/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|  3.83k|  Segment(Vertex v) : a{v.a}, b{v.b}, c{v.b} {}
   17|  10.1k|  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|  8.93k|auto operator+(const Segment &l, const Segment &r) -> Segment {
   25|  8.93k|  u32 x = u64(l.a) * r.a % P;
   26|  8.93k|  u32 y = (u64(l.a) * r.b + l.b) % P;
   27|  8.93k|  u32 z = (u64(r.a) * l.c + r.c) % P;
   28|  8.93k|  return {x, y, z};
   29|  8.93k|}
   30|  2.59k|auto operator+(const Segment &l, u32 r) -> u32 {
   31|  2.59k|  return (u64(l.a) * r + l.b) % P;
   32|  2.59k|}
   33|    617|auto operator+(u32 l, const Segment &r) -> u32 {
   34|    617|  return (u64(r.a) * l + r.c) % P;
   35|    617|}
   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|  1.21k|def build_step_1(int u, int p) -> void {
   53|  1.21k|  size[u] = 1;
   54|  3.64k|  for (int e = head[u]; e; e = edge[e].next) {
                                         ^2.43k
  ------------------
  |  Branch (54:25): [True: 66.65%, False: 33.35%]
  ------------------
   55|  2.43k|    int v = edge[e].to;
   56|  2.43k|    if (v != p) {
  ------------------
  |  Branch (56:9): [True: 50.00%, False: 50.00%]
  ------------------
   57|  1.21k|      build_step_1(v, u);
   58|  1.21k|      size[u] += size[v];
   59|  1.21k|      if (heavy[u] == 0 || size[v] > size[heavy[u]]) {
                                         ^593
  ------------------
  |  Branch (59:11): [True: 51.23%, False: 48.77%]
  |  Branch (59:28): [True: 47.05%, False: 52.95%]
  ------------------
   60|    902|        heavy[u] = v;
   61|    902|      }
   62|  1.21k|    }
   63|  2.43k|  }
   64|  1.21k|}
   65|       |
   66|  1.21k|def build_step_2(int u, int w, int p, int d) -> void {
   67|  1.21k|  int i = ++id;
   68|  1.21k|  node2id[u] = i;
   69|  1.21k|  depth[i] = d;
   70|  1.21k|  ances[i] = node2id[w];
   71|  1.21k|  parent[i] = node2id[p];
   72|  1.21k|  node[i].v = {a[u], b[u]};
   73|  3.64k|  for (int e = head[u]; e; e = edge[e].next) {
                                         ^2.43k
  ------------------
  |  Branch (73:25): [True: 66.65%, False: 33.35%]
  ------------------
   74|  2.43k|    int v = edge[e].to;
   75|  2.43k|    if (v != p && v != heavy[u]) {
                                ^1.21k
  ------------------
  |  Branch (75:9): [True: 50.00%, False: 50.00%]
  |  Branch (75:19): [True: 48.77%, False: 51.23%]
  ------------------
   76|    593|      build_step_2(v, v, u, d + 1);
   77|    593|    }
   78|  2.43k|  }
   79|  1.21k|  priority[i] = u8(log(i ^ (id + 1)));
   80|  1.21k|  if (u != w) {
  ------------------
  |  Branch (80:7): [True: 51.19%, False: 48.81%]
  ------------------
   81|    623|    int p = parent[i];
   82|    623|    int l = 0;
   83|    965|    while (p && priority[p] < priority[i]) {
                              ^804
  ------------------
  |  Branch (83:12): [True: 83.32%, False: 16.68%]
  |  Branch (83:17): [True: 42.54%, False: 57.46%]
  ------------------
   84|    342|      l = p;
   85|    342|      p = node[p].p;
   86|    342|    }
   87|    623|    node[p].r = i;
   88|    623|    node[i].p = p;
   89|    623|    node[i].l = l;
   90|    623|    node[l].p = i;
