/**
 * date   : 2024-09-28 16:35:37
 * author : Nyaan
 */

#define NDEBUG


#include <ranges>



using namespace std;

// intrinstic
#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tr2/dynamic_bitset>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// utility

namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;

template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;

template <typename T, typename U>
struct P : pair<T, U> {
  template <typename... Args>
  constexpr P(Args... args) : pair<T, U>(args...) {}

  using pair<T, U>::first;
  using pair<T, U>::second;

  P &operator+=(const P &r) {
    first += r.first;
    second += r.second;
    return *this;
  }
  P &operator-=(const P &r) {
    first -= r.first;
    second -= r.second;
    return *this;
  }
  P &operator*=(const P &r) {
    first *= r.first;
    second *= r.second;
    return *this;
  }
  template <typename S>
  P &operator*=(const S &r) {
    first *= r, second *= r;
    return *this;
  }
  P operator+(const P &r) const { return P(*this) += r; }
  P operator-(const P &r) const { return P(*this) -= r; }
  P operator*(const P &r) const { return P(*this) *= r; }
  template <typename S>
  P operator*(const S &r) const {
    return P(*this) *= r;
  }
  P operator-() const { return P{-first, -second}; }
};

using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;

constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;

template <typename T>
int sz(const T &t) {
  return t.size();
}

template <typename T, typename U>
inline bool amin(T &x, U y) {
  return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
  return (x < y) ? (x = y, true) : false;
}

template <typename T>
inline T Max(const vector<T> &v) {
  return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
  return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
  return accumulate(begin(v), end(v), 0LL);
}

template <typename T>
int lb(const vector<T> &v, const T &a) {
  return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
  return upper_bound(begin(v), end(v), a) - begin(v);
}

constexpr long long TEN(int n) {
  long long ret = 1, x = 10;
  for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
  return ret;
}

template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
  return make_pair(t, u);
}

template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
  vector<T> ret(v.size() + 1);
  if (rev) {
    for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
  } else {
    for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
  }
  return ret;
};

template <typename T>
vector<T> mkuni(const vector<T> &v) {
  vector<T> ret(v);
  sort(ret.begin(), ret.end());
  ret.erase(unique(ret.begin(), ret.end()), ret.end());
  return ret;
}

template <typename F>
vector<int> mkord(int N, F f) {
  vector<int> ord(N);
  iota(begin(ord), end(ord), 0);
  sort(begin(ord), end(ord), f);
  return ord;
}

template <typename T>
vector<int> mkinv(vector<T> &v) {
  int max_val = *max_element(begin(v), end(v));
  vector<int> inv(max_val + 1, -1);
  for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
  return inv;
}

vector<int> mkiota(int n) {
  vector<int> ret(n);
  iota(begin(ret), end(ret), 0);
  return ret;
}

template <typename T>
T mkrev(const T &v) {
  T w{v};
  reverse(begin(w), end(w));
  return w;
}

template <typename T>
bool nxp(T &v) {
  return next_permutation(begin(v), end(v));
}

// 返り値の型は入力の T に依存
// i 要素目 : [0, a[i])
template <typename T>
vector<vector<T>> product(const vector<T> &a) {
  vector<vector<T>> ret;
  vector<T> v;
  auto dfs = [&](auto rc, int i) -> void {
    if (i == (int)a.size()) {
      ret.push_back(v);
      return;
    }
    for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back();
  };
  dfs(dfs, 0);
  return ret;
}

// F : function(void(T&)), mod を取る操作
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I, const function<void(T &)> &f) {
  T res = I;
  for (; n; f(a = a * a), n >>= 1) {
    if (n & 1) f(res = res * a);
  }
  return res;
}
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I = T{1}) {
  return Power(a, n, I, function<void(T &)>{[](T &) -> void {}});
}

template <typename T>
T Rev(const T &v) {
  T res = v;
  reverse(begin(res), end(res));
  return res;
}

template <typename T>
vector<T> Transpose(const vector<T> &v) {
  using U = typename T::value_type;
  if(v.empty()) return {};
  int H = v.size(), W = v[0].size();
  vector res(W, T(H, U{}));
  for (int i = 0; i < H; i++) {
    for (int j = 0; j < W; j++) {
      res[j][i] = v[i][j];
    }
  }
  return res;
}

template <typename T>
vector<T> Rotate(const vector<T> &v, int clockwise = true) {
  using U = typename T::value_type;
  int H = v.size(), W = v[0].size();
  vector res(W, T(H, U{}));
  for (int i = 0; i < H; i++) {
    for (int j = 0; j < W; j++) {
      if (clockwise) {
        res[W - 1 - j][i] = v[i][j];
      } else {
        res[j][H - 1 - i] = v[i][j];
      }
    }
  }
  return res;
}

}  // namespace Nyaan


// bit operation

namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
  return __builtin_popcountll(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
  return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
  if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
}  // namespace Nyaan


// inout

namespace Nyaan {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << p.first << " " << p.second;
  return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  int s = (int)v.size();
  for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
  return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v) is >> x;
  return is;
}

istream &operator>>(istream &is, __int128_t &x) {
  string S;
  is >> S;
  x = 0;
  int flag = 0;
  for (auto &c : S) {
    if (c == '-') {
      flag = true;
      continue;
    }
    x *= 10;
    x += c - '0';
  }
  if (flag) x = -x;
  return is;
}

istream &operator>>(istream &is, __uint128_t &x) {
  string S;
  is >> S;
  x = 0;
  for (auto &c : S) {
    x *= 10;
    x += c - '0';
  }
  return is;
}

ostream &operator<<(ostream &os, __int128_t x) {
  if (x == 0) return os << 0;
  if (x < 0) os << '-', x = -x;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
  if (x == 0) return os << 0;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
  cin >> t;
  in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}

struct IoSetupNya {
  IoSetupNya() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    cerr << fixed << setprecision(7);
  }
} iosetupnya;

