/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|  13.8M|  Segment(Vertex v) : a{v.a}, b{v.b}, c{v.b} {}
   17|  41.8M|  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|  38.8M|auto operator+(const Segment &l, const Segment &r) -> Segment {
   25|  38.8M|  u32 x = u64(l.a) * r.a % P;
   26|  38.8M|  u32 y = (u64(l.a) * r.b + l.b) % P;
   27|  38.8M|  u32 z = (u64(r.a) * l.c + r.c) % P;
   28|  38.8M|  return {x, y, z};
   29|  38.8M|}
   30|  11.8M|auto operator+(const Segment &l, u32 r) -> u32 {
   31|  11.8M|  return (u64(l.a) * r + l.b) % P;
   32|  11.8M|}
   33|  1.49M|auto operator+(u32 l, const Segment &r) -> u32 {
   34|  1.49M|  return (u64(r.a) * l + r.c) % P;
   35|  1.49M|}
   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|  2.33M|def build_step_1(int u, int p) -> void {
   53|  2.33M|  size[u] = 1;
   54|  7.00M|  for (int e = head[u]; e; e = edge[e].next) {
                                         ^4.66M
  ------------------
  |  Branch (54:25): [True: 66.67%, False: 33.33%]
  ------------------
   55|  4.66M|    int v = edge[e].to;
   56|  4.66M|    if (v != p) {
  ------------------
  |  Branch (56:9): [True: 50.00%, False: 50.00%]
  ------------------
   57|  2.33M|      build_step_1(v, u);
   58|  2.33M|      size[u] += size[v];
   59|  2.33M|      if (heavy[u] == 0 || size[v] > size[heavy[u]]) {
                                         ^682k
  ------------------
  |  Branch (59:11): [True: 70.74%, False: 29.26%]
  |  Branch (59:28): [True: 50.48%, False: 49.52%]
  ------------------
   60|  1.99M|        heavy[u] = v;
   61|  1.99M|      }
   62|  2.33M|    }
   63|  4.66M|  }
   64|  2.33M|}
   65|       |
   66|  2.33M|def build_step_2(int u, int w, int p, int d) -> void {
   67|  2.33M|  int i = ++id;
   68|  2.33M|  node2id[u] = i;
   69|  2.33M|  depth[i] = d;
   70|  2.33M|  ances[i] = node2id[w];
   71|  2.33M|  parent[i] = node2id[p];
   72|  2.33M|  node[i].v = {a[u], b[u]};
   73|  7.00M|  for (int e = head[u]; e; e = edge[e].next) {
                                         ^4.66M
  ------------------
  |  Branch (73:25): [True: 66.67%, False: 33.33%]
  ------------------
   74|  4.66M|    int v = edge[e].to;
   75|  4.66M|    if (v != p && v != heavy[u]) {
                                ^2.33M
  ------------------
  |  Branch (75:9): [True: 50.00%, False: 50.00%]
  |  Branch (75:19): [True: 29.26%, False: 70.74%]
  ------------------
   76|   682k|      build_step_2(v, v, u, d + 1);
   77|   682k|    }
   78|  4.66M|  }
   79|  2.33M|  priority[i] = u8(log(i ^ (id + 1)));
   80|  2.33M|  if (u != w) {
  ------------------
  |  Branch (80:7): [True: 70.74%, False: 29.26%]
  ------------------
   81|  1.65M|    int p = parent[i];
   82|  1.65M|    int l = 0;
   83|  3.01M|    while (p && priority[p] < priority[i]) {
                              ^2.84M
  ------------------
  |  Branch (83:12): [True: 94.24%, False: 5.76%]
  |  Branch (83:17): [True: 48.00%, False: 52.00%]
  ------------------
   84|  1.36M|      l = p;
   85|  1.36M|      p = node[p].p;
   86|  1.36M|    }
   87|  1.65M|    node[p].r = i;
   88|  1.65M|    node[i].p = p;
   89|  1.65M|    node[i].l = l;
   90|  1.65M|    node[l].p = i;
   91|  1.65M|  }
   92|  2.33M|  if (int v = heavy[u]; v) {
  ------------------
