This documentation is automatically generated by online-judge-tools/verification-helper
#include "graph/ds/rolling_hash_on_tree.hpp"
#include "random/base.hpp"
#include "graph/tree.hpp"
#include "mod/modint61.hpp"
// 木の辺に文字がちょうどひとつ書いてある (static)
template <typename TREE, bool EDGE>
struct Rolling_Hash_On_Tree {
using mint = modint61;
TREE& tree;
int N;
mint base;
// edge に文字があると思って
// dp1: [root,v]
// dp2: [v,root]
vc<int> dat;
vc<mint> dp1, dp2;
vc<mint> pow, ipow;
template <typename F>
Rolling_Hash_On_Tree(TREE& tree, F f, mint base_ = 0)
: tree(tree), N(tree.N), base(base_) {
if (base == mint(0)) base = RNG(mint::get_mod());
build(f);
}
template <typename F>
void build(F f) {
dat.resize(N);
if constexpr (EDGE) {
FOR(i, N - 1) { dat[tree.e_to_v(i)] = f(i); }
} else {
FOR(i, N) { dat[i] = f(i); }
}
pow.resize(N + 1), ipow.resize(N + 1);
pow[0] = 1, pow[1] = base;
ipow[0] = 1, ipow[1] = base.inverse();
FOR(i, 2, N + 1) pow[i] = pow[i - 1] * pow[1];
FOR(i, 2, N + 1) ipow[i] = ipow[i - 1] * ipow[1];
int root = tree.V[0];
dp1.resize(N), dp2.resize(N);
dp1[root] = dp2[root] = dat[0];
FOR(i, 1, N) {
int v = tree.V[i];
int d = tree.depth[v], p = tree.parent[v];
dp1[v] = base * dp1[p] + dat[v];
dp2[v] = dp2[p] + pow[d] * dat[v];
}
}
mint get(int a, int b) {
int c = tree.lca(a, b);
mint x1 = get_du(a, c), x2 = get_ud(c, b);
int n2 = tree.depth[b] - tree.depth[c];
if constexpr (!EDGE) { x1 = x1 * base + dat[c]; }
return x1 * pow[n2] + x2;
}
int lcp(int s1, int t1, int s2, int t2) {
return lcp_and_comp(s1, t1, s2, t2).fi;
}
// <=>
char comp(int s1, int t1, int s2, int t2) {
return lcp_and_comp(s1, t1, s2, t2).se;
}
pair<int, char> lcp_and_comp(int s1, int t1, int s2, int t2) {
int lcp = 0;
// heavy path の頂点列
auto path1 = tree.get_path_decomposition(s1, t1, EDGE);
auto path2 = tree.get_path_decomposition(s2, t2, EDGE);
reverse(all(path1));
reverse(all(path2));
while (len(path1) && len(path2)) {
int a, b, c, d;
tie(a, b) = POP(path1), tie(c, d) = POP(path2);
ll n1 = abs(a - b) + 1, n2 = abs(c - d) + 1;
ll n = min(n1, n2);
if (n < n1) {
if (a <= b) { path1.eb(a + n, b), b = a + n - 1; }
if (a > b) { path1.eb(a - n, b), b = a - n + 1; }
}
if (n < n2) {
if (c <= d) { path2.eb(c + n, d), d = c + n - 1; }
if (c > d) { path2.eb(c - n, d), d = c - n + 1; }
}
mint x1 = from_hld_pair(a, b), x2 = from_hld_pair(c, d);
if (x1 == x2) {
lcp += n;
continue;
}
auto check = [&](ll n) -> bool {
if (n == 0) return 1;
mint x1 = (a <= b ? from_hld_pair(a, a + n - 1)
: from_hld_pair(a, a - n + 1));
mint x2 = (c <= d ? from_hld_pair(c, c + n - 1)
: from_hld_pair(c, c - n + 1));
return x1 == x2;
};
ll k = binary_search(check, 0, n);
lcp += k;
a = (a <= b ? a + k : a - k);
c = (c <= d ? c + k : c - k);
a = tree.V[a], c = tree.V[c];
if (dat[a] < dat[c]) return {lcp, '<'};
if (dat[a] == dat[c]) return {lcp, '='};
if (dat[a] > dat[c]) return {lcp, '>'};
}
if (!path1.empty()) return {lcp, '>'};
if (!path2.empty()) return {lcp, '<'};
return {lcp, '='};
}
private:
mint get_ud(int a, int b) {
return (a == -1 ? dp1[b]