}  // namespace Nyaan


// debug


#ifdef NyaanDebug
#define trc(...) (void(0))
#else
#define trc(...) (void(0))
#endif

#ifdef NyaanLocal
#define trc2(...) (void(0))
#else
#define trc2(...) (void(0))
#endif


// macro

#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...)   \
  int __VA_ARGS__; \
  in(__VA_ARGS__)
#define inl(...)         \
  long long __VA_ARGS__; \
  in(__VA_ARGS__)
#define ins(...)      \
  string __VA_ARGS__; \
  in(__VA_ARGS__)
#define in2(s, t)                           \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i]);                         \
  }
#define in3(s, t, u)                        \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i]);                   \
  }
#define in4(s, t, u, v)                     \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i], v[i]);             \
  }
#define die(...)             \
  do {                       \
    Nyaan::out(__VA_ARGS__); \
    return;                  \
  } while (0)


namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }


//


template <typename T>
struct edge {
  int src, to;
  T cost;

  edge(int _to, T _cost) : src(-1), to(_to), cost(_cost) {}
  edge(int _src, int _to, T _cost) : src(_src), to(_to), cost(_cost) {}

  edge &operator=(const int &x) {
    to = x;
    return *this;
  }

  operator int() const { return to; }
};
template <typename T>
using Edges = vector<edge<T>>;
template <typename T>
using WeightedGraph = vector<Edges<T>>;
using UnweightedGraph = vector<vector<int>>;

// Input of (Unweighted) Graph
UnweightedGraph graph(int N, int M = -1, bool is_directed = false,
                      bool is_1origin = true) {
  UnweightedGraph g(N);
  if (M == -1) M = N - 1;
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    if (is_1origin) x--, y--;
    g[x].push_back(y);
    if (!is_directed) g[y].push_back(x);
  }
  return g;
}

// Input of Weighted Graph
template <typename T>
WeightedGraph<T> wgraph(int N, int M = -1, bool is_directed = false,
                        bool is_1origin = true) {
  WeightedGraph<T> g(N);
  if (M == -1) M = N - 1;
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    T c;
    cin >> c;
    if (is_1origin) x--, y--;
    g[x].emplace_back(x, y, c);
    if (!is_directed) g[y].emplace_back(y, x, c);
  }
  return g;
}

// Input of Edges
template <typename T>
Edges<T> esgraph([[maybe_unused]] int N, int M, int is_weighted = true,
                 bool is_1origin = true) {
  Edges<T> es;
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    T c;
    if (is_weighted)
      cin >> c;
    else
      c = 1;
    if (is_1origin) x--, y--;
    es.emplace_back(x, y, c);
  }
  return es;
}

// Input of Adjacency Matrix
template <typename T>
vector<vector<T>> adjgraph(int N, int M, T INF, int is_weighted = true,
                           bool is_directed = false, bool is_1origin = true) {
  vector<vector<T>> d(N, vector<T>(N, INF));
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    T c;
    if (is_weighted)
      cin >> c;
    else
      c = 1;
    if (is_1origin) x--, y--;
    d[x][y] = c;
    if (!is_directed) d[y][x] = c;
  }
  return d;
}

/**
 * @brief グラフテンプレート
 * @docs docs/graph/graph-template.md
 */






// 一般のグラフのstからの距離！！！！
// unvisited nodes : d = -1
vector<int> Depth(const UnweightedGraph &g, int start = 0) {
  int n = g.size();
  vector<int> ds(n, -1);
  ds[start] = 0;
  queue<int> q;
  q.push(start);
  while (!q.empty()) {
    int c = q.front();
    q.pop();
    int dc = ds[c];
    for (auto &d : g[c]) {
      if (ds[d] == -1) {
        ds[d] = dc + 1;
        q.push(d);
      }
    }
  }
  return ds;
}

// Depth of Rooted Weighted Tree
// unvisited nodes : d = -1
template <typename T>
vector<T> Depth(const WeightedGraph<T> &g, int start = 0) {
  vector<T> d(g.size(), -1);
  auto dfs = [&](auto rec, int cur, T val, int par = -1) -> void {
    d[cur] = val;
    for (auto &dst : g[cur]) {
      if (dst == par) continue;
      rec(rec, dst, val + dst.cost, cur);
    }
  };
  dfs(dfs, start, 0);
  return d;
}

// Diameter of Tree
// return value : { {u, v}, length }
pair<pair<int, int>, int> Diameter(const UnweightedGraph &g) {
  auto d = Depth(g, 0);
  int u = max_element(begin(d), end(d)) - begin(d);
  d = Depth(g, u);
  int v = max_element(begin(d), end(d)) - begin(d);
  return make_pair(make_pair(u, v), d[v]);
}

// Diameter of Weighted Tree
// return value : { {u, v}, length }
template <typename T>
pair<pair<int, int>, T> Diameter(const WeightedGraph<T> &g) {
  auto d = Depth(g, 0);
  int u = max_element(begin(d), end(d)) - begin(d);
  d = Depth(g, u);
  int v = max_element(begin(d), end(d)) - begin(d);
  return make_pair(make_pair(u, v), d[v]);
}

// nodes on the path u-v ( O(N) )
template <typename G>
vector<int> Path(G &g, int u, int v) {
  vector<int> ret;
  int end = 0;
  auto dfs = [&](auto rec, int cur, int par = -1) -> void {
    ret.push_back(cur);
    if (cur == v) {
      end = 1;
      return;
    }
    for (int dst : g[cur]) {
      if (dst == par) continue;
      rec(rec, dst, cur);
      if (end) return;
    }
    if (end) return;
    ret.pop_back();
  };
  dfs(dfs, u);
  return ret;
}

