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struct SegTree {
using T = ll; using U = ll;
int n, h;
static constexpr T E = 0; // Neutral element for combine
static constexpr U UF = 0; // Unused value by updates
vector<T> tree; vector<U> lazy;
vector<ll> k; // size of segments (optional)
SegTree(const vector<T>& a) : n(sz(a) + 1), tree(2 * n, E),
//SegTree(int size, T def = E) : n(size + 1), tree(2 * n, def),
h(__lg(2 * n)), lazy(n, UF), k(2 * n, 1) {
copy(all(a), tree.begin() + n);
for (int i = n - 1; i > 0; i--) {
k[i] = 2 * k[2 * i];
tree[i] = comb(tree[2 * i], tree[2 * i + 1]);
}}
T comb(T a, T b) {return a + b;} // Modify this + E
void apply(int i, U val) { // And this + UF
tree[i] = val * k[i];
if (i < n) lazy[i] = val; // Don't forget this
}
void push_down(int i) {
if (lazy[i] != UF) {
apply(2 * i, lazy[i]);
apply(2 * i + 1, lazy[i]);
lazy[i] = UF;
}}
void push(int i) {
for (int s = h; s > 0; s--) push_down(i >> s);
}
void build(int i) {
while (i /= 2) {
push_down(i);
tree[i] = comb(tree[2 * i], tree[2 * i + 1]);
}}
void update(int l, int r, U val) {
l += n, r += n;
int l0 = l, r0 = r;
push(l0), push(r0 - 1);
for (; l < r; l /= 2, r /= 2) {
if (l&1) apply(l++, val);
if (r&1) apply(--r, val);
}
build(l0), build(r0 - 1);
}
T query(int l, int r) {
l += n, r += n;
push(l), push(r - 1);
T resL = E, resR = E;
for (; l < r; l /= 2, r /= 2) {
if (l&1) resL = comb(resL, tree[l++]);
if (r&1) resR = comb(tree[--r], resR);
}
return comb(resL, resR);
}
// Optional:
ll lower_bound(int l, int r, T x) {
l += n, r += n;
push(l), push(r - 1);
vector<int> a, st;
for (; l < r; l /= 2, r /= 2) {
if (l&1) a.push_back(l++);
if (r&1) st.push_back(--r);
}
a.insert(a.end(), st.rbegin(), st.rend());
for (int i : a) if (tree[i] >= x) { // Modify this
while (i < n) {
push_down(i);
if (tree[2 * i] >= x) i = 2 * i; // And this
else i = 2 * i + 1;
}
return i - n;
}
return -1;
}
};
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