: dp1[b] - dp1[a] * pow[tree.depth[b] - tree.depth[a]]);
}
mint get_du(int a, int b) {
return (b == -1 ? dp2[a] : (dp2[a] - dp2[b]) * ipow[tree.depth[b] + 1]);
}
mint from_hld_pair(int a, int b) {
if (a <= b) { return get_ud(tree.parent[tree.V[a]], tree.V[b]); }
return get_du(tree.V[a], tree.parent[tree.V[b]]);
}
};
#line 2 "random/base.hpp"
u64 RNG_64() {
static u64 x_ = u64(chrono::duration_cast<chrono::nanoseconds>(chrono::high_resolution_clock::now().time_since_epoch()).count()) * 10150724397891781847ULL;
x_ ^= x_ << 7;
return x_ ^= x_ >> 9;
}
u64 RNG(u64 lim) { return RNG_64() % lim; }
ll RNG(ll l, ll r) { return l + RNG_64() % (r - l); }
#line 2 "graph/tree.hpp"
#line 2 "ds/hashmap.hpp"
// u64 -> Val
template <typename Val>
struct HashMap {
// n は入れたいものの個数で ok
HashMap(u32 n = 0) { build(n); }
void build(u32 n) {
u32 k = 8;
while (k < n * 2) k *= 2;
cap = k / 2, mask = k - 1;
key.resize(k), val.resize(k), used.assign(k, 0);
}
// size を保ったまま. size=0 にするときは build すること.
void clear() {
used.assign(len(used), 0);
cap = (mask + 1) / 2;
}
int size() { return len(used) / 2 - cap; }
int index(const u64& k) {
int i = 0;
for (i = hash(k); used[i] && key[i] != k; i = (i + 1) & mask) {}
return i;
}
Val& operator[](const u64& k) {
if (cap == 0) extend();
int i = index(k);
if (!used[i]) { used[i] = 1, key[i] = k, val[i] = Val{}, --cap; }
return val[i];
}
Val get(const u64& k, Val default_value) {
int i = index(k);
return (used[i] ? val[i] : default_value);
}
bool count(const u64& k) {
int i = index(k);
return used[i] && key[i] == k;
}
// f(key, val)
template <typename F>
void enumerate_all(F f) {
FOR(i, len(used)) if (used[i]) f(key[i], val[i]);
}
private:
u32 cap, mask;
vc<u64> key;
vc<Val> val;
vc<bool> used;
u64 hash(u64 x) {
static const u64 FIXED_RANDOM = std::chrono::steady_clock::now().time_since_epoch().count();
x += FIXED_RANDOM;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return (x ^ (x >> 31)) & mask;
}
void extend() {
vc<pair<u64, Val>> dat;
dat.reserve(len(used) / 2 - cap);
FOR(i, len(used)) {
if (used[i]) dat.eb(key[i], val[i]);
}
build(2 * len(dat));
for (auto& [a, b]: dat) (*this)[a] = b;
}
};
#line 3 "graph/base.hpp"
template <typename T>
struct Edge {
int frm, to;
T cost;
int id;
};
template <typename T = int, bool directed = false>
struct Graph {
static constexpr bool is_directed = directed;
int N, M;
using cost_type = T;
using edge_type = Edge<T>;
vector<edge_type> edges;
vector<int> indptr;
vector<edge_type> csr_edges;
vc<int> vc_deg, vc_indeg, vc_outdeg;
bool prepared;
class OutgoingEdges {
public:
OutgoingEdges(const Graph* G, int l, int r) : G(G), l(l), r(r) {}
const edge_type* begin() const {
if (l == r) { return 0; }
return &G->csr_edges[l];
}
const edge_type* end() const {
if (l == r) { return 0; }
return &G->csr_edges[r];
}
private:
const Graph* G;
int l, r;
};
bool is_prepared() { return prepared; }
Graph() : N(0), M(0), prepared(0) {}
Graph(int N) : N(N), M(0), prepared(0) {}
void build(int n) {
N = n, M = 0;
prepared = 0;