  |  Branch (92:25): [True: 70.74%, False: 29.26%]
  ------------------
   93|  1.65M|    build_step_2(v, w, u, d + 1);
   94|  1.65M|  }
   95|  2.33M|}
   96|       |
   97|  8.33M|def maintain(int u) -> void {
   98|  8.33M|  node[u].s = (node[u].t = node[node[u].l].s + node[u].v) + node[node[u].r].s;
   99|  8.33M|}
  100|       |
  101|  10.5M|template <typename T> T apply(int k, T x) {
  102|  34.2M|  for (int u = k; u; u = node[u].p) {
                                   ^23.6M
  ------------------
  |  Branch (102:19): [True: 69.70%, False: 30.30%]
  ------------------
  |  Branch (102:19): [True: 68.79%, False: 31.21%]
  ------------------
  103|  23.6M|    if (u <= k) {
  ------------------
  |  Branch (103:9): [True: 74.82%, False: 25.18%]
  ------------------
  |  Branch (103:9): [True: 75.67%, False: 24.33%]
  ------------------
  104|  17.8M|      x = node[u].t + x;
  105|  17.8M|    }
  106|  23.6M|  }
  107|  10.5M|  return x;
  108|  10.5M|}
  ------------------
  | vertex_set_path_composite-logn.cpp:_ZN12_GLOBAL__N_15applyIjEET_iS1_:
  |  101|  5.06M|template <typename T> T apply(int k, T x) {
  |  102|  16.7M|  for (int u = k; u; u = node[u].p) {
  |                                   ^11.6M
  |  ------------------
  |  |  Branch (102:19): [True: 69.70%, False: 30.30%]
  |  ------------------
  |  103|  11.6M|    if (u <= k) {
  |  ------------------
  |  |  Branch (103:9): [True: 74.82%, False: 25.18%]
  |  ------------------
  |  104|  8.71M|      x = node[u].t + x;
  |  105|  8.71M|    }
  |  106|  11.6M|  }
  |  107|  5.06M|  return x;
  |  108|  5.06M|}
  ------------------
  | vertex_set_path_composite-logn.cpp:_ZN12_GLOBAL__N_15applyINS_7SegmentEEET_iS2_:
  |  101|  5.46M|template <typename T> T apply(int k, T x) {
  |  102|  17.5M|  for (int u = k; u; u = node[u].p) {
  |                                   ^12.0M
  |  ------------------
  |  |  Branch (102:19): [True: 68.79%, False: 31.21%]
  |  ------------------
  |  103|  12.0M|    if (u <= k) {
  |  ------------------
  |  |  Branch (103:9): [True: 75.67%, False: 24.33%]
  |  ------------------
  |  104|  9.11M|      x = node[u].t + x;
  |  105|  9.11M|    }
  |  106|  12.0M|  }
  |  107|  5.46M|  return x;
  |  108|  5.46M|}
  ------------------
  109|       |
  110|  1.49M|template <typename T> T apply(int l, int r, T x) {
  111|  1.49M|  Segment t = {1, 0, 0};
  112|  1.49M|  int u = l;
  113|  1.49M|  int v = r;
  114|  15.3M|  while (u != v) {
  ------------------
  |  Branch (114:10): [True: 88.22%, False: 11.78%]
  ------------------
  |  Branch (114:10): [True: 91.53%, False: 8.47%]
  ------------------
  115|  13.8M|    if (priority[u] < priority[v]) {
  ------------------
  |  Branch (115:9): [True: 37.07%, False: 62.93%]
  ------------------
  |  Branch (115:9): [True: 41.01%, False: 58.99%]
  ------------------
  116|  5.46M|      if (l <= u) {
  ------------------
  |  Branch (116:11): [True: 63.43%, False: 36.57%]
  ------------------
  |  Branch (116:11): [True: 79.96%, False: 20.04%]
  ------------------
  117|  4.05M|        t = (t + node[u].v) + node[node[u].r].s;
  118|  4.05M|      }
  119|  5.46M|      u = node[u].p;
  120|  8.35M|    } else {
  121|  8.35M|      if (v <= r) {
  ------------------
  |  Branch (121:11): [True: 54.70%, False: 45.30%]