/**
 * @brief グラフユーティリティ
 * @docs docs/graph/graph-utility.md
 */


//




using namespace std;




using namespace std;

namespace internal {
template <typename T>
using is_broadly_integral =
    typename conditional_t<is_integral_v<T> || is_same_v<T, __int128_t> ||
                               is_same_v<T, __uint128_t>,
                           true_type, false_type>::type;

template <typename T>
using is_broadly_signed =
    typename conditional_t<is_signed_v<T> || is_same_v<T, __int128_t>,
                           true_type, false_type>::type;

template <typename T>
using is_broadly_unsigned =
    typename conditional_t<is_unsigned_v<T> || is_same_v<T, __uint128_t>,
                           true_type, false_type>::type;

#define ENABLE_VALUE(x) \
  template <typename T> \
  constexpr bool x##_v = x<T>::value;

ENABLE_VALUE(is_broadly_integral);
ENABLE_VALUE(is_broadly_signed);
ENABLE_VALUE(is_broadly_unsigned);
#undef ENABLE_VALUE

#define ENABLE_HAS_TYPE(var)                                   \
  template <class, class = void>                               \
  struct has_##var : false_type {};                            \
  template <class T>                                           \
  struct has_##var<T, void_t<typename T::var>> : true_type {}; \
  template <class T>                                           \
  constexpr auto has_##var##_v = has_##var<T>::value;

#define ENABLE_HAS_VAR(var)                                     \
  template <class, class = void>                                \
  struct has_##var : false_type {};                             \
  template <class T>                                            \
  struct has_##var<T, void_t<decltype(T::var)>> : true_type {}; \
  template <class T>                                            \
  constexpr auto has_##var##_v = has_##var<T>::value;

}  // namespace internal


namespace fastio {
static constexpr int SZ = 1 << 17;
static constexpr int offset = 64;
char inbuf[SZ], outbuf[SZ];
int in_left = 0, in_right = 0, out_right = 0;

struct Pre {
  char num[40000];
  constexpr Pre() : num() {
    for (int i = 0; i < 10000; i++) {
      int n = i;
      for (int j = 3; j >= 0; j--) {
        num[i * 4 + j] = n % 10 + '0';
        n /= 10;
      }
    }
  }
} constexpr pre;

void load() {
  int len = in_right - in_left;
  memmove(inbuf, inbuf + in_left, len);
  in_right = len + fread(inbuf + len, 1, SZ - len, stdin);
  in_left = 0;
}
void flush() {
  fwrite(outbuf, 1, out_right, stdout);
  out_right = 0;
}
void skip_space() {
  if (in_left + offset > in_right) load();
  while (inbuf[in_left] <= ' ') in_left++;
}

void single_read(char& c) {
  if (in_left + offset > in_right) load();
  skip_space();
  c = inbuf[in_left++];
}
void single_read(string& S) {
  skip_space();
  while (true) {
    if (in_left == in_right) load();
    int i = in_left;
    for (; i != in_right; i++) {
      if (inbuf[i] <= ' ') break;
    }
    copy(inbuf + in_left, inbuf + i, back_inserter(S));
    in_left = i;
    if (i != in_right) break;
  }
}
template <typename T,
          enable_if_t<internal::is_broadly_integral_v<T>>* = nullptr>
void single_read(T& x) {
  if (in_left + offset > in_right) load();
  skip_space();
  char c = inbuf[in_left++];
  [[maybe_unused]] bool minus = false;
  if constexpr (internal::is_broadly_signed_v<T>) {
    if (c == '-') minus = true, c = inbuf[in_left++];
  }
  x = 0;
  while (c >= '0') {
    x = x * 10 + (c & 15);
    c = inbuf[in_left++];
  }
  if constexpr (internal::is_broadly_signed_v<T>) {
    if (minus) x = -x;
  }
}
void rd() {}
template <typename Head, typename... Tail>
void rd(Head& head, Tail&... tail) {
  single_read(head);
  rd(tail...);
}

void single_write(const char& c) {
  if (out_right > SZ - offset) flush();
  outbuf[out_right++] = c;
}
void single_write(const bool& b) {
  if (out_right > SZ - offset) flush();
  outbuf[out_right++] = b ? '1' : '0';
}
void single_write(const string& S) {
  flush(), fwrite(S.data(), 1, S.size(), stdout);
}
void single_write(const char* p) { flush(), fwrite(p, 1, strlen(p), stdout); }
template <typename T,
          enable_if_t<internal::is_broadly_integral_v<T>>* = nullptr>
void single_write(const T& _x) {
  if (out_right > SZ - offset) flush();
  if (_x == 0) {
    outbuf[out_right++] = '0';
    return;
  }
  T x = _x;
  if constexpr (internal::is_broadly_signed_v<T>) {
    if (x < 0) outbuf[out_right++] = '-', x = -x;
  }
  constexpr int buffer_size = sizeof(T) * 10 / 4;
  char buf[buffer_size];
  int i = buffer_size;
  while (x >= 10000) {
    i -= 4;
    memcpy(buf + i, pre.num + (x % 10000) * 4, 4);
    x /= 10000;
  }
  if (x < 100) {
    if (x < 10) {
      outbuf[out_right] = '0' + x;
      ++out_right;
    } else {
      uint32_t q = (uint32_t(x) * 205) >> 11;
      uint32_t r = uint32_t(x) - q * 10;
      outbuf[out_right] = '0' + q;
      outbuf[out_right + 1] = '0' + r;
      out_right += 2;
    }
  } else {
    if (x < 1000) {
      memcpy(outbuf + out_right, pre.num + (x << 2) + 1, 3);
      out_right += 3;
    } else {
      memcpy(outbuf + out_right, pre.num + (x << 2), 4);
      out_right += 4;
    }
  }
  memcpy(outbuf + out_right, buf + i, buffer_size - i);
  out_right += buffer_size - i;
}
void wt() {}
template <typename Head, typename... Tail>
void wt(const Head& head, const Tail&... tail) {
  single_write(head);
  wt(std::forward<const Tail>(tail)...);
}
template <typename... Args>
void wtn(const Args&... x) {
  wt(std::forward<const Args>(x)...);
  wt('\n');
}

struct Dummy {
  Dummy() { atexit(flush); }
} dummy;

