i)
            ansdn[i] = max(ansdn[i], dntu[f][0].val + dntu[f][2].val);
        else
            ansdn[i] = max(ansdn[i], dntu[f][0].val + dntu[f][1].val);
        // ansdn[i] = max(ansdn[i], val[fa[i]] + (dntu[f][0].u != i ? dntu[f][0].val : dntu[f][1].val));
        // printf("ansdn[%d] = %d + %d\n", i, val[fa[i]], dntu[f][0].u != i ? dntu[f][0].val : dntu[f][1].val);
    }
    for (int e = head[i]; e; e = nxt[e])
        if(e != fa[i] && !del[e >> 1])
            down(to[e]);
}

int findroot(int i){
    while(fa[i] && !del[fa[i] >> 1])
        i = to[fa[i]];
    return i;
}

void solve(int i) {
    up(i);
    down(i);
}

int ans[N];

void getans(int u) {
    for (int e = head[u]; e; e = nxt[e])
        if(e != fa[u] && !del[e >> 1]) {
            ans[to[e]] = ans[u];
            getans(to[e]);
        }
}

int main(){
    scanf("%d%d", &n, &k);
    for (int i = 1; i < n; i++) {
        scanf("%d%d%d", &u[i], &v[i], &w[i]);
        addedge(u[i], v[i], w[i]);
        addedge(v[i], u[i], w[i]);
    }
    getfa(1);
    for (int i = 1; i < n; i++)
        if(to[fa[v[i]]] == u[i])
            swap(u[i], v[i]);
    solve(1);
    long long now = ansup[1];
    printf("%lld ", now);
    for (int i = 1; i <= k; i++) {
        memset(ans + 1, -1, sizeof(int) * n);
        for (int j = 1; j <= n; j++) {
            if(ans[j] == -1) {
                // printf("init %d\n", j);
                int u = findroot(j);
                solve(u);
                ans[u] = ansup[u];
                getans(u);
                // puts("init success");
            }
        }
        int candi = 1;
        long long candians = 0;
        for (int j = 1; j < n; j++) 
            if(!del[j]) {
                // printf("j %d ansup[%d] %lld ansdn[%d] %lld\n", j, u[j], ansup[u[j]], u[j], ansdn[u[j]]);
                // printf("j %d u %d v %d\n", j, u[j], v[j]);
                long long nowans = ansup[u[j]] + ansdn[u[j]] + w[j] - ans[u[j]];
                if(n > 50 && k > 0)
                    printf("%d %d ", u[j], v[j]);
                if(nowans > candians) {
                    candians = nowans;
                    candi = j;
                }
            }
        // printf("candi %d %d %d, candians %lld\n", candi, u[candi], v[candi], candians);
        now += candians;
        del[candi] = true;
        printf("%lld ", now);
    }
    return 0;
}