#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using Int = long long; template ostream &operator<<(ostream &os, const pair &a) { return os << "(" << a.first << ", " << a.second << ")"; }; template ostream &operator<<(ostream &os, const vector &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; } template void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; } template bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; } template bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; } // T: monoid representing information of an interval. // T() should return the identity. // T(S s) should represent a single element of the array. // T::push(T &l, T &r) should push the lazy update. // T::merge(const T &l, const T &r) should merge two intervals. template struct SegmentTreeRange { int logN, n; vector ts; SegmentTreeRange() {} explicit SegmentTreeRange(int n_) { for (logN = 0, n = 1; n < n_; ++logN, n <<= 1) {} ts.resize(n << 1); } template explicit SegmentTreeRange(const vector &ss) { const int n_ = ss.size(); for (logN = 0, n = 1; n < n_; ++logN, n <<= 1) {} ts.resize(n << 1); for (int i = 0; i < n_; ++i) at(i) = T(ss[i]); build(); } T &at(int i) { return ts[n + i]; } void build() { for (int u = n; --u; ) merge(u); } inline void push(int u) { ts[u].push(ts[u << 1], ts[u << 1 | 1]); } inline void merge(int u) { ts[u].merge(ts[u << 1], ts[u << 1 | 1]); } // Applies T::f(args...) to [a, b). template void ch(int a, int b, F f, Args &&... args) { assert(0 <= a); assert(a <= b); assert(b <= n); if (a == b) return; a += n; b += n; for (int h = logN; h; --h) { const int aa = a >> h, bb = b >> h; if (aa == bb) { if ((aa << h) != a || (bb << h) != b) push(aa); } else { if ((aa << h) != a) push(aa); if ((bb << h) != b) push(bb); } } for (int aa = a, bb = b; aa < bb; aa >>= 1, bb >>= 1) { if (aa & 1) (ts[aa++].*f)(args...); if (bb & 1) (ts[--bb].*f)(args...); } for (int h = 1; h <= logN; ++h) { const int aa = a >> h, bb = b >> h; if (aa == bb) { if ((aa << h) != a || (bb << h) != b) merge(aa); } else { if ((aa << h) != a) merge(aa); if ((bb << h) != b) merge(bb); } } } // Calculates the product for [a, b). T get(int a, int b) { assert(0 <= a); assert(a <= b); assert(b <= n); if (a == b) return T(); a += n; b += n; for (int h = logN; h; --h) { const int aa = a >> h, bb = b >> h; if (aa == bb) { if ((aa << h) != a || (bb << h) != b) push(aa); } else { if ((aa << h) != a) push(aa); if ((bb << h) != b) push(bb); } } T prodL, prodR, t; for (int aa = a, bb = b; aa < bb; aa >>= 1, bb >>= 1) { if (aa & 1) { t.merge(prodL, ts[aa++]); prodL = t; } if (bb & 1) { t.merge(ts[--bb], prodR); prodR = t; } } t.merge(prodL, prodR); return t; } // Calculates T::f(args...) of a monoid type for [a, b). // op(-, -) should calculate the product. // e() should return the identity. template #if __cplusplus >= 201402L auto #else decltype((std::declval().*F())()) #endif get(int a, int b, Op op, E e, F f, Args &&... args) { assert(0 <= a); assert(a <= b); assert(b <= n); if (a == b) return e(); a += n; b += n; for (int h = logN; h; --h) { const int aa = a >> h, bb = b >> h; if (aa == bb) { if ((aa << h) != a || (bb << h) != b) push(aa); } else { if ((aa << h) != a) push(aa); if ((bb << h) != b) push(bb); } } auto prodL = e(), prodR = e(); for (int aa = a, bb = b; aa < bb; aa >>= 1, bb >>= 1) { if (aa & 1) prodL = op(prodL, (ts[aa++].*f)(args...)); if (bb & 1) prodR = op((ts[--bb].*f)(args...), prodR); } return op(prodL, prodR); } // Find min b s.t. T::f(args...) returns true, // when called for the partition of [a, b) from left to right. // Returns n + 1 if there is no such b. template int findRight(int a, F f, Args &&... args) { assert(0 <= a); assert(a <= n); if ((T().*f)(args...)) return a; if (a == n) return n + 1; a += n; for (int h = logN; h; --h) push(a >> h); for (; ; a >>= 1) if (a & 1) { if ((ts[a].*f)(args...)) { for (; a < n; ) { push(a); if (!(ts[a <<= 1].*f)(args...)) ++a; } return a - n + 1; } ++a; if (!(a & (a - 1))) return n + 1; } } // Find max a s.t. T::f(args...) returns true, // when called for the partition of [a, b) from right to left. // Returns -1 if there is no such a. template int findLeft(int b, F f, Args &&... args) { assert(0 <= b); assert(b <= n); if ((T().*f)(args...)) return b; if (b == 0) return -1; b += n; for (int h = logN; h; --h) push((b - 1) >> h); for (; ; b >>= 1) if ((b & 1) || b == 2) { if ((ts[b - 1].*f)(args...)) { for (; b <= n; ) { push(b - 1); if (!(ts[(b <<= 1) - 1].*f)(args...)) --b; } return b - n - 1; } --b; if (!(b & (b - 1))) return -1; } } }; //////////////////////////////////////////////////////////////////////////////// struct Node { Int sum0, sum1, sum2; Int lz; Node() : sum0(0), sum1(0), sum2(0), lz(0) {} void push(Node &l, Node &r) { if (lz) { l.add(lz); r.add(lz); lz = 0; } } void merge(const Node &l, const Node &r) { sum0 = l.sum0 + r.sum0; sum1 = l.sum1 + r.sum1; sum2 = l.sum2 + r.sum2; } void add(Int val) { // binom(x + val, 2) - binom(x, 2) sum2 += sum1 * val + sum0 * val * (val - 1) / 2; sum1 += sum0 * val; lz += val; } }; int N, Q; vector A, B; vector> graph; vector par, sz; int zeit; vector dis, fin; vector head; void dfsSz(int u) { sz[u] = 1; for (const int v : graph[u]) { graph[v].erase(find(graph[v].begin(), graph[v].end(), u)); par[v] = u; dfsSz(v); sz[u] += sz[v]; } } void dfsHLD(int u) { dis[u] = zeit++; const int deg = graph[u].size(); if (deg > 0) { int vm = graph[u][0]; int jm = 0; for (int j = 1; j < deg; ++j) { const int v = graph[u][j]; if (sz[vm] < sz[v]) { vm = v; jm = j; } } swap(graph[u][0], graph[u][jm]); head[vm] = head[u]; dfsHLD(vm); for (int j = 1; j < deg; ++j) { const int v = graph[u][j]; head[v] = v; dfsHLD(v); } } fin[u] = zeit; } void runHLD(int rt) { par.assign(N, -1); sz.resize(N); zeit = 0; dis.resize(N); fin.resize(N); head.resize(N); dfsSz(rt); head[rt] = rt; dfsHLD(rt); } constexpr int R0 = 0; Int tot; vector on; SegmentTreeRange seg, segOne; void init() { tot = 0; on.assign(N, 0); seg = SegmentTreeRange(N); segOne = SegmentTreeRange(N); for (int u = 0; u < N; ++u) { seg.at(dis[u]).sum0 = u - par[u]; segOne.at(dis[u]).sum0 = 1; } seg.build(); segOne.build(); } void add(int u, int val) { // cerr<<"add "<