edges.clear();
indptr.clear();
csr_edges.clear();
vc_deg.clear();
vc_indeg.clear();
vc_outdeg.clear();
}
void add(int frm, int to, T cost = 1, int i = -1) {
assert(!prepared);
assert(0 <= frm && 0 <= to && to < N);
if (i == -1) i = M;
auto e = edge_type({frm, to, cost, i});
edges.eb(e);
++M;
}
#ifdef FASTIO
// wt, off
void read_tree(bool wt = false, int off = 1) { read_graph(N - 1, wt, off); }
void read_graph(int M, bool wt = false, int off = 1) {
for (int m = 0; m < M; ++m) {
INT(a, b);
a -= off, b -= off;
if (!wt) {
add(a, b);
} else {
T c;
read(c);
add(a, b, c);
}
}
build();
}
#endif
void build() {
assert(!prepared);
prepared = true;
indptr.assign(N + 1, 0);
for (auto&& e: edges) {
indptr[e.frm + 1]++;
if (!directed) indptr[e.to + 1]++;
}
for (int v = 0; v < N; ++v) { indptr[v + 1] += indptr[v]; }
auto counter = indptr;
csr_edges.resize(indptr.back() + 1);
for (auto&& e: edges) {
csr_edges[counter[e.frm]++] = e;
if (!directed) csr_edges[counter[e.to]++] = edge_type({e.to, e.frm, e.cost, e.id});
}
}
OutgoingEdges operator[](int v) const {
assert(prepared);
return {this, indptr[v], indptr[v + 1]};
}
vc<int> deg_array() {
if (vc_deg.empty()) calc_deg();
return vc_deg;
}
pair<vc<int>, vc<int>> deg_array_inout() {
if (vc_indeg.empty()) calc_deg_inout();
return {vc_indeg, vc_outdeg};
}
int deg(int v) {
if (vc_deg.empty()) calc_deg();
return vc_deg[v];
}
int in_deg(int v) {
if (vc_indeg.empty()) calc_deg_inout();
return vc_indeg[v];
}
int out_deg(int v) {
if (vc_outdeg.empty()) calc_deg_inout();
return vc_outdeg[v];
}
#ifdef FASTIO
void debug() {
#ifdef LOCAL
print("Graph");
if (!prepared) {
print("frm to cost id");
for (auto&& e: edges) print(e.frm, e.to, e.cost, e.id);
} else {
print("indptr", indptr);
print("frm to cost id");
FOR(v, N) for (auto&& e: (*this)[v]) print(e.frm, e.to, e.cost, e.id);
}
#endif
}
#endif
vc<int> new_idx;
vc<bool> used_e;
// G における頂点 V[i] が、新しいグラフで i になるようにする
// {G, es}
// sum(deg(v)) の計算量になっていて、
// 新しいグラフの n+m より大きい可能性があるので注意
Graph<T, directed> rearrange(vc<int> V, bool keep_eid = 0) {
if (len(new_idx) != N) new_idx.assign(N, -1);
int n = len(V);
FOR(i, n) new_idx[V[i]] = i;
Graph<T, directed> G(n);
vc<int> history;
FOR(i, n) {
for (auto&& e: (*this)[V[i]]) {
if (len(used_e) <= e.id) used_e.resize(e.id + 1);
if (used_e[e.id]) continue;
int a = e.frm, b = e.to;
if (new_idx[a] != -1 && new_idx[b] != -1) {
history.eb(e.id);
used_e[e.id] = 1;
int eid = (keep_eid ? e.id : -1);
G.add(new_idx[a], new_idx[b], e.cost, eid);
}
}
}
FOR(i, n) new_idx[V[i]] = -1;
for (auto&& eid: history) used_e[eid] = 0;
G.build();
return G;
}
Graph<T, true> to_directed_tree(int root = -1) {
if (root == -1) root = 0;
assert(!is_directed && prepared && M == N - 1);
Graph<T, true> G1(N);
vc<int> par(N, -1);
auto dfs = [&](auto& dfs, int v) -> void {
for (auto& e: (*this)[v]) {
if (e.to == par[v]) continue;
par[e.to] = v, dfs(dfs, e.to);
}
};
dfs(dfs, root);
for (auto& e: edges) {
int a = e.frm, b = e.to;
if (par[a] == b) swap(a, b);
assert(par[b] == a);
G1.add(a, b, e.cost);