}  // namespace fastio
using fastio::rd;
using fastio::skip_space;
using fastio::wt;
using fastio::wtn;





using namespace std;

struct Timer {
  chrono::high_resolution_clock::time_point st;

  Timer() { reset(); }
  void reset() { st = chrono::high_resolution_clock::now(); }

  long long elapsed() {
    auto ed = chrono::high_resolution_clock::now();
    return chrono::duration_cast<chrono::milliseconds>(ed - st).count();
  }
  long long operator()() { return elapsed(); }
};


//



using namespace std;




using namespace std;





template <typename T>
struct has_cost {
 private:
  template <typename U>
  static auto confirm(U u) -> decltype(u.cost, std::true_type());
  static auto confirm(...) -> std::false_type;

 public:
  enum : bool { value = decltype(confirm(std::declval<T>()))::value };
};

template <typename T>
vector<vector<T>> inverse_tree(const vector<vector<T>>& g) {
  int N = (int)g.size();
  vector<vector<T>> rg(N);
  for (int i = 0; i < N; i++) {
    for (auto& e : g[i]) {
      if constexpr (is_same<T, int>::value) {
        rg[e].push_back(i);
      } else if constexpr (has_cost<T>::value) {
        rg[e].emplace_back(e.to, i, e.cost);
      } else {
        assert(0);
      }
    }
  }
  return rg;
}

template <typename T>
vector<vector<T>> rooted_tree(const vector<vector<T>>& g, int root = 0) {
  int N = (int)g.size();
  vector<vector<T>> rg(N);
  vector<char> v(N, false);
  v[root] = true;
  queue<int> que;
  que.emplace(root);
  while (!que.empty()) {
    auto p = que.front();
    que.pop();
    for (auto& e : g[p]) {
      if (v[e] == false) {
        v[e] = true;
        que.push(e);
        rg[p].push_back(e);
      }
    }
  }
  return rg;
}

/**
 * @brief 根付き木・逆辺からなる木への変換
 */




template <typename G>
struct HeavyLightDecomposition {
 private:
  void dfs_sz(int cur) {
    size[cur] = 1;
    for (auto& dst : g[cur]) {
      if (dst == par[cur]) {
        if (g[cur].size() >= 2 && int(dst) == int(g[cur][0]))
          swap(g[cur][0], g[cur][1]);
        else
          continue;
      }
      depth[dst] = depth[cur] + 1;
      par[dst] = cur;
      dfs_sz(dst);
      size[cur] += size[dst];
      if (size[dst] > size[g[cur][0]]) {
        swap(dst, g[cur][0]);
      }
    }
  }

  void dfs_hld(int cur) {
    down[cur] = id++;
    for (auto dst : g[cur]) {
      if (dst == par[cur]) continue;
      nxt[dst] = (int(dst) == int(g[cur][0]) ? nxt[cur] : int(dst));
      dfs_hld(dst);
    }
    up[cur] = id;
  }

  // [u, v)
  vector<pair<int, int>> ascend(int u, int v) const {
    vector<pair<int, int>> res;
    while (nxt[u] != nxt[v]) {
      res.emplace_back(down[u], down[nxt[u]]);
      u = par[nxt[u]];
    }
    if (u != v) res.emplace_back(down[u], down[v] + 1);
    return res;
  }

  // (u, v]
  vector<pair<int, int>> descend(int u, int v) const {
    if (u == v) return {};
    if (nxt[u] == nxt[v]) return {{down[u] + 1, down[v]}};
    auto res = descend(u, par[nxt[v]]);
    res.emplace_back(down[nxt[v]], down[v]);
    return res;
  }

 public:
  G& g;
  int root, id;
  vector<int> size, depth, down, up, nxt, par;
  HeavyLightDecomposition(G& _g, int _root = 0)
      : g(_g),
        root(_root),
        id(0),
        size(g.size(), 0),
        depth(g.size(), 0),
        down(g.size(), -1),
        up(g.size(), -1),
        nxt(g.size(), root),
        par(g.size(), root) {
    dfs_sz(root);
    dfs_hld(root);
  }

  pair<int, int> idx(int i) const { return make_pair(down[i], up[i]); }

  template <typename F>
  void path_query(int u, int v, bool vertex, const F& f) {
    int l = lca(u, v);
    for (auto&& [a, b] : ascend(u, l)) {
      int s = a + 1, t = b;
      s > t ? f(t, s) : f(s, t);
    }
    if (vertex) f(down[l], down[l] + 1);
    for (auto&& [a, b] : descend(l, v)) {
      int s = a, t = b + 1;
      s > t ? f(t, s) : f(s, t);
    }
  }

  template <typename F>
  void path_noncommutative_query(int u, int v, bool vertex, const F& f) {
    int l = lca(u, v);
    for (auto&& [a, b] : ascend(u, l)) f(a + 1, b);
    if (vertex) f(down[l], down[l] + 1);
    for (auto&& [a, b] : descend(l, v)) f(a, b + 1);
  }

  template <typename F>
  void subtree_query(int u, bool vertex, const F& f) {
    f(down[u] + int(!vertex), up[u]);
  }

  int lca(int a, int b) {
    while (nxt[a] != nxt[b]) {
      if (down[a] < down[b]) swap(a, b);
      a = par[nxt[a]];
    }
    return depth[a] < depth[b] ? a : b;
  }

  int dist(int a, int b) { return depth[a] + depth[b] - depth[lca(a, b)] * 2; }
};

