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| #include <bits/stdc++.h>
using namespace std;
struct Node {
long long g;
int lpos, rpos;
Node() {
g = 0;
}
Node(long long _g) {
g = _g;
}
Node& operator+=(const Node& n) {
this->g += n.g;
return *this;
}
Node push_up(const Node& ln, const Node& rn) {
this->g = gcd(ln.g, rn.g);
return *this;
}
};
struct SegmentTree {
#define lp (p << 1)
#define rp (p << 1 | 1)
vector<Node> val;
SegmentTree(int n = 0) {
resize(n);
}
void resize(int n) {
val.resize((n + 1) * 4);
}
void build(int l, int r, int p = 1) {
val[p].lpos = l;
val[p].rpos = r;
if (l == r) {
return;
}
int mid = (l + r) >> 1;
build(l, mid, lp);
build(mid + 1, r, rp);
val[p].push_up(val[lp], val[rp]);
}
void update(int pos, const Node& k, int p = 1) {
if (val[p].lpos == pos && pos == val[p].rpos) {
val[p] += k;
return;
}
int mid = (val[p].lpos + val[p].rpos) >> 1;
if (pos <= mid) {
update(pos, k, lp);
} else {
update(pos, k, rp);
}
val[p].push_up(val[lp], val[rp]);
}
Node query(const int& l, const int& r, int p = 1) {
if (l <= val[p].lpos && val[p].rpos <= r) {
return val[p];
}
int mid = (val[p].lpos + val[p].rpos) >> 1;
if (r <= mid) {
return query(l, r, lp);
}
if (mid < l) {
return query(l, r ,rp);
}
return Node().push_up(query(l, r, lp), query(l, r, rp));
}
};
inline void Tecy() {
const long long inf = 1e18;
long long n, k;
cin >> n >> k;
vector<int> c(k);
vector<int> ok(n + 1);
for (auto& x : c) {
cin >> x;
ok[x] = true;
}
vector<vector<pair<int, long long>>> tree(n + 1);
for (int i = 1; i < n; i++) {
int u, v;
long long w;
cin >> u >> v >> w;
tree[u].push_back({ v, w });
tree[v].push_back({ u, w });
}
if (k <= 1) {
cout << 0;
return;
}
int tot = 0;
vector<long long> dfn(n + 1);
vector<long long> siz(n + 1);
vector<long long> l(n + 1);
vector<long long> r(n + 1);
long long last = 0;
auto get = [&](auto get, int u, int f) -> void {
l[u] = last + 1;
if (ok[u]) {
dfn[u] = ++tot;
siz[u] = 1;
last = tot;
}
for (auto& [v, w] : tree[u]) {
if (v != f) {
get(get, v, u);
siz[u] += siz[v];
}
}
r[u] = l[u] + siz[u];
};
get(get, 1, 0);
vector<long long> sum(n + 1);
SegmentTree sgt(k);
sgt.build(1, k);
auto dfs = [&](auto dfs, int u, int f) -> void {
for (auto& [v, w] : tree[u]) {
if (v != f) {
dfs(dfs, v, u);
sum[u] += sum[v] + siz[v] * w;
if (siz[v]) {
sgt.update(l[v], { w });
if (r[v] <= k) {
sgt.update(r[v], { -w });
}
}
}
}
};
dfs(dfs, 1, 0);
vector<long long> g(n + 1);
auto dp = [&](auto dp, int u, int f) -> void {
g[u] = abs(gcd(sgt.val[1].g, sgt.query(2, k).g));
for (auto& [v, w] : tree[u]) {
if (v != f) {
sum[v] += sum[u] - sum[v] + (k - siz[v] * 2) * w;
sgt.update(1, { w });
if (siz[v]) {
sgt.update(l[v], { -w * 2 });
if (r[v] <= k) {
sgt.update(r[v], { w * 2 });
}
}
dp(dp, v, u);
sgt.update(1, { -w });
if (siz[v]) {
sgt.update(l[v], { w * 2 });
if (r[v] <= k) {
sgt.update(r[v], { -w * 2 });
}
}
}
}
};
dp(dp, 1, 0);
long long ans = inf;
for (int i = 1; i <= n; i++) {
ans = min(ans, sum[i] * 2 / g[i]);
}
cout << ans;
}
int main() {
ios::sync_with_stdio(false);
cout.tie(0);
cin.tie(0);
int T = 1;
while (T--) {
Tecy();
}
return 0;
}
|