}
G1.build();
return G1;
}
HashMap<int> MP_FOR_EID;
int get_eid(u64 a, u64 b) {
if (len(MP_FOR_EID) == 0) {
MP_FOR_EID.build(N - 1);
for (auto& e: edges) {
u64 a = e.frm, b = e.to;
u64 k = to_eid_key(a, b);
MP_FOR_EID[k] = e.id;
}
}
return MP_FOR_EID.get(to_eid_key(a, b), -1);
}
u64 to_eid_key(u64 a, u64 b) {
if (!directed && a > b) swap(a, b);
return N * a + b;
}
private:
void calc_deg() {
assert(vc_deg.empty());
vc_deg.resize(N);
for (auto&& e: edges) vc_deg[e.frm]++, vc_deg[e.to]++;
}
void calc_deg_inout() {
assert(vc_indeg.empty());
vc_indeg.resize(N);
vc_outdeg.resize(N);
for (auto&& e: edges) { vc_indeg[e.to]++, vc_outdeg[e.frm]++; }
}
};
#line 4 "graph/tree.hpp"
// HLD euler tour をとっていろいろ。
template <typename GT>
struct Tree {
using Graph_type = GT;
GT &G;
using WT = typename GT::cost_type;
int N;
vector<int> LID, RID, head, V, parent, VtoE;
vc<int> depth;
vc<WT> depth_weighted;
Tree(GT &G, int r = 0, bool hld = 1) : G(G) { build(r, hld); }
void build(int r = 0, bool hld = 1) {
if (r == -1) return; // build を遅延したいとき
N = G.N;
LID.assign(N, -1), RID.assign(N, -1), head.assign(N, r);
V.assign(N, -1), parent.assign(N, -1), VtoE.assign(N, -1);
depth.assign(N, -1), depth_weighted.assign(N, 0);
assert(G.is_prepared());
int t1 = 0;
dfs_sz(r, -1, hld);
dfs_hld(r, t1);
}
void dfs_sz(int v, int p, bool hld) {
auto &sz = RID;
parent[v] = p;
depth[v] = (p == -1 ? 0 : depth[p] + 1);
sz[v] = 1;
int l = G.indptr[v], r = G.indptr[v + 1];
auto &csr = G.csr_edges;
// 使う辺があれば先頭にする
for (int i = r - 2; i >= l; --i) {
if (hld && depth[csr[i + 1].to] == -1) swap(csr[i], csr[i + 1]);
}
int hld_sz = 0;
for (int i = l; i < r; ++i) {
auto e = csr[i];
if (depth[e.to] != -1) continue;
depth_weighted[e.to] = depth_weighted[v] + e.cost;
VtoE[e.to] = e.id;
dfs_sz(e.to, v, hld);
sz[v] += sz[e.to];
if (hld && chmax(hld_sz, sz[e.to]) && l < i) { swap(csr[l], csr[i]); }
}
}
void dfs_hld(int v, int ×) {
LID[v] = times++;
RID[v] += LID[v];
V[LID[v]] = v;
bool heavy = true;
for (auto &&e: G[v]) {
if (depth[e.to] <= depth[v]) continue;
head[e.to] = (heavy ? head[v] : e.to);
heavy = false;
dfs_hld(e.to, times);
}
}
vc<int> heavy_path_at(int v) {
vc<int> P = {v};
while (1) {
int a = P.back();
for (auto &&e: G[a]) {
if (e.to != parent[a] && head[e.to] == v) {
P.eb(e.to);
break;
}
}
if (P.back() == a) break;
}
return P;
}
int heavy_child(int v) {
int k = LID[v] + 1;
if (k == N) return -1;
int w = V[k];
return (parent[w] == v ? w : -1);
}
vc<int> memo_tail;
int tail(int v) {
if (memo_tail.empty()) {
memo_tail.assign(N, -1);
FOR_R(i, N) {
int v = V[i];
int w = heavy_child(v);
memo_tail[v] = (w == -1 ? v : memo_tail[w]);
}
}
return memo_tail[v];
}
int e_to_v(int eid) {
auto e = G.edges[eid];
return (parent[e.frm] == e.to ? e.frm : e.to);
}
int v_to_e(int v) { return VtoE[v]; }
int get_eid(int u, int v) {
if (parent[u] != v) swap(u, v);
assert(parent[u] == v);
return VtoE[u];
}
int ELID(int v) { return 2 * LID[v] - depth[v]; }
int ERID(int v) { return 2 * RID[v] - depth[v] - 1; }
// 目標地点へ進む個数が k
int LA(int v, int k) {