/**
 * @brief Heavy Light Decomposition(重軽分解)
 * @docs docs/tree/heavy-light-decomposition.md
 */


namespace StaticTopTreeVertexBasedImpl {

enum Type { Vertex, Compress, Rake, Add_Edge, Add_Vertex };

template <typename G>
struct StaticTopTreeVertexBased {
  const HeavyLightDecomposition<G>& hld;
  vector<vector<int>> g;
  int root;     // 元の木の root
  int tt_root;  // top tree の root
  vector<int> P, L, R;
  vector<Type> T;

  StaticTopTreeVertexBased(const HeavyLightDecomposition<G>& _hld) : hld(_hld) {
    root = hld.root;
    g = rooted_tree(hld.g, root);
    int n = g.size();
    P.resize(n, -1), L.resize(n, -1), R.resize(n, -1);
    T.resize(n, Type::Vertex);
    build();
  }

 private:
  int add(int l, int r, Type t) {
    if (t == Type::Compress or t == Type::Rake) {
      assert(l != -1 and r != -1);
    }
    if (t == Type::Add_Edge) {
      assert(l != -1 and r == -1);
    }
    assert(t != Type::Vertex and t != Type::Add_Vertex);
    int k = P.size();
    P.push_back(-1), L.push_back(l), R.push_back(r), T.push_back(t);
    if (l != -1) P[l] = k;
    if (r != -1) P[r] = k;
    return k;
  }
  int add2(int k, int l, int r, Type t) {
    assert(k < (int)g.size());
    assert(t == Type::Vertex or t == Type::Add_Vertex);
    if (t == Type::Vertex) {
      assert(l == -1 and r == -1);
    } else {
      assert(l != -1 and r == -1);
    }
    P[k] = -1, L[k] = l, R[k] = r, T[k] = t;
    if (l != -1) P[l] = k;
    if (r != -1) P[r] = k;
    return k;
  }
  pair<int, int> merge(const vector<pair<int, int>>& a, Type t) {
    assert(!a.empty());
    if (a.size() == 1) return a[0];
    int sum_s = 0;
    for (auto& [_, s] : a) sum_s += s;
    vector<pair<int, int>> b, c;
    for (auto& [i, s] : a) {
      (sum_s > s ? b : c).emplace_back(i, s);
      sum_s -= s * 2;
    }
    auto [i, si] = merge(b, t);
    auto [j, sj] = merge(c, t);
    return {add(i, j, t), si + sj};
  }
  pair<int, int> compress(int i) {
    vector<pair<int, int>> chs;
    while (true) {
      chs.push_back(add_vertex(i));
      if (g[i].empty()) break;
      i = g[i][0];
    }
    return merge(chs, Type::Compress);
  }
  pair<int, int> rake(int i) {
    vector<pair<int, int>> chs;
    for (int j = 1; j < (int)g[i].size(); j++) chs.push_back(add_edge(g[i][j]));
    if (chs.empty()) return {-1, 0};
    return merge(chs, Type::Rake);
  }
  pair<int, int> add_edge(int i) {
    auto [j, sj] = compress(i);
    return {add(j, -1, Type::Add_Edge), sj};
  }
  pair<int, int> add_vertex(int i) {
    auto [j, sj] = rake(i);
    return {add2(i, j, -1, j == -1 ? Type::Vertex : Type::Add_Vertex), sj + 1};
  }
  void build() {
    auto [i, n] = compress(root);
    assert((int)g.size() == n);
    tt_root = i;
  }
};

template <typename G, typename Path, typename Point, typename Vertex,
          typename Compress, typename Rake, typename Add_edge,
          typename Add_vertex>
struct DPonStaticTopTreeVertexBased {
  const StaticTopTreeVertexBased<G> tt;
  vector<Path> path;
  vector<Point> point;
  const Vertex vertex;
  const Compress compress;
  const Rake rake;
  const Add_edge add_edge;
  const Add_vertex add_vertex;

  DPonStaticTopTreeVertexBased(const HeavyLightDecomposition<G>& hld,
                               const Vertex& _vertex, const Compress& _compress,
                               const Rake& _rake, const Add_edge& _add_edge,
                               const Add_vertex& _add_vertex)
      : tt(hld),
        vertex(_vertex),
        compress(_compress),
        rake(_rake),
        add_edge(_add_edge),
        add_vertex(_add_vertex) {
    int n = tt.P.size();
    path.resize(n), point.resize(n);
    dfs(tt.tt_root);
  }

  Path get() { return path[tt.tt_root]; }
  void update(int k) {
    while (k != -1) _update(k), k = tt.P[k];
  }

 private:
  void _update(int k) {
    if (tt.T[k] == Type::Vertex) {
      path[k] = vertex(k);
    } else if (tt.T[k] == Type::Compress) {
      path[k] = compress(path[tt.L[k]], path[tt.R[k]]);
    } else if (tt.T[k] == Type::Rake) {
      point[k] = rake(point[tt.L[k]], point[tt.R[k]]);
    } else if (tt.T[k] == Type::Add_Edge) {
      point[k] = add_edge(path[tt.L[k]]);
    } else {
      path[k] = add_vertex(point[tt.L[k]], k);
    }
  }

  void dfs(int k) {
    if (tt.L[k] != -1) dfs(tt.L[k]);
    if (tt.R[k] != -1) dfs(tt.R[k]);
    _update(k);
  }
};

