/tmp/solutions/build/vertex_set_path_composite-slow.cpp:
    1|       |#include <common.h>
    2|       |#include <toy/bit.h>
    3|       |prelude;
    4|       |
    5|       |namespace {
    6|       |
    7|       |constexpr int N = 2e5;
    8|       |constexpr int P = 998244353;
    9|       |
   10|       |struct Node {
   11|       |  u32 a, b, c;
   12|  1.00M|  auto operator+(const Node &t) const -> Node {
   13|  1.00M|    u32 x = u64(a) * t.a % P;
   14|  1.00M|    u32 y = (u64(a) * t.b + b) % P;
   15|  1.00M|    u32 z = (u64(t.a) * c + t.c) % P;
   16|  1.00M|    return {x, y, z};
   17|  1.00M|  }
   18|       |} node[N * 2];
   19|   384k|auto operator+(const Node &l, u32 r) -> u32 { return (u64(l.a) * r + l.b) % P; }
   20|   394k|auto operator+(u32 l, const Node &r) -> u32 { return (u64(r.a) * l + r.c) % P; }
   21|       |u32 a[N];
   22|       |u32 b[N];
   23|       |int head[N];
   24|       |int size[N];
   25|       |int depth[N];
   26|       |int heavy[N];
   27|       |int ances[N];
   28|       |int parent[N];
   29|       |int node2id[N];
   30|       |int id;
   31|       |struct {
   32|       |  int to;
   33|       |  int next;
   34|       |} edge[N * 2];
   35|       |
   36|  53.3k|def build_step_1(int u, int p) -> void {
   37|  53.3k|  size[u] = 1;
   38|   160k|  for (int e = head[u]; e; e = edge[e].next) {
                                         ^106k
  ------------------
  |  Branch (38:25): [True: 66.67%, False: 33.33%]
  ------------------
   39|   106k|    int v = edge[e].to;
   40|   106k|    if (v != p) {
  ------------------
  |  Branch (40:9): [True: 50.00%, False: 50.00%]
  ------------------
   41|  53.3k|      build_step_1(v, u);
   42|  53.3k|      size[u] += size[v];
   43|  53.3k|      if (heavy[u] == 0 || size[v] > size[heavy[u]]) {
                                         ^26.6k
  ------------------
  |  Branch (43:11): [True: 49.99%, False: 50.01%]
  |  Branch (43:28): [True: 46.69%, False: 53.31%]
  ------------------
   44|  39.1k|        heavy[u] = v;
   45|  39.1k|      }
   46|  53.3k|    }
   47|   106k|  }
   48|  53.3k|}
   49|       |
   50|  53.3k|def build_step_2(int u, int w, int p, int d) -> void {
   51|  53.3k|  int i = id++;
   52|  53.3k|  node2id[u] = i;
   53|  53.3k|  node[i] = {a[u], b[u], b[u]};
   54|  53.3k|  depth[i] = d;
   55|  53.3k|  ances[i] = node2id[w];
   56|  53.3k|  parent[i] = node2id[p];
   57|  53.3k|  if (int v = heavy[u]; v) {
  ------------------
  |  Branch (57:25): [True: 49.99%, False: 50.01%]
  ------------------
   58|  26.6k|    build_step_2(v, w, u, d + 1);
   59|  26.6k|  }
   60|   160k|  for (int e = head[u]; e; e = edge[e].next) {
                                         ^106k
  ------------------
  |  Branch (60:25): [True: 66.67%, False: 33.33%]
  ------------------
   61|   106k|    int v = edge[e].to;
   62|   106k|    if (v != p && v != heavy[u]) {
                                ^53.3k
  ------------------
  |  Branch (62:9): [True: 50.00%, False: 50.00%]
  |  Branch (62:19): [True: 50.01%, False: 49.99%]
  ------------------
   63|  26.6k|      build_step_2(v, v, u, d + 1);
   64|  26.6k|    }
   65|   106k|  }
   66|  53.3k|}
   67|       |
   68|       |} // namespace
   69|       |
   70|      1|int main() {
   71|      1|  rd rd;
   72|      1|  wt wt;
   73|      1|  int n = rd.uh();
   74|      1|  int q = rd.uh();
   75|      1|#ifdef LOCAL
   76|      1|  id = 0;
   77|      1|  std::memset(head, 0, 4 * n);
   78|      1|  std::memset(heavy, 0, 4 * n);
   79|      1|#endif
   80|  53.3k|  for (int i = 0; i < n; ++i) a[i] = rd.uw(), b[i] = rd.uw();
                                       ^53.3k^53.3k
  ------------------
  |  Branch (80:19): [True: 100.00%, False: 0.00%]
  ------------------
   81|  53.3k|  for (int i = 1; i < n; ++i) {
                                       ^53.3k
  ------------------
  |  Branch (81:19): [True: 100.00%, False: 0.00%]
  ------------------
   82|  53.3k|    int u = rd.uh();
   83|  53.3k|    int v = rd.uh();
   84|  53.3k|    edge[i * 2 | 0] = {v, head[u]}, head[u] = i * 2 | 0;
   85|  53.3k|    edge[i * 2 | 1] = {u, head[v]}, head[v] = i * 2 | 1;
   86|  53.3k|  }
   87|      1|  build_step_1(0, 0);
   88|      1|  build_step_2(0, 0, 0, 0);
   89|      1|  std::memcpy(node + n, node, sizeof(Node) * n);