   91|    623|  }
   92|  1.21k|  if (int v = heavy[u]; v) {
  ------------------
  |  Branch (92:25): [True: 51.19%, False: 48.81%]
  ------------------
   93|    623|    build_step_2(v, w, u, d + 1);
   94|    623|  }
   95|  1.21k|}
   96|       |
   97|  2.43k|def maintain(int u) -> void {
   98|  2.43k|  node[u].s = (node[u].t = node[node[u].l].s + node[u].v) + node[node[u].r].s;
   99|  2.43k|}
  100|       |
  101|  2.49k|template <typename T> T apply(int k, T x) {
  102|  7.17k|  for (int u = k; u; u = node[u].p) {
                                   ^4.67k
  ------------------
  |  Branch (102:19): [True: 65.05%, False: 34.95%]
  ------------------
  |  Branch (102:19): [True: 65.29%, False: 34.71%]
  ------------------
  103|  4.67k|    if (u <= k) {
  ------------------
  |  Branch (103:9): [True: 77.85%, False: 22.15%]
  ------------------
  |  Branch (103:9): [True: 78.52%, False: 21.48%]
  ------------------
  104|  3.65k|      x = node[u].t + x;
  105|  3.65k|    }
  106|  4.67k|  }
  107|  2.49k|  return x;
  108|  2.49k|}
  ------------------
  | vertex_set_path_composite-logn.cpp:_ZN12_GLOBAL__N_15applyIjEET_iS1_:
  |  101|  1.25k|template <typename T> T apply(int k, T x) {
  |  102|  3.58k|  for (int u = k; u; u = node[u].p) {
  |                                   ^2.33k
  |  ------------------
  |  |  Branch (102:19): [True: 65.05%, False: 34.95%]
  |  ------------------
  |  103|  2.33k|    if (u <= k) {
  |  ------------------
  |  |  Branch (103:9): [True: 77.85%, False: 22.15%]
  |  ------------------
  |  104|  1.81k|      x = node[u].t + x;
  |  105|  1.81k|    }
  |  106|  2.33k|  }
  |  107|  1.25k|  return x;
  |  108|  1.25k|}
  ------------------
  | vertex_set_path_composite-logn.cpp:_ZN12_GLOBAL__N_15applyINS_7SegmentEEET_iS2_:
  |  101|  1.24k|template <typename T> T apply(int k, T x) {
  |  102|  3.59k|  for (int u = k; u; u = node[u].p) {
  |                                   ^2.34k
  |  ------------------
  |  |  Branch (102:19): [True: 65.29%, False: 34.71%]
  |  ------------------
  |  103|  2.34k|    if (u <= k) {
  |  ------------------
  |  |  Branch (103:9): [True: 78.52%, False: 21.48%]
  |  ------------------
  |  104|  1.84k|      x = node[u].t + x;
  |  105|  1.84k|    }
  |  106|  2.34k|  }
  |  107|  1.24k|  return x;
  |  108|  1.24k|}
  ------------------
  109|       |
  110|    617|template <typename T> T apply(int l, int r, T x) {
  111|    617|  Segment t = {1, 0, 0};
  112|    617|  int u = l;
  113|    617|  int v = r;
  114|  1.71k|  while (u != v) {
  ------------------
  |  Branch (114:10): [True: 57.55%, False: 42.45%]
  ------------------
  |  Branch (114:10): [True: 69.62%, False: 30.38%]
  ------------------
  115|  1.09k|    if (priority[u] < priority[v]) {
  ------------------
  |  Branch (115:9): [True: 75.48%, False: 24.52%]
  ------------------
  |  Branch (115:9): [True: 75.96%, False: 24.04%]
  ------------------
  116|    828|      if (l <= u) {
  ------------------
  |  Branch (116:11): [True: 95.73%, False: 4.27%]
  ------------------
  |  Branch (116:11): [True: 93.50%, False: 6.50%]
  ------------------
  117|    782|        t = (t + node[u].v) + node[node[u].r].s;
