#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef vector<int> vi;
typedef vector<ld> vld;
typedef vector<ll> vll;
typedef vector<pair<ll, ll>> vp;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
#define fr first
#define sc second
#define all(a) a.begin(),a.end()
void Hendi() {
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
#ifndef ONLINE_JUDGE
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
freopen("error.txt", "w", stderr);
#endif
}
const ll INF = 1e18;
const ll MOD = 1e9 + 7;
const double EPS = 1e-7;
const int N = 1e4 + 5;
const int N1 = 1e5 + 5;
int dx[] = {0, 0, 1, -1, -1, -1, 1, 1};
int dy[] = {1, -1, 0, 0, 1, -1, 1, -1};
char di[] = {'R', 'L', 'D', 'U'};
ll mul(ll a, ll b) {
return ((a % MOD) * (b % MOD)) % MOD;
}
ll sub(ll a, ll b) {
return ((a % MOD) - (b % MOD) + MOD) % MOD;
}
ll add(ll a, ll b) {
return ((a % MOD) + (b % MOD)) % MOD;
}
int n , k;
ll dp[N][25], dist[N], sz[N], in[N];
vp adj[N];
ll dfs2(int p, int ch){
sz[ch] = 1;
for(auto &i : adj[ch]){
if(i.fr != p){
sz[ch] += dfs2(ch,i.fr);
}
}
return sz[ch];
}
ll dfs(int p, int ch, int w){
dist[ch] = w;
for(auto &i : adj[ch]){
if(i.fr != p){
dist[ch] += dfs(ch,i.fr, i.sc);
}
}
return dist[ch];
}
ll calc(int i , int tot){
if(i == n) return (tot == k? 0: -INF);
ll &ret = dp[i][tot];
if(~ret) return ret;
ret = 0;
if(i == 0 && adj[0].size() == 1 && k) ret = max(ret,calc(i + 1, tot + 1) + adj[0].back().sc);
if(sz[i] + tot <= k) ret = max(ret, calc(i + 1, tot + sz[i]) + dist[i]);
ret = max(ret, calc(i + 1, tot));
return ret;
}
void solve() {
cin>> n >> k;
int x , y , w;
for (int i = 0; i < n; ++i) {
adj[i].clear();
dist[i] = 0;
sz[i] = 0;
}
for (int i = 0; i < n - 1; ++i) {
cin>> x >> y >> w;
adj[x].push_back({y,w});
adj[y].push_back({x,w});
}
memset(dp, - 1, sizeof dp);
dfs(-1,0,0);
dfs2(-1,0);
cout<< (dist[0] - calc(0, 0)) * 2 << endl;
}
int main() {
Hendi();
int T = 1;
cin >> T;
while (T--) {
solve();
}
}
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