   90|  53.3k|  for (int i = n - 1; i > 0; --i) node[i] = node[i * 2] + node[i * 2 + 1];
                                           ^53.3k^53.3k
  ------------------
  |  Branch (90:23): [True: 100.00%, False: 0.00%]
  ------------------
   91|   236k|  let apply_1 = [&](int l, int r, u32 x) -> u32 {
                ^1
   92|   236k|    l += n - 1;
   93|   236k|    r += n + 1;
   94|   236k|    int k = log(l ^ r);
   95|   236k|    int R = r >> k;
   96|   431k|    for (r = r >> __builtin_ctz(r) ^ 1; r > R; r = r >> __builtin_ctz(r) ^ 1)
                                                             ^194k
  ------------------
  |  Branch (96:41): [True: 45.12%, False: 54.88%]
  ------------------
   97|   194k|      x = node[r] + x;
   98|   426k|    for (int t = ~l & ~(-1 << k), i; t > 0; t -= 1 << i) {
                                                          ^189k
  ------------------
  |  Branch (98:38): [True: 44.49%, False: 55.51%]
  ------------------
   99|   189k|      i = log(t);
  100|   189k|      x = node[l >> i ^ 1] + x;
  101|   189k|    }
  102|   236k|    return x;
  103|   236k|  };
  104|   246k|  let apply_2 = [&](int l, int r, u32 x) -> u32 {
                ^1
  105|   246k|    l += n - 1;
  106|   246k|    r += n + 1;
  107|   246k|    int k = log(l ^ r);
  108|   246k|    int R = r >> k;
  109|   444k|    for (l = l >> __builtin_ctz(~l) ^ 1; l > R; l = l >> __builtin_ctz(~l) ^ 1)
                                                              ^197k
  ------------------
  |  Branch (109:42): [True: 44.47%, False: 55.53%]
  ------------------
  110|   197k|      x = x + node[l];
  111|   443k|    for (int t = r & ~(-1 << k), i; t > 0; t -= 1 << i) {
                                                         ^197k
  ------------------
  |  Branch (111:37): [True: 44.38%, False: 55.62%]
  ------------------
  112|   197k|      i = log(t);
  113|   197k|      x = x + node[r >> i ^ 1];
  114|   197k|    }
  115|   246k|    return x;
  116|   246k|  };
  117|   120k|  while (q--) {
  ------------------
  |  Branch (117:10): [True: 100.00%, False: 0.00%]
  ------------------
  118|   120k|    let t = rd.u1();
  119|   120k|    if (t == 0) {
  ------------------
  |  Branch (119:9): [True: 50.22%, False: 49.78%]
  ------------------
  120|  60.3k|      int k = n + node2id[rd.uh()];
  121|  60.3k|      u32 c = rd.uw();
  122|  60.3k|      u32 d = rd.uw();
  123|  60.3k|      node[k] = {c, d, d};
  124|  1.01M|      for (k /= 2; k > 0; k /= 2) {
                                        ^952k
  ------------------
  |  Branch (124:20): [True: 94.04%, False: 5.96%]
  ------------------
  125|   952k|        node[k] = node[k * 2] + node[k * 2 + 1];
  126|   952k|      }
  127|  60.3k|    }
  128|   120k|    if (t == 1) {
  ------------------
  |  Branch (128:9): [True: 49.78%, False: 50.22%]
  ------------------
  129|  59.8k|      int u = node2id[rd.uh()];
  130|  59.8k|      int v = node2id[rd.uh()];
  131|  59.8k|      u32 x = rd.uw();
  132|  59.8k|      std::pair<int, int> vec[20];
  133|  59.8k|      int c = 0;
  134|   483k|      while (ances[u] != ances[v]) {
  ------------------
  |  Branch (134:14): [True: 87.63%, False: 12.37%]
  ------------------
  135|   424k|        if (depth[ances[u]] > depth[ances[v]]) {
  ------------------
  |  Branch (135:13): [True: 50.00%, False: 50.00%]
  ------------------
  136|   212k|          x = apply_1(ances[u], u, x);
  137|   212k|          u = parent[ances[u]];
  138|   212k|        } else {
  139|   211k|          vec[++c] = {ances[v], v};
  140|   211k|          v = parent[ances[v]];
  141|   211k|        }
  142|   424k|      }
  143|  59.8k|      if (u > v) {
  ------------------
  |  Branch (143:11): [True: 41.61%, False: 58.39%]
  ------------------
  144|  24.8k|        x = apply_1(v, u, x);
  145|  34.9k|      } else {
  146|  34.9k|        x = apply_2(u, v, x);
  147|  34.9k|      }
  148|   271k|      for (; c > 0; --c) {
                                  ^211k
  ------------------
  |  Branch (148:14): [True: 77.99%, False: 22.01%]
  ------------------
  149|   211k|        def[l, r] = vec[c];
  150|   211k|        x = apply_2(l, r, x);
  151|   211k|      }
  152|  59.8k|      wt.uw(x);
  153|  59.8k|    }
  154|   120k|  }
  155|      1|  return 0;
  156|      1|}