/tmp/solutions/build/vertex_set_path_composite-logn.cpp:
    1|       |#include <common.h>
    2|       |#include <toy/bit.h>
    3|       |prelude;
    4|       |
    5|       |namespace {
    6|       |
    7|       |constexpr int N = 200001;
    8|       |constexpr int P = 998244353;
    9|       |
   10|       |struct Vertex {
   11|       |  u32 a, b;
   12|       |};
   13|       |struct Segment {
   14|       |  u32 a, b, c;
   15|       |  Segment() = default;
   16|  1.86k|  Segment(Vertex v) : a{v.a}, b{v.b}, c{v.b} {}
   17|  5.47k|  Segment(u32 a, u32 b, u32 c) : a{a}, b{b}, c{c} {}
   18|       |};
   19|       |struct Node {
   20|       |  Vertex v;
   21|       |  Segment s, t;
   22|       |  int l, r, p;
   23|       |} node[N];
   24|  4.61k|auto operator+(const Segment &l, const Segment &r) -> Segment {
   25|  4.61k|  u32 x = u64(l.a) * r.a % P;
   26|  4.61k|  u32 y = (u64(l.a) * r.b + l.b) % P;
   27|  4.61k|  u32 z = (u64(r.a) * l.c + r.c) % P;
   28|  4.61k|  return {x, y, z};
   29|  4.61k|}
   30|  1.88k|auto operator+(const Segment &l, u32 r) -> u32 {
   31|  1.88k|  return (u64(l.a) * r + l.b) % P;
   32|  1.88k|}
   33|    432|auto operator+(u32 l, const Segment &r) -> u32 {
   34|    432|  return (u64(r.a) * l + r.c) % P;
   35|    432|}
   36|       |u32 a[N];
   37|       |u32 b[N];
   38|       |int head[N];
   39|       |int size[N];
   40|       |int depth[N];
   41|       |int heavy[N];
   42|       |int ances[N];
   43|       |int parent[N];
   44|       |int node2id[N];
   45|       |u8 priority[N];
   46|       |int id;
   47|       |struct {
   48|       |  int to;
   49|       |  int next;
   50|       |} edge[N * 2];
   51|       |
   52|    532|def build_step_1(int u, int p) -> void {
   53|    532|  size[u] = 1;
   54|  1.59k|  for (int e = head[u]; e; e = edge[e].next) {
                                         ^1.06k
  ------------------
  |  Branch (54:25): [True: 66.62%, False: 33.38%]
  ------------------
   55|  1.06k|    int v = edge[e].to;
   56|  1.06k|    if (v != p) {
  ------------------
  |  Branch (56:9): [True: 50.00%, False: 50.00%]
  ------------------
   57|    531|      build_step_1(v, u);
   58|    531|      size[u] += size[v];
   59|    531|      if (heavy[u] == 0 || size[v] > size[heavy[u]]) {
                                         ^254
  ------------------
  |  Branch (59:11): [True: 52.17%, False: 47.83%]
  |  Branch (59:28): [True: 49.61%, False: 50.39%]
  ------------------
   60|    403|        heavy[u] = v;
   61|    403|      }
   62|    531|    }
   63|  1.06k|  }
   64|    532|}
   65|       |
   66|    532|def build_step_2(int u, int w, int p, int d) -> void {
   67|    532|  int i = ++id;
   68|    532|  node2id[u] = i;
   69|    532|  depth[i] = d;
   70|    532|  ances[i] = node2id[w];
   71|    532|  parent[i] = node2id[p];
   72|    532|  node[i].v = {a[u], b[u]};
   73|  1.59k|  for (int e = head[u]; e; e = edge[e].next) {
                                         ^1.06k
  ------------------
  |  Branch (73:25): [True: 66.62%, False: 33.38%]
  ------------------
   74|  1.06k|    int v = edge[e].to;
   75|  1.06k|    if (v != p && v != heavy[u]) {
                                ^531
  ------------------
  |  Branch (75:9): [True: 50.00%, False: 50.00%]
  |  Branch (75:19): [True: 47.83%, False: 52.17%]
  ------------------
   76|    254|      build_step_2(v, v, u, d + 1);
   77|    254|    }
   78|  1.06k|  }
   79|    532|  priority[i] = u8(log(i ^ (id + 1)));
   80|    532|  if (u != w) {