}  // namespace StaticTopTreeVertexBasedImpl

using StaticTopTreeVertexBasedImpl::DPonStaticTopTreeVertexBased;
using StaticTopTreeVertexBasedImpl::StaticTopTreeVertexBased;

/*

  // template
  using Path = ;
  using Point = ;
  auto vertex = [&](int i) -> Path {

  };
  auto compress = [&](const Path& p, const Path& c) -> Path {

  };
  auto rake = [&](const Point& a, const Point& b) -> Point {

  };
  auto add_edge = [&](const Path& a) -> Point {

  };
  auto add_vertex = [&](const Point& a, int i) -> Path {

  };
  HeavyLightDecomposition hld{g};
  DPonStaticTopTreeVertexBased<vector<vector<int>>, Path, Point,
  decltype(vertex), decltype(compress), decltype(rake), decltype(add_edge),
                    decltype(add_vertex)>
      dp(hld, vertex, compress, rake, add_edge, add_vertex);
*/

/**
 * @brief Static Top Tree
 */


namespace DynamicDiameterImpl {

template <typename T>
struct HalfPath {
  T d;
  // int u;
  friend HalfPath max(const HalfPath& lhs, const HalfPath& rhs) {
    return lhs.d > rhs.d ? lhs : rhs;
    //  return lhs.u > rhs.u ? lhs : rhs;
  }
};
template <typename T>
struct Path {
  T d;
  // int u, v;
  friend Path max(const Path& lhs, const Path& rhs) {
    return lhs.d > rhs.d ? lhs : rhs;
    // if (lhs.u != rhs.u) return lhs.u > rhs.u ? lhs : rhs;
    // return lhs.v > rhs.v ? lhs : rhs;
  }
};
template <typename T>
struct L {
  Path<T> dia;
  HalfPath<T> d1, d2;
};
template <typename T>
struct H {
  Path<T> dia;
  HalfPath<T> pd, cd;
  T p_to_c;
  // int p, c;
};

template <typename T>
H<T> vertex(T x) {
  H<T> r;
  r.dia = {x};
  r.pd = r.cd = {x};
  r.p_to_c = x;
  // r.p = r.c = i;
  return r;
}

template <typename T>
H<T> compress(const H<T>& p, const H<T>& c) {
  H<T> r;
  r.dia = max(max(p.dia, c.dia), {p.cd.d + c.pd.d});
  r.pd = max(p.pd, {p.p_to_c + c.pd.d});
  r.cd = max(c.cd, {c.p_to_c + p.cd.d});
  r.p_to_c = p.p_to_c + c.p_to_c;
  // r.p = p.p, r.c = c.c;
  return r;
}

template <typename T>
L<T> rake(const L<T>& a, const L<T>& b) {
  L<T> r;
  r.dia = max(a.dia, b.dia);
  if (a.d1.d > b.d1.d) {
    r.d1 = a.d1;
    r.d2 = max(a.d2, b.d1);
  } else {
    r.d1 = b.d1;
    r.d2 = max(b.d2, a.d1);
  }
  return r;
}

template <typename T>
L<T> add_edge(const H<T>& a) {
  L<T> r;
  r.dia = a.dia;
  r.d1 = a.pd;
  r.d2 = {0};
  return r;
}

template <typename T>
H<T> add_vertex(const L<T>& a, T x) {
  H<T> r;
  r.dia = max(a.dia, {a.d1.d + x + a.d2.d});
  r.pd = r.cd = {a.d1.d + x};
  r.p_to_c = x;
  // r.p = r.c = i;
  return r;
}

template <typename T>
struct Aux_Tree {
  int N, _buf;
  const WeightedGraph<T>& g;
  vector<vector<int>> aux;
  vector<T> w;
  vector<pair<pair<int, int>, int>> e_to_id;

  Aux_Tree(const WeightedGraph<T>& _g) : g(_g) {
    N = g.size();
    aux.resize(2 * N - 1);
    w.resize(2 * N - 1);
    _buf = N;
    dfs(0, -1);
    assert(_buf == 2 * N - 1);
    sort(begin(e_to_id), end(e_to_id));
  }

  void dfs(int c, int p) {
    for (auto& d : g[c]) {
      if (d == p) continue;
      int id = _buf++;
      aux[id].push_back(c), aux[c].push_back(id);
      aux[id].push_back(d), aux[d].push_back(id);
      w[id] = d.cost;
      e_to_id.emplace_back(minmax<int>(c, d), id);
      dfs(d, c);
    }
  }

  int get_id(int u, int v) {
    pair<int, int> p = minmax(u, v);
    return lower_bound(begin(e_to_id), end(e_to_id), make_pair(p, -1))->second;
  }
};

template <typename T>
struct DynamicDiameter {
  const WeightedGraph<T>& g;
  int n;
  Aux_Tree<T> aux;
  HeavyLightDecomposition<vector<vector<int>>> hld;
  DPonStaticTopTreeVertexBased<
      vector<vector<int>>, H<T>, L<T>, function<H<T>(int)>,
      function<H<T>(const H<T>&, const H<T>&)>,
      function<L<T>(const L<T>&, const L<T>&)>, function<L<T>(const H<T>&)>,
      function<H<T>(const L<T>&, int)>>
      dp;

