#1142616 (C++23) No.583 鉄道同好会

• 問題: No.583 鉄道同好会
• ユーザー: OnjoujiToki
• 提出日時: 2026-01-03 07:47:27
• 言語: C++23 (gcc 15.2.0 + boost 1.89.0)
• 結果: AC
• 実行時間: 162 ms / 2,000 ms
• コード長: 39,525 bytes
• コンパイル時間: 3,408 ms
• コンパイル使用メモリ: 309,036 KB
• 実行使用メモリ: 15,872 KB
• 最終ジャッジ日時: 2026-01-03 07:47:32
• 合計ジャッジ時間: 5,238 ms
• ジャッジサーバーID （参考情報）: judge5 / judge2

ファイルパターン	結果
sample	AC * 3
other	AC * 16

コンパイルメッセージ

main.cpp:1209:9: warning: '#pragma once' in main file [-Wpragma-once-outside-header]
 1209 | #pragma once
      |         ^~~~
main.cpp: In function 'int kth(int, int, int)':
main.cpp:1345:1: warning: control reaches end of non-void function [-Wreturn-type]
 1345 | }
      | ^

ソースコード

#include <algorithm>
#include <bit>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <cstdint>
#include <functional>
#include <iostream>
#include <iterator>
#include <limits>
#include <map>
#include <numeric>
#include <optional>
#include <queue>
#include <ranges>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#ifdef _MSC_VER
#include <intrin.h>
#endif
#include <iomanip>
#include <random>

namespace internal {

// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
  x %= m;
  if (x < 0) x += m;
  return x;
}

// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
  unsigned int _m;
  unsigned long long im;

  // @param m `1 <= m < 2^31`
  explicit barrett(unsigned int m)
      : _m(m), im((unsigned long long)(-1) / m + 1) {}

  // @return m
  unsigned int umod() const { return _m; }

  // @param a `0 <= a < m`
  // @param b `0 <= b < m`
  // @return `a * b % m`
  unsigned int mul(unsigned int a, unsigned int b) const {
    // [1] m = 1
    // a = b = im = 0, so okay

    // [2] m >= 2
    // im = ceil(2^64 / m)
    // -> im * m = 2^64 + r (0 <= r < m)
    // let z = a*b = c*m + d (0 <= c, d < m)
    // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
    // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) <
    // 2^64 * 2
    // ((ab * im) >> 64) == c or c + 1
    unsigned long long z = a;
    z *= b;
#ifdef _MSC_VER
    unsigned long long x;
    _umul128(z, im, &x);
#else
    unsigned long long x =
        (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
    unsigned int v = (unsigned int)(