/* AUTHOR: TUAN ANH - BUI */
// ~~ icebear ~~
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> ii;
typedef pair<int, ii> iii;
template<class X, class Y>
bool minimize(X &x, const Y &y) {
if (x > y) return x = y, true;
return false;
}
template<class X, class Y>
bool maximize(X &x, const Y &y) {
if (x < y) return x = y, true;
return false;
}
#define FOR(i,a,b) for(int i=(a); i<=(b); ++i)
#define FORR(i,a,b) for(int i=(a); i>=(b); --i)
#define REP(i, n) for(int i=0; i<(n); ++i)
#define RED(i, n) for(int i=(n)-1; i>=0; --i)
#define MASK(i) (1LL << (i))
#define BIT(S, i) (((S) >> (i)) & 1)
#define mp make_pair
#define pb push_back
#define fi first
#define se second
#define all(x) x.begin(), x.end()
#define task "qtree"
/*END OF TEMPLATE. ICEBEAR AND THE CAT WILL WIN VOI26 */
const int MOD = 1e9 + 7;
const int inf = (int)1e9 + 27092008;
const ll INF = (ll)1e18 + 27092008;
const int N = 1e5 + 5;
const int Q = 5e5 + 5;
int n, q, t, m;
vector<int> G[N];
int diff[N];
ll f[N][10];
int x[Q], y[Q], k[Q], minHigh[N << 1][20], pos[N], tour[N << 1], timer, ans, h[N];
void dfs(int u, int par) {
pos[u] = ++timer;
tour[timer] = u;
for(int v : G[u]) if (v != par) {
h[v] = h[u] + 1;
dfs(v, u);
tour[++timer] = u;
}
}
void DFS(int u, int par) {
FOR(j, 0, m) f[u][j] = -inf;
f[u][0] = 0;
for(int v : G[u]) if (v != par) {
DFS(v, u);
diff[u] += diff[v];
FORR(k, m, 1) FORR(j, k - 1, 0)
maximize(f[u][k], f[u][j] + diff[v] + f[v][k - 1 - j]);
}
maximize(ans, f[u][m]);
}
#define MIN_HIGH(x, y) (h[x] < h[y] ? x : y)
int LCA(int u, int v) {
int l = pos[u], r = pos[v];
if (l > r) swap(l, r);
int k = __lg(r - l + 1);
return MIN_HIGH(minHigh[l][k], minHigh[r - MASK(k) + 1][k]);
}
void init(void) {
cin >> n >> q >> t >> m;
FOR(i, 2, n) {
int u, v;
cin >> u >> v;
G[u].pb(v);
G[v].pb(u);
}
FOR(i, 1, q) cin >> x[i] >> y[i] >> k[i];
}
void process(void) {
dfs(1, -1);
FOR(i, 1, timer) minHigh[i][0] = tour[i];
FOR(j, 1, 19) FOR(i, 1, timer - MASK(j) + 1)
minHigh[i][j] = MIN_HIGH(minHigh[i][j - 1], minHigh[i + MASK(j - 1)][j - 1]);
while(t--) {
int l, r;
cin >> l >> r;
FOR(i, l, r) {
diff[x[i]] += k[i];
diff[y[i]] += k[i];
diff[LCA(x[i], y[i])] -= 2 * k[i];
}
ans = -inf;
DFS(1, -1);
cout << ans << '\n';
FOR(i, 1, n) diff[i] = 0;
}
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
if (fopen(task".inp", "r")) {
freopen(task".inp", "r", stdin);
freopen(task".out", "w", stdout);
}
int tc = 1;
// cin >> tc;
while(tc--) {
init();
process();
}
return 0;
}
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