  ------------------
  |  Branch (121:11): [True: 66.76%, False: 33.24%]
  ------------------
  122|  5.18M|        x = node[v].t + x;
  123|  5.18M|      }
  124|  8.35M|      v = node[v].p;
  125|  8.35M|    }
  126|  13.8M|  }
  127|  1.49M|  x = t + (node[u].v + x);
  128|  1.49M|  return x;
  129|  1.49M|}
  ------------------
  | vertex_set_path_composite-logn.cpp:_ZN12_GLOBAL__N_15applyIjEET_iiS1_:
  |  110|   694k|template <typename T> T apply(int l, int r, T x) {
  |  111|   694k|  Segment t = {1, 0, 0};
  |  112|   694k|  int u = l;
  |  113|   694k|  int v = r;
  |  114|  5.89M|  while (u != v) {
  |  ------------------
  |  |  Branch (114:10): [True: 88.22%, False: 11.78%]
  |  ------------------
  |  115|  5.20M|    if (priority[u] < priority[v]) {
  |  ------------------
  |  |  Branch (115:9): [True: 37.07%, False: 62.93%]
  |  ------------------
  |  116|  1.92M|      if (l <= u) {
  |  ------------------
  |  |  Branch (116:11): [True: 63.43%, False: 36.57%]
  |  ------------------
  |  117|  1.22M|        t = (t + node[u].v) + node[node[u].r].s;
  |  118|  1.22M|      }
  |  119|  1.92M|      u = node[u].p;
  |  120|  3.27M|    } else {
  |  121|  3.27M|      if (v <= r) {
  |  ------------------
  |  |  Branch (121:11): [True: 54.70%, False: 45.30%]
  |  ------------------
  |  122|  1.79M|        x = node[v].t + x;
  |  123|  1.79M|      }
  |  124|  3.27M|      v = node[v].p;
  |  125|  3.27M|    }
  |  126|  5.20M|  }
  |  127|   694k|  x = t + (node[u].v + x);
  |  128|   694k|  return x;
  |  129|   694k|}
  ------------------
  | vertex_set_path_composite-logn.cpp:_ZN12_GLOBAL__N_15applyINS_7SegmentEEET_iiS2_:
  |  110|   798k|template <typename T> T apply(int l, int r, T x) {
  |  111|   798k|  Segment t = {1, 0, 0};
  |  112|   798k|  int u = l;
  |  113|   798k|  int v = r;
  |  114|  9.42M|  while (u != v) {
  |  ------------------
  |  |  Branch (114:10): [True: 91.53%, False: 8.47%]
  |  ------------------
  |  115|  8.62M|    if (priority[u] < priority[v]) {
  |  ------------------
  |  |  Branch (115:9): [True: 41.01%, False: 58.99%]
  |  ------------------
  |  116|  3.53M|      if (l <= u) {
  |  ------------------
  |  |  Branch (116:11): [True: 79.96%, False: 20.04%]
  |  ------------------
  |  117|  2.82M|        t = (t + node[u].v) + node[node[u].r].s;
  |  118|  2.82M|      }
  |  119|  3.53M|      u = node[u].p;
  |  120|  5.08M|    } else {
  |  121|  5.08M|      if (v <= r) {
  |  ------------------
  |  |  Branch (121:11): [True: 66.76%, False: 33.24%]
  |  ------------------
  |  122|  3.39M|        x = node[v].t + x;
  |  123|  3.39M|      }
  |  124|  5.08M|      v = node[v].p;
  |  125|  5.08M|    }
  |  126|  8.62M|  }
  |  127|   798k|  x = t + (node[u].v + x);
  |  128|   798k|  return x;
  |  129|   798k|}
  ------------------
  130|       |
  131|       |} // namespace
  132|       |
  133|     20|int main() {
  134|     20|  rd rd;
  135|     20|  wt wt;
  136|     20|  int n = rd.uh();
  137|     20|  int q = rd.uh();
  138|     20|#ifdef LOCAL
  139|     20|  id = 0;
  140|     20|  std::memset(head, 0, 4 * n);
  141|     20|  std::memset(heavy, 0, 4 * n);
  142|     20|  std::memset(node, 0, (n + 1) * sizeof(Node));
  143|     20|#endif
  144|     20|  node[0].s.a = 1;