  DynamicDiameter(const WeightedGraph<T>& _g)
      : g(_g),
        n(g.size()),
        aux(g),
        hld(aux.aux),
        dp(
            hld, [&](int i) { return vertex(aux.w[i], i < n ? i : -1); },
            [&](const H<T>& p, const H<T>& c) { return compress(p, c); },
            [&](const L<T>& a, const L<T>& b) { return rake(a, b); },
            [&](const H<T>& a) { return add_edge(a); },
            [&](const L<T>& a, int i) {
              return add_vertex(a, aux.w[i], i < n ? i : -1);
            }) {}

  pair<T, pair<int, int>> get() {
    auto [d, u, v] = dp.get().dia;
    return make_pair(d, make_pair(u, v));
  }

  void update(int u, int v, T x) {
    assert(aux.e_to_id.count(minmax(u, v)));
    int i = aux.e_to_id[minmax(u, v)];
    aux.w[i] = x;
    dp.update(i);
  }
};
}  // namespace DynamicDiameterImpl

using DynamicDiameterImpl::DynamicDiameter;


using namespace Nyaan;

namespace yosupo {

using ull = unsigned long long;

template <class T>
struct FlattenVector {
  std::vector<T> v;
  std::vector<int> start;
  FlattenVector(int n, const std::vector<std::pair<int, T>>& _v)
      : start(n + 1) {
    for (const auto& x : _v) {
      start[x.first + 1]++;
    }
    for (int i = 1; i <= n; i++) {
      start[i] += start[i - 1];
    }
    v = std::vector<T>(start[n]);

    auto pos = start;
    for (const auto& x : _v) {
      v[pos[x.first]] = x.second;
      pos[x.first]++;
    }
  }

  auto at(int i) {
    return v | std::ranges::views::take(start[i + 1]) |
           std::ranges::views::drop(start[i]);
  }
};

template <class TreeDP>
struct StaticTopTree {
  using Point = TreeDP::Point;
  using Path = TreeDP::Path;

  int n;
  std::vector<std::pair<int, int>> edges;
  TreeDP& dp;

  StaticTopTree(int _n, TreeDP& _dp)
      : n(_n), dp(_dp), points(n + 1, dp.id()), node_ids(n, {n, -1, -1}) {
    edges.reserve(2 * (n - 1));
  }

  void add_edge(int u, int v) {
    edges.push_back({u, v});
    edges.push_back({v, u});
  }

  // compress / rake
  template <class D>
  struct Inner {
    pair<D, D> d;
    int par;
  };
  V<Inner<Path>> compressed;
  V<Inner<Point>> raked;

  Path op(const Path& l, const Path& r) { return dp.compress(l, r); }
  Point op(const Point& l, const Point& r) { return dp.rake(l, r); }

  // compress / rake / leaf
  template <class D>
  struct Node {
    D p;
    int* par;
  };
  template <class D>
  Node<D> merge(const Node<D>& l, const Node<D>& r, V<Inner<D>>& nodes) {
    int id = int(nodes.size());
    assert(nodes.size() < nodes.capacity());
    *l.par = 2 * id;
    *r.par = 2 * id + 1;
    nodes.push_back({{l.p, r.p}, -1});
    return {op(l.p, r.p), &nodes[id].par};
  }

  void init(int r = 0) {
    FlattenVector tree(n, edges);
    V<int> topo;
    {
      V<int> parent(n, -1);
      topo.reserve(n);
      topo.push_back(r);
      for (int i = 0; i < n; i++) {
        int u = topo[i];
        for (int v : tree.at(u)) {
          if (v == parent[u]) continue;
          parent[v] = u;
          topo.push_back(v);
        }
      }
      edges.erase(remove_if(edges.begin(), edges.end(),
                            [&](auto edge) {
                              return parent[edge.second] != edge.first;
                            }),
                  edges.end());
      tree = FlattenVector(n, edges);
    }

    V<int> heavy_child(n, -1);
    V<ull> mask(n);

    V<pair<int, Node<Path>>> b;
    b.reserve(n);
    auto build_compress = [&](int u) {
      b.clear();
      auto merge_last = [&]() {
        auto y = b.back();
        b.pop_back();
        auto x = b.back();
        b.pop_back();
        b.push_back(
            {max(x.first, y.first) + 1, merge(x.second, y.second, compressed)});
      };
      while (u != -1) {
        b.push_back({countr_zero(bit_ceil(mask[u])),
                     {dp.add_vertex(points[u], u), &node_ids[u].c_id}});
        while (true) {
          int len = int(b.size());
          if (len >= 3 && (b[len - 3].first == b[len - 2].first ||
                           b[len - 3].first <= b[len - 1].first)) {
            auto last = b.back();
            b.pop_back();
            merge_last();
            b.push_back(last);
          } else if (len >= 2 && b[len - 2].first <= b[len - 1].first) {
            merge_last();
          } else {
            break;
          }
        }
        u = heavy_child[u];
      }
      while (b.size() != 1) {
        merge_last();
      }
      return b.back().second.p;
    };

    compressed.reserve(n - 1);
    raked.reserve(n - 1);

    const int MAX_H = 128;
    array<Node<Point>, MAX_H> q;
    bitset<MAX_H> has = {};
    for (int u : topo | std::ranges::views::reverse) {
      ull sum_rake = 0;
      for (int v : tree.at(u)) {
        sum_rake += bit_ceil(mask[v]) << 1;
      }
      mask[u] = bit_ceil(sum_rake);
      for (int v : tree.at(u)) {
        int d = countr_zero(bit_ceil(sum_rake - (bit_ceil(mask[v]) << 1)));
        ull s = ((mask[v] + (1ull << d) - 1) >> d << d) + (1ull << d);
        if (s <= mask[u]) {
          mask[u] = s;
          heavy_child[u] = v;
        }
      }

      for (int v : tree.at(u)) {
        if (v == heavy_child[u]) continue;
        int d = countr_zero(bit_ceil(sum_rake - (bit_ceil(mask[v]) << 1)));
        Point point = dp.to_point(build_compress(v));
        Node<Point> data = {point, &node_ids[v].r_id};
        while (has.test(d)) {
          has.reset(d);
          data = merge(q[d], data, raked);
          d++;
        }
        q[d] = data;
        has.set(d);
      }
      int d = int(has._Find_first());
      if (d == int(has.size())) continue;