  118|    782|      }
  119|    828|      u = node[u].p;
  120|    828|    } else {
  121|    265|      if (v <= r) {
  ------------------
  |  Branch (121:11): [True: 79.82%, False: 20.18%]
  ------------------
  |  Branch (121:11): [True: 80.79%, False: 19.21%]
  ------------------
  122|    213|        x = node[v].t + x;
  123|    213|      }
  124|    265|      v = node[v].p;
  125|    265|    }
  126|  1.09k|  }
  127|    617|  x = t + (node[u].v + x);
  128|    617|  return x;
  129|    617|}
  ------------------
  | vertex_set_path_composite-logn.cpp:_ZN12_GLOBAL__N_15applyIjEET_iiS1_:
  |  110|    343|template <typename T> T apply(int l, int r, T x) {
  |  111|    343|  Segment t = {1, 0, 0};
  |  112|    343|  int u = l;
  |  113|    343|  int v = r;
  |  114|    808|  while (u != v) {
  |  ------------------
  |  |  Branch (114:10): [True: 57.55%, False: 42.45%]
  |  ------------------
  |  115|    465|    if (priority[u] < priority[v]) {
  |  ------------------
  |  |  Branch (115:9): [True: 75.48%, False: 24.52%]
  |  ------------------
  |  116|    351|      if (l <= u) {
  |  ------------------
  |  |  Branch (116:11): [True: 95.73%, False: 4.27%]
  |  ------------------
  |  117|    336|        t = (t + node[u].v) + node[node[u].r].s;
  |  118|    336|      }
  |  119|    351|      u = node[u].p;
  |  120|    351|    } else {
  |  121|    114|      if (v <= r) {
  |  ------------------
  |  |  Branch (121:11): [True: 79.82%, False: 20.18%]
  |  ------------------
  |  122|     91|        x = node[v].t + x;
  |  123|     91|      }
  |  124|    114|      v = node[v].p;
  |  125|    114|    }
  |  126|    465|  }
  |  127|    343|  x = t + (node[u].v + x);
  |  128|    343|  return x;
  |  129|    343|}
  ------------------
  | vertex_set_path_composite-logn.cpp:_ZN12_GLOBAL__N_15applyINS_7SegmentEEET_iiS2_:
  |  110|    274|template <typename T> T apply(int l, int r, T x) {
  |  111|    274|  Segment t = {1, 0, 0};
  |  112|    274|  int u = l;
  |  113|    274|  int v = r;
  |  114|    902|  while (u != v) {
  |  ------------------
  |  |  Branch (114:10): [True: 69.62%, False: 30.38%]
  |  ------------------
  |  115|    628|    if (priority[u] < priority[v]) {
  |  ------------------
  |  |  Branch (115:9): [True: 75.96%, False: 24.04%]
  |  ------------------
  |  116|    477|      if (l <= u) {
  |  ------------------
  |  |  Branch (116:11): [True: 93.50%, False: 6.50%]
  |  ------------------
  |  117|    446|        t = (t + node[u].v) + node[node[u].r].s;
  |  118|    446|      }
  |  119|    477|      u = node[u].p;
  |  120|    477|    } else {
  |  121|    151|      if (v <= r) {
  |  ------------------
  |  |  Branch (121:11): [True: 80.79%, False: 19.21%]
  |  ------------------
  |  122|    122|        x = node[v].t + x;
  |  123|    122|      }
  |  124|    151|      v = node[v].p;
  |  125|    151|    }
  |  126|    628|  }
  |  127|    274|  x = t + (node[u].v + x);
  |  128|    274|  return x;
  |  129|    274|}
  ------------------
  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|  1.21k|  for (int i = 0; i < n; ++i) a[i] = rd.uw(), b[i] = rd.uw();