  ------------------
  |  Branch (80:7): [True: 52.07%, False: 47.93%]
  ------------------
   81|    277|    int p = parent[i];
   82|    277|    int l = 0;
   83|    437|    while (p && priority[p] < priority[i]) {
                              ^352
  ------------------
  |  Branch (83:12): [True: 80.55%, False: 19.45%]
  |  Branch (83:17): [True: 45.45%, False: 54.55%]
  ------------------
   84|    160|      l = p;
   85|    160|      p = node[p].p;
   86|    160|    }
   87|    277|    node[p].r = i;
   88|    277|    node[i].p = p;
   89|    277|    node[i].l = l;
   90|    277|    node[l].p = i;
   91|    277|  }
   92|    532|  if (int v = heavy[u]; v) {
  ------------------
  |  Branch (92:25): [True: 52.07%, False: 47.93%]
  ------------------
   93|    277|    build_step_2(v, w, u, d + 1);
   94|    277|  }
   95|    532|}
   96|       |
   97|  1.26k|def maintain(int u) -> void {
   98|  1.26k|  node[u].s = (node[u].t = node[node[u].l].s + node[u].v) + node[node[u].r].s;
   99|  1.26k|}
  100|       |
  101|  1.60k|template <typename T> T apply(int k, T x) {
  102|  4.76k|  for (int u = k; u; u = node[u].p) {
                                   ^3.16k
  ------------------
  |  Branch (102:19): [True: 66.11%, False: 33.89%]
  ------------------
  |  Branch (102:19): [True: 66.60%, False: 33.40%]
  ------------------
  103|  3.16k|    if (u <= k) {
  ------------------
  |  Branch (103:9): [True: 75.57%, False: 24.43%]
  ------------------
  |  Branch (103:9): [True: 75.17%, False: 24.83%]
  ------------------
  104|  2.38k|      x = node[u].t + x;
  105|  2.38k|    }
  106|  3.16k|  }
  107|  1.60k|  return x;
  108|  1.60k|}
  ------------------
  | vertex_set_path_composite-logn.cpp:_ZN12_GLOBAL__N_15applyIjEET_iS1_:
  |  101|    812|template <typename T> T apply(int k, T x) {
  |  102|  2.39k|  for (int u = k; u; u = node[u].p) {
  |                                   ^1.58k
  |  ------------------
  |  |  Branch (102:19): [True: 66.11%, False: 33.89%]
  |  ------------------
  |  103|  1.58k|    if (u <= k) {
  |  ------------------
  |  |  Branch (103:9): [True: 75.57%, False: 24.43%]
  |  ------------------
  |  104|  1.19k|      x = node[u].t + x;
  |  105|  1.19k|    }
  |  106|  1.58k|  }
  |  107|    812|  return x;
  |  108|    812|}
  ------------------
  | vertex_set_path_composite-logn.cpp:_ZN12_GLOBAL__N_15applyINS_7SegmentEEET_iS2_:
  |  101|    792|template <typename T> T apply(int k, T x) {
  |  102|  2.37k|  for (int u = k; u; u = node[u].p) {
  |                                   ^1.57k
  |  ------------------
  |  |  Branch (102:19): [True: 66.60%, False: 33.40%]
  |  ------------------
  |  103|  1.57k|    if (u <= k) {
  |  ------------------
  |  |  Branch (103:9): [True: 75.17%, False: 24.83%]
  |  ------------------
  |  104|  1.18k|      x = node[u].t + x;
  |  105|  1.18k|    }
  |  106|  1.57k|  }
  |  107|    792|  return x;
  |  108|    792|}
  ------------------
  109|       |
  110|    432|template <typename T> T apply(int l, int r, T x) {
  111|    432|  Segment t = {1, 0, 0};
  112|    432|  int u = l;
  113|    432|  int v = r;
  114|  1.06k|  while (u != v) {
  ------------------
  |  Branch (114:10): [True: 53.90%, False: 46.10%]
  ------------------
  |  Branch (114:10): [True: 65.15%, False: 34.85%]
  ------------------
  115|    634|    if (priority[u] < priority[v]) {
  ------------------
  |  Branch (115:9): [True: 28.28%, False: 71.72%]
  ------------------
  |  Branch (115:9): [True: 31.69%, False: 68.31%]