      Node data = q[d];
      has.reset(d);
      while (true) {
        d = int(has._Find_first());
        if (d == int(has.size())) break;
        has.reset(d);
        data = merge(q[d], data, raked);
      }
      points[u] = data.p;

      for (int v0 : tree.at(u)) {
        if (v0 == heavy_child[u]) continue;
        int v = v0;
        while (v != -1) {
          node_ids[v].h_par = u;
          node_ids[v].r_id = node_ids[v0].r_id;
          v = heavy_child[v];
        }
      }
    }
    build_compress(r);
  }

  V<Point> points;
  struct ID {
    int h_par, c_id, r_id;
  };
  V<ID> node_ids;

  Point update(int u) {
    auto up = [&](int id, auto p, auto& nodes) {
      while (id >= 0) {
        if (id % 2 == 0) {
          nodes[id / 2].d.first = p;
        } else {
          nodes[id / 2].d.second = p;
        }
        p = op(nodes[id / 2].d.first, nodes[id / 2].d.second);
        id = nodes[id / 2].par;
      }
      return p;
    };
    while (u != n) {
      auto [h_par, c_id, r_id] = node_ids[u];
      Point p = dp.to_point(up(c_id, dp.add_vertex(points[u], u), compressed));
      points[h_par] = up(r_id, p, raked);
      u = h_par;
    }
    return points[n];
  }
};

struct TreeDP {
  using T = ll;

  struct Point {
    T dia, d1, d2;
  };
  struct Path {
    T dia, pd, cd, p_to_c;
  };
  using Vertex = T;

  vector<Vertex> f;

  Point id() { return Point{T{0}, T{0}, T{0}}; }

  Path compress(const Path& p, const Path& c) {
    Path r;
    r.dia = max(max(p.dia, c.dia), {p.cd + c.pd});
    r.pd = max(p.pd, {p.p_to_c + c.pd});
    r.cd = max(c.cd, {c.p_to_c + p.cd});
    r.p_to_c = p.p_to_c + c.p_to_c;
    // r.p = p.p, r.c = c.c;
    return r;
  }

  Point rake(const Point& a, const Point& b) {
    Point r;
    r.dia = max(a.dia, b.dia);
    if (a.d1 > b.d1) {
      r.d1 = a.d1;
      r.d2 = max(a.d2, b.d1);
    } else {
      r.d1 = b.d1;
      r.d2 = max(b.d2, a.d1);
    }
    return r;
  }

  Point to_point(const Path& a) {
    Point r;
    r.dia = a.dia;
    r.d1 = a.pd;
    r.d2 = {0};
    return r;
  }

  Path add_vertex(const Point& a, int i) {
    Path r;
    r.dia = max(a.dia, {a.d1 + f[i] + a.d2});
    r.pd = r.cd = {a.d1 + f[i]};
    r.p_to_c = f[i];
    return r;
  }
};

}  // namespace yosupo

void q() {
  Timer timer;
  int N, Q;
  rd(N, Q);
  vi U(N - 1), V(N - 1), W(N - 1);
  rep(i, N - 1) rd(U[i], V[i], W[i]);
  each(x, U)-- x;
  each(x, V)-- x;
  vi A(Q), B(Q), K(Q);
  rep(i, Q) rd(A[i], B[i], K[i]);
  each(x, A)-- x;

  map<pair<int, int>, int> mp;
  rep(i, N - 1) mp[minmax(U[i], V[i])] = i;

  vvi on(N / 2 + 1);
  {
    vvi g(N);
    rep(i, N - 1) g[U[i]].push_back(V[i]), g[V[i]].push_back(U[i]);
    auto dfs = [&](auto rc, int c, int p) -> int {
      int res = 1;
      each(d, g[c]) {
        if (d == p) continue;
        int cur = rc(rc, d, c);
        int idx = mp[minmax<int>(c, d)];
        on[min(cur, N - cur)].push_back(idx);
        res += cur;
      }
      return res;
    };
    dfs(dfs, 0, -1);
  }

  vvi qs(N / 2 + 1);
  rep(i, Q) qs[K[i]].push_back(i);
  vi flag(N - 1);
  vl ans(Q, -1);

  WeightedGraph<ll> g(N);
  rep(i, N - 1) {
    g[U[i]].emplace_back(U[i], V[i], -inf);
    g[V[i]].emplace_back(V[i], U[i], -inf);
  }

  DynamicDiameterImpl::Aux_Tree aux(g);

  yosupo::TreeDP dp;
  dp.f = aux.w;
  yosupo::StaticTopTree tr(2 * N - 1, dp);
  rep(i, 2 * N - 1) each(j, aux.aux[i]) if (i < j) tr.add_edge(i, j);
  tr.init();

  ll cur = 0;
  auto update = [&](int u, int v, ll x) {
    int i = aux.get_id(u, v);
    dp.f[i] = aux.w[i] = x;
    cur = tr.update(i).dia;
  };

  repr1(n, N / 2) {
    each(i, on[n]) {
      flag[i] = 1;
      update(U[i], V[i], W[i]);
    }
    each(q, qs[n]) {
      int a = A[q], b = B[q];
      if (flag[a]) update(U[a], V[a], b);
      ans[q] = cur;
      if (flag[a]) update(U[a], V[a], W[a]);
    }
  }
  each(x, ans) wtn(x);

  cerr << timer() << endl;
}

void Nyaan::solve() {
  int t = 1;
  // in(t);
  while (t--) q();
}