assert(k <= depth[v]);
while (1) {
int u = head[v];
if (LID[v] - k >= LID[u]) return V[LID[v] - k];
k -= LID[v] - LID[u] + 1;
v = parent[u];
}
}
int la(int u, int v) { return LA(u, v); }
int LCA(int u, int v) {
for (;; v = parent[head[v]]) {
if (LID[u] > LID[v]) swap(u, v);
if (head[u] == head[v]) return u;
}
}
int meet(int a, int b, int c) { return LCA(a, b) ^ LCA(a, c) ^ LCA(b, c); }
int lca(int u, int v) { return LCA(u, v); }
int subtree_size(int v, int root = -1) {
if (root == -1) return RID[v] - LID[v];
if (v == root) return N;
int x = jump(v, root, 1);
if (in_subtree(v, x)) return RID[v] - LID[v];
return N - RID[x] + LID[x];
}
int dist(int a, int b) {
int c = LCA(a, b);
return depth[a] + depth[b] - 2 * depth[c];
}
WT dist_weighted(int a, int b) {
int c = LCA(a, b);
return depth_weighted[a] + depth_weighted[b] - WT(2) * depth_weighted[c];
}
// a is in b
bool in_subtree(int a, int b) { return LID[b] <= LID[a] && LID[a] < RID[b]; }
int jump(int a, int b, ll k) {
if (k == 1) {
if (a == b) return -1;
return (in_subtree(b, a) ? LA(b, depth[b] - depth[a] - 1) : parent[a]);
}
int c = LCA(a, b);
int d_ac = depth[a] - depth[c];
int d_bc = depth[b] - depth[c];
if (k > d_ac + d_bc) return -1;
if (k <= d_ac) return LA(a, k);
return LA(b, d_ac + d_bc - k);
}
vc<int> collect_child(int v) {
vc<int> res;
for (auto &&e: G[v])
if (e.to != parent[v]) res.eb(e.to);
return res;
}
vc<int> collect_subtree(int v) { return {V.begin() + LID[v], V.begin() + RID[v]}; }
vc<int> collect_light(int v) {
vc<int> res;
bool skip = true;
for (auto &&e: G[v])
if (e.to != parent[v]) {
if (!skip) res.eb(e.to);
skip = false;
}
return res;
}
vc<pair<int, int>> get_path_decomposition(int u, int v, bool edge) {
// [始点, 終点] の"閉"区間列。
vc<pair<int, int>> up, down;
while (1) {
if (head[u] == head[v]) break;
if (LID[u] < LID[v]) {
down.eb(LID[head[v]], LID[v]);
v = parent[head[v]];
} else {
up.eb(LID[u], LID[head[u]]);
u = parent[head[u]];
}
}
if (LID[u] < LID[v]) down.eb(LID[u] + edge, LID[v]);
elif (LID[v] + edge <= LID[u]) up.eb(LID[u], LID[v] + edge);
reverse(all(down));
up.insert(up.end(), all(down));
return up;
}
// 辺の列の情報 (frm,to,str)
// str = "heavy_up", "heavy_down", "light_up", "light_down"
vc<tuple<int, int, string>> get_path_decomposition_detail(int u, int v) {
vc<tuple<int, int, string>> up, down;
while (1) {
if (head[u] == head[v]) break;
if (LID[u] < LID[v]) {
if (v != head[v]) down.eb(head[v], v, "heavy_down"), v = head[v];
down.eb(parent[v], v, "light_down"), v = parent[v];
} else {
if (u != head[u]) up.eb(u, head[u], "heavy_up"), u = head[u];
up.eb(u, parent[u], "light_up"), u = parent[u];
}
}
if (LID[u] < LID[v]) down.eb(u, v, "heavy_down");
elif (LID[v] < LID[u]) up.eb(u, v, "heavy_up");
reverse(all(down));
concat(up, down);
return up;
}
vc<int> restore_path(int u, int v) {
vc<int> P;
for (auto &&[a, b]: get_path_decomposition(u, v, 0)) {
if (a <= b) {
FOR(i, a, b + 1) P.eb(V[i]);
} else {
FOR_R(i, b, a + 1) P.eb(V[i]);
}
}
return P;
}
// path [a,b] と [c,d] の交わり. 空ならば {-1,-1}.