  ------------------
  116|    191|      if (l <= u) {
  ------------------
  |  Branch (116:11): [True: 92.68%, False: 7.32%]
  ------------------
  |  Branch (116:11): [True: 82.57%, False: 17.43%]
  ------------------
  117|    166|        t = (t + node[u].v) + node[node[u].r].s;
  118|    166|      }
  119|    191|      u = node[u].p;
  120|    443|    } else {
  121|    443|      if (v <= r) {
  ------------------
  |  Branch (121:11): [True: 90.38%, False: 9.62%]
  ------------------
  |  Branch (121:11): [True: 84.68%, False: 15.32%]
  ------------------
  122|    387|        x = node[v].t + x;
  123|    387|      }
  124|    443|      v = node[v].p;
  125|    443|    }
  126|    634|  }
  127|    432|  x = t + (node[u].v + x);
  128|    432|  return x;
  129|    432|}
  ------------------
  | vertex_set_path_composite-logn.cpp:_ZN12_GLOBAL__N_15applyIjEET_iiS1_:
  |  110|    248|template <typename T> T apply(int l, int r, T x) {
  |  111|    248|  Segment t = {1, 0, 0};
  |  112|    248|  int u = l;
  |  113|    248|  int v = r;
  |  114|    538|  while (u != v) {
  |  ------------------
  |  |  Branch (114:10): [True: 53.90%, False: 46.10%]
  |  ------------------
  |  115|    290|    if (priority[u] < priority[v]) {
  |  ------------------
  |  |  Branch (115:9): [True: 28.28%, False: 71.72%]
  |  ------------------
  |  116|     82|      if (l <= u) {
  |  ------------------
  |  |  Branch (116:11): [True: 92.68%, False: 7.32%]
  |  ------------------
  |  117|     76|        t = (t + node[u].v) + node[node[u].r].s;
  |  118|     76|      }
  |  119|     82|      u = node[u].p;
  |  120|    208|    } else {
  |  121|    208|      if (v <= r) {
  |  ------------------
  |  |  Branch (121:11): [True: 90.38%, False: 9.62%]
  |  ------------------
  |  122|    188|        x = node[v].t + x;
  |  123|    188|      }
  |  124|    208|      v = node[v].p;
  |  125|    208|    }
  |  126|    290|  }
  |  127|    248|  x = t + (node[u].v + x);
  |  128|    248|  return x;
  |  129|    248|}
  ------------------
  | vertex_set_path_composite-logn.cpp:_ZN12_GLOBAL__N_15applyINS_7SegmentEEET_iiS2_:
  |  110|    184|template <typename T> T apply(int l, int r, T x) {
  |  111|    184|  Segment t = {1, 0, 0};
  |  112|    184|  int u = l;
  |  113|    184|  int v = r;
  |  114|    528|  while (u != v) {
  |  ------------------
  |  |  Branch (114:10): [True: 65.15%, False: 34.85%]
  |  ------------------
  |  115|    344|    if (priority[u] < priority[v]) {
  |  ------------------
  |  |  Branch (115:9): [True: 31.69%, False: 68.31%]
  |  ------------------
  |  116|    109|      if (l <= u) {
  |  ------------------
  |  |  Branch (116:11): [True: 82.57%, False: 17.43%]
  |  ------------------
  |  117|     90|        t = (t + node[u].v) + node[node[u].r].s;
  |  118|     90|      }
  |  119|    109|      u = node[u].p;
  |  120|    235|    } else {
  |  121|    235|      if (v <= r) {
  |  ------------------
  |  |  Branch (121:11): [True: 84.68%, False: 15.32%]
  |  ------------------
  |  122|    199|        x = node[v].t + x;
  |  123|    199|      }
  |  124|    235|      v = node[v].p;
  |  125|    235|    }
  |  126|    344|  }
  |  127|    184|  x = t + (node[u].v + x);
  |  128|    184|  return x;
  |  129|    184|}
  ------------------
  130|       |
  131|       |} // namespace
  132|       |
  133|      1|int main() {
  134|      1|  rd rd;
  135|      1|  wt wt;
  136|      1|  int n = rd.uh();
  137|      1|  int q = rd.uh();