  145|  2.33M|  for (int i = 0; i < n; ++i) a[i] = rd.uw(), b[i] = rd.uw();
                                       ^2.33M^2.33M
  ------------------
  |  Branch (145:19): [True: 100.00%, False: 0.00%]
  ------------------
  146|  2.33M|  for (int i = 1; i < n; ++i) {
                                       ^2.33M
  ------------------
  |  Branch (146:19): [True: 100.00%, False: 0.00%]
  ------------------
  147|  2.33M|    int u = rd.uh();
  148|  2.33M|    int v = rd.uh();
  149|  2.33M|    edge[i * 2 | 0] = {v, head[u]}, head[u] = i * 2 | 0;
  150|  2.33M|    edge[i * 2 | 1] = {u, head[v]}, head[v] = i * 2 | 1;
  151|  2.33M|  }
  152|     20|  build_step_1(0, 0);
  153|     20|  build_step_2(0, 0, 0, 0);
  154|  2.33M|  for (int i = 1; i <= n; ++i) {
                                        ^2.33M
  ------------------
  |  Branch (154:19): [True: 100.00%, False: 0.00%]
  ------------------
  155|  2.33M|    if (node[i].r == 0) {
  ------------------
  |  Branch (155:9): [True: 62.68%, False: 37.32%]
  ------------------
  156|  3.79M|      for (int u = i; u && u <= i; u = node[u].p) {
                                         ^3.11M  ^2.33M
  ------------------
  |  Branch (156:23): [True: 82.02%, False: 17.98%]
  |  Branch (156:28): [True: 74.95%, False: 25.05%]
  ------------------
  157|  2.33M|        maintain(u);
  158|  2.33M|      }
  159|  1.46M|    }
  160|  2.33M|  }
  161|  2.42M|  while (q--) {
  ------------------
  |  Branch (161:10): [True: 100.00%, False: 0.00%]
  ------------------
  162|  2.42M|    let t = rd.u1();
  163|  2.42M|    if (t == 0) {
  ------------------
  |  Branch (163:9): [True: 38.40%, False: 61.60%]
  ------------------
  164|   930k|      int u = node2id[rd.uh()];
  165|   930k|      node[u].v = {rd.uw(), rd.uw()};
  166|  6.93M|      for (; u; u = node[u].p) {
                              ^6.00M
  ------------------
  |  Branch (166:14): [True: 86.58%, False: 13.42%]
  ------------------
  167|  6.00M|        maintain(u);
  168|  6.00M|      }
  169|   930k|    }
  170|  2.42M|    if (t == 1) {
  ------------------
  |  Branch (170:9): [True: 61.60%, False: 38.40%]
  ------------------
  171|  1.49M|      int u = node2id[rd.uh()];
  172|  1.49M|      int v = node2id[rd.uh()];
  173|  1.49M|      u32 x = rd.uw();
  174|  1.49M|      Segment f = {1, 0, 0};
  175|  12.0M|      while (ances[u] != ances[v]) {
  ------------------
  |  Branch (175:14): [True: 87.58%, False: 12.42%]
  ------------------
  176|  10.5M|        if (depth[ances[u]] >= depth[ances[v]]) {
  ------------------
  |  Branch (176:13): [True: 48.10%, False: 51.90%]
  ------------------
  177|  5.06M|          x = apply(u, x);
  178|  5.06M|          u = parent[ances[u]];
  179|  5.46M|        } else {
  180|  5.46M|          f = apply(v, f);
  181|  5.46M|          v = parent[ances[v]];
  182|  5.46M|        }
  183|  10.5M|      }
  184|  1.49M|      if (u >= v) {
  ------------------
  |  Branch (184:11): [True: 46.53%, False: 53.47%]
  ------------------
  185|   694k|        x = apply(v, u, x);
  186|   798k|      } else {
  187|   798k|        f = apply(u, v, f);
  188|   798k|      }
  189|  1.49M|      x = x + f;
  190|  1.49M|      wt.uw(x);
  191|  1.49M|    }
  192|  2.42M|  }
  193|     20|  return 0;
  194|     20|}