// Skyqwq
#include <bits/stdc++.h>

#define pb push_back
#define fi first
#define se second
#define mp make_pair

using namespace std;

typedef long long LL;
typedef pair<int, int> PII;

template <typename T> bool chkMax(T &x, T y) { return (y > x) ? x = y, 1 : 0; }
template <typename T> bool chkMin(T &x, T y) { return (y < x) ? x = y, 1 : 0; }

template <typename T> void inline read(T &x) {
    int f = 1; x = 0; char s = getchar();
    while (s < '0' || s > '9') { if (s == '-') f = -1; s = getchar(); }
    while (s <= '9' && s >= '0') x = x * 10 + (s ^ 48), s = getchar();
    x *= f;
}

const int N = 3e5 + 5, S = 102;
const LL INF = 0xcfcfcfcfcfcfcfcf;

int n, k, sz[N];
LL f[N][3], h[3], c[N][3], W, C[3];

vector<PII> g[N];

void inline mg(int u, int v, int w) {
	for (int x = 0; x < 3; x++) {
		for (int y = 0; y < 3; y++) {
			if (chkMax(h[x], f[u][x] + f[v][y])) C[x] = c[u][x] + c[v][y];
			if (!x && y == 1)
				if (chkMax(h[1], f[u][x] + f[v][y] + w)) C[1] = c[u][x] + c[v][y]; 
			if (x == 1 && y == 1)
				if (chkMax(h[2], f[u][x] + f[v][y] + w + W)) C[2] = c[u][x] + c[v][y] - 1;
		}
	}
	for (int x = 0; x < 3; x++) f[u][x] = h[x], c[u][x] = C[x], h[x] = INF;
}

void dfs(int u, int fa) {
	sz[u] = 1;
	f[u][0] = 0;
	for (PII t: g[u]) {
		int v = t.fi;
		if (v == fa) continue;
		dfs(v, u);
		mg(u, v, t.se);
		sz[u] += sz[v];
	}
	if (chkMax(f[u][1], f[u][0] - W)) c[u][1] = c[u][0] + 1;
}

int inline get(LL X) {
	W = X;
	memset(f, 0xcf, sizeof f);
	memset(h, 0xcf, sizeof h);
	memset(c, 0, sizeof c);
	dfs(1, 0);
	LL mx = INF; int cnt = 0;
	for (int i = 0; i < 3; i++)
		if (chkMax(mx, f[1][i])) cnt = c[1][i];
	return cnt;
}

int main() {
//	freopen("b.in", "r", stdin);
//	freopen("lct.in", "r", stdin);
	read(n), read(k); ++k;
	for (int i = 1, u, v, w; i < n; i++)
		read(u), read(v), read(w), g[u].pb(mp(v, w)), g[v].pb(mp(u, w));
	LL l = -4e11, r = 4e11;
	while (l < r) {
		LL mid = (l + r) >> 1;
		if (get(mid) <= k) r = mid;
		else l = mid + 1; 
	} 
	get(r);
	LL ans = max(max(f[1][0], f[1][1]), f[1][2]) + k * r;
    printf("%lld\n", ans);
	return 0;
}