  138|      1|#ifdef LOCAL
  139|      1|  id = 0;
  140|      1|  std::memset(head, 0, 4 * n);
  141|      1|  std::memset(heavy, 0, 4 * n);
  142|      1|  std::memset(node, 0, (n + 1) * sizeof(Node));
  143|      1|#endif
  144|      1|  node[0].s.a = 1;
  145|    533|  for (int i = 0; i < n; ++i) a[i] = rd.uw(), b[i] = rd.uw();
                                       ^532 ^532
  ------------------
  |  Branch (145:19): [True: 99.81%, False: 0.19%]
  ------------------
  146|    532|  for (int i = 1; i < n; ++i) {
                                       ^531
  ------------------
  |  Branch (146:19): [True: 99.81%, False: 0.19%]
  ------------------
  147|    531|    int u = rd.uh();
  148|    531|    int v = rd.uh();
  149|    531|    edge[i * 2 | 0] = {v, head[u]}, head[u] = i * 2 | 0;
  150|    531|    edge[i * 2 | 1] = {u, head[v]}, head[v] = i * 2 | 1;
  151|    531|  }
  152|      1|  build_step_1(0, 0);
  153|      1|  build_step_2(0, 0, 0, 0);
  154|    533|  for (int i = 1; i <= n; ++i) {
                                        ^532
  ------------------
  |  Branch (154:19): [True: 99.81%, False: 0.19%]
  ------------------
  155|    532|    if (node[i].r == 0) {
  ------------------
  |  Branch (155:9): [True: 69.92%, False: 30.08%]
  ------------------
  156|    904|      for (int u = i; u && u <= i; u = node[u].p) {
                                         ^649    ^532
  ------------------
  |  Branch (156:23): [True: 71.79%, False: 28.21%]
  |  Branch (156:28): [True: 81.97%, False: 18.03%]
  ------------------
  157|    532|        maintain(u);
  158|    532|      }
  159|    372|    }
  160|    532|  }
  161|    814|  while (q--) {
  ------------------
  |  Branch (161:10): [True: 99.88%, False: 0.12%]
  ------------------
  162|    813|    let t = rd.u1();
  163|    813|    if (t == 0) {
  ------------------
  |  Branch (163:9): [True: 46.86%, False: 53.14%]
  ------------------
  164|    381|      int u = node2id[rd.uh()];
  165|    381|      node[u].v = {rd.uw(), rd.uw()};
  166|  1.11k|      for (; u; u = node[u].p) {
                              ^730
  ------------------
  |  Branch (166:14): [True: 65.71%, False: 34.29%]
  ------------------
  167|    730|        maintain(u);
  168|    730|      }
  169|    381|    }
  170|    813|    if (t == 1) {
  ------------------
  |  Branch (170:9): [True: 53.14%, False: 46.86%]
  ------------------
  171|    432|      int u = node2id[rd.uh()];
  172|    432|      int v = node2id[rd.uh()];
  173|    432|      u32 x = rd.uw();
  174|    432|      Segment f = {1, 0, 0};
  175|  2.03k|      while (ances[u] != ances[v]) {
  ------------------
  |  Branch (175:14): [True: 78.78%, False: 21.22%]
  ------------------
  176|  1.60k|        if (depth[ances[u]] >= depth[ances[v]]) {
  ------------------
  |  Branch (176:13): [True: 50.62%, False: 49.38%]
  ------------------
  177|    812|          x = apply(u, x);
  178|    812|          u = parent[ances[u]];
  179|    812|        } else {
  180|    792|          f = apply(v, f);
  181|    792|          v = parent[ances[v]];
  182|    792|        }
  183|  1.60k|      }
  184|    432|      if (u >= v) {
  ------------------
  |  Branch (184:11): [True: 57.41%, False: 42.59%]
  ------------------
  185|    248|        x = apply(v, u, x);
  186|    248|      } else {
  187|    184|        f = apply(u, v, f);
  188|    184|      }
  189|    432|      x = x + f;
  190|    432|      wt.uw(x);
  191|    432|    }
  192|    813|  }
  193|      1|  return 0;
  194|      1|}