// https://codeforces.com/problemset/problem/500/G
pair<int, int> path_intersection(int a, int b, int c, int d) {
int ab = lca(a, b), ac = lca(a, c), ad = lca(a, d);
int bc = lca(b, c), bd = lca(b, d), cd = lca(c, d);
int x = ab ^ ac ^ bc, y = ab ^ ad ^ bd; // meet(a,b,c), meet(a,b,d)
if (x != y) return {x, y};
int z = ac ^ ad ^ cd;
if (x != z) x = -1;
return {x, x};
}
// uv path 上で check(v) を満たす最後の v
// なければ (つまり check(v) が ng )-1
template <class F>
int max_path(F check, int u, int v) {
if (!check(u)) return -1;
auto pd = get_path_decomposition(u, v, false);
for (auto [a, b]: pd) {
if (!check(V[a])) return u;
if (check(V[b])) {
u = V[b];
continue;
}
int c = binary_search([&](int c) -> bool { return check(V[c]); }, a, b, 0);
return V[c];
}
return u;
}
};
#line 2 "mod/modint61.hpp"
struct modint61 {
static constexpr u64 mod = (1ULL << 61) - 1;
u64 val;
constexpr modint61() : val(0ULL) {}
constexpr modint61(u32 x) : val(x) {}
constexpr modint61(u64 x) : val(x % mod) {}
constexpr modint61(int x) : val((x < 0) ? (x + static_cast<ll>(mod)) : x) {}
constexpr modint61(ll x) : val(((x %= static_cast<ll>(mod)) < 0) ? (x + static_cast<ll>(mod)) : x) {}
static constexpr u64 get_mod() { return mod; }
modint61 &operator+=(const modint61 &a) {
val = ((val += a.val) >= mod) ? (val - mod) : val;
return *this;
}
modint61 &operator-=(const modint61 &a) {
val = ((val -= a.val) >= mod) ? (val + mod) : val;
return *this;
}
modint61 &operator*=(const modint61 &a) {
const unsigned __int128 y = static_cast<unsigned __int128>(val) * a.val;
val = (y >> 61) + (y & mod);
val = (val >= mod) ? (val - mod) : val;
return *this;
}
modint61 operator-() const { return modint61(val ? mod - val : u64(0)); }
modint61 &operator/=(const modint61 &a) { return (*this *= a.inverse()); }
modint61 operator+(const modint61 &p) const { return modint61(*this) += p; }
modint61 operator-(const modint61 &p) const { return modint61(*this) -= p; }
modint61 operator*(const modint61 &p) const { return modint61(*this) *= p; }
modint61 operator/(const modint61 &p) const { return modint61(*this) /= p; }
bool operator<(const modint61 &other) const { return val < other.val; }
bool operator==(const modint61 &p) const { return val == p.val; }
bool operator!=(const modint61 &p) const { return val != p.val; }
modint61 inverse() const {
ll a = val, b = mod, u = 1, v = 0, t;
while (b > 0) {
t = a / b;
swap(a -= t * b, b), swap(u -= t * v, v);
}
return modint61(u);
}
modint61 pow(ll n) const {
assert(n >= 0);
modint61 ret(1), mul(val);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul, n >>= 1;
}
return ret;
}
};
#ifdef FASTIO
void rd(modint61 &x) {
fastio::rd(x.val);
assert(0 <= x.val && x.val < modint61::mod);
}
void wt(modint61 x) { fastio::wt(x.val); }
#endif
#line 4 "graph/ds/rolling_hash_on_tree.hpp"
// 木の辺に文字がちょうどひとつ書いてある (static)
template <typename TREE, bool EDGE>
struct Rolling_Hash_On_Tree {
using mint = modint61;
TREE& tree;
int N;
mint base;
// edge に文字があると思って