                                       ^1.21k^1.21k
  ------------------
  |  Branch (145:19): [True: 99.92%, False: 0.08%]
  ------------------
  146|  1.21k|  for (int i = 1; i < n; ++i) {
                                       ^1.21k
  ------------------
  |  Branch (146:19): [True: 99.92%, False: 0.08%]
  ------------------
  147|  1.21k|    int u = rd.uh();
  148|  1.21k|    int v = rd.uh();
  149|  1.21k|    edge[i * 2 | 0] = {v, head[u]}, head[u] = i * 2 | 0;
  150|  1.21k|    edge[i * 2 | 1] = {u, head[v]}, head[v] = i * 2 | 1;
  151|  1.21k|  }
  152|      1|  build_step_1(0, 0);
  153|      1|  build_step_2(0, 0, 0, 0);
  154|  1.21k|  for (int i = 1; i <= n; ++i) {
                                        ^1.21k
  ------------------
  |  Branch (154:19): [True: 99.92%, False: 0.08%]
  ------------------
  155|  1.21k|    if (node[i].r == 0) {
  ------------------
  |  Branch (155:9): [True: 70.83%, False: 29.17%]
  ------------------
  156|  2.07k|      for (int u = i; u && u <= i; u = node[u].p) {
                                         ^1.48k  ^1.21k
  ------------------
  |  Branch (156:23): [True: 71.43%, False: 28.57%]
  |  Branch (156:28): [True: 81.95%, False: 18.05%]
  ------------------
  157|  1.21k|        maintain(u);
  158|  1.21k|      }
  159|    862|    }
  160|  1.21k|  }
  161|  1.26k|  while (q--) {
  ------------------
  |  Branch (161:10): [True: 99.92%, False: 0.08%]
  ------------------
  162|  1.26k|    let t = rd.u1();
  163|  1.26k|    if (t == 0) {
  ------------------
  |  Branch (163:9): [True: 51.15%, False: 48.85%]
  ------------------
  164|    646|      int u = node2id[rd.uh()];
  165|    646|      node[u].v = {rd.uw(), rd.uw()};
  166|  1.86k|      for (; u; u = node[u].p) {
                              ^1.21k
  ------------------
  |  Branch (166:14): [True: 65.27%, False: 34.73%]
  ------------------
  167|  1.21k|        maintain(u);
  168|  1.21k|      }
  169|    646|    }
  170|  1.26k|    if (t == 1) {
  ------------------
  |  Branch (170:9): [True: 48.85%, False: 51.15%]
  ------------------
  171|    617|      int u = node2id[rd.uh()];
  172|    617|      int v = node2id[rd.uh()];
  173|    617|      u32 x = rd.uw();
  174|    617|      Segment f = {1, 0, 0};
  175|  3.11k|      while (ances[u] != ances[v]) {
  ------------------
  |  Branch (175:14): [True: 80.20%, False: 19.80%]
  ------------------
  176|  2.49k|        if (depth[ances[u]] >= depth[ances[v]]) {
  ------------------
  |  Branch (176:13): [True: 50.10%, False: 49.90%]
  ------------------
  177|  1.25k|          x = apply(u, x);
  178|  1.25k|          u = parent[ances[u]];
  179|  1.25k|        } else {
  180|  1.24k|          f = apply(v, f);
  181|  1.24k|          v = parent[ances[v]];
  182|  1.24k|        }
  183|  2.49k|      }
  184|    617|      if (u >= v) {
  ------------------
  |  Branch (184:11): [True: 55.59%, False: 44.41%]
  ------------------
  185|    343|        x = apply(v, u, x);
  186|    343|      } else {
  187|    274|        f = apply(u, v, f);
  188|    274|      }
  189|    617|      x = x + f;
  190|    617|      wt.uw(x);
  191|    617|    }
  192|  1.26k|  }
  193|      1|  return 0;
  194|      1|}