// dp1: [root,v]
// dp2: [v,root]
vc<int> dat;
vc<mint> dp1, dp2;
vc<mint> pow, ipow;
template <typename F>
Rolling_Hash_On_Tree(TREE& tree, F f, mint base_ = 0)
: tree(tree), N(tree.N), base(base_) {
if (base == mint(0)) base = RNG(mint::get_mod());
build(f);
}
template <typename F>
void build(F f) {
dat.resize(N);
if constexpr (EDGE) {
FOR(i, N - 1) { dat[tree.e_to_v(i)] = f(i); }
} else {
FOR(i, N) { dat[i] = f(i); }
}
pow.resize(N + 1), ipow.resize(N + 1);
pow[0] = 1, pow[1] = base;
ipow[0] = 1, ipow[1] = base.inverse();
FOR(i, 2, N + 1) pow[i] = pow[i - 1] * pow[1];
FOR(i, 2, N + 1) ipow[i] = ipow[i - 1] * ipow[1];
int root = tree.V[0];
dp1.resize(N), dp2.resize(N);
dp1[root] = dp2[root] = dat[0];
FOR(i, 1, N) {
int v = tree.V[i];
int d = tree.depth[v], p = tree.parent[v];
dp1[v] = base * dp1[p] + dat[v];
dp2[v] = dp2[p] + pow[d] * dat[v];
}
}
mint get(int a, int b) {
int c = tree.lca(a, b);
mint x1 = get_du(a, c), x2 = get_ud(c, b);
int n2 = tree.depth[b] - tree.depth[c];
if constexpr (!EDGE) { x1 = x1 * base + dat[c]; }
return x1 * pow[n2] + x2;
}
int lcp(int s1, int t1, int s2, int t2) {
return lcp_and_comp(s1, t1, s2, t2).fi;
}
// <=>
char comp(int s1, int t1, int s2, int t2) {
return lcp_and_comp(s1, t1, s2, t2).se;
}
pair<int, char> lcp_and_comp(int s1, int t1, int s2, int t2) {
int lcp = 0;
// heavy path の頂点列
auto path1 = tree.get_path_decomposition(s1, t1, EDGE);
auto path2 = tree.get_path_decomposition(s2, t2, EDGE);
reverse(all(path1));
reverse(all(path2));
while (len(path1) && len(path2)) {
int a, b, c, d;
tie(a, b) = POP(path1), tie(c, d) = POP(path2);
ll n1 = abs(a - b) + 1, n2 = abs(c - d) + 1;
ll n = min(n1, n2);
if (n < n1) {
if (a <= b) { path1.eb(a + n, b), b = a + n - 1; }
if (a > b) { path1.eb(a - n, b), b = a - n + 1; }
}
if (n < n2) {
if (c <= d) { path2.eb(c + n, d), d = c + n - 1; }
if (c > d) { path2.eb(c - n, d), d = c - n + 1; }
}
mint x1 = from_hld_pair(a, b), x2 = from_hld_pair(c, d);
if (x1 == x2) {
lcp += n;
continue;
}
auto check = [&](ll n) -> bool {
if (n == 0) return 1;
mint x1 = (a <= b ? from_hld_pair(a, a + n - 1)
: from_hld_pair(a, a - n + 1));
mint x2 = (c <= d ? from_hld_pair(c, c + n - 1)
: from_hld_pair(c, c - n + 1));
return x1 == x2;
};
ll k = binary_search(check, 0, n);
lcp += k;
a = (a <= b ? a + k : a - k);
c = (c <= d ? c + k : c - k);
a = tree.V[a], c = tree.V[c];
if (dat[a] < dat[c]) return {lcp, '<'};
if (dat[a] == dat[c]) return {lcp, '='};
if (dat[a] > dat[c]) return {lcp, '>'};
}
if (!path1.empty()) return {lcp, '>'};
if (!path2.empty()) return {lcp, '<'};
return {lcp, '='};
}
private:
mint get_ud(int a, int b) {
return (a == -1 ? dp1[b]
: dp1[b] - dp1[a] * pow[tree.depth[b] - tree.depth[a]]);
}
mint get_du(int a, int b) {
return (b == -1 ? dp2[a] : (dp2[a] - dp2[b]) * ipow[tree.depth[b] + 1]);
}
mint from_hld_pair(int a, int b) {
if (a <= b) { return get_ud(tree.parent[tree.V[a]], tree.V[b]); }
return get_du(tree.V[a], tree.parent[tree.V[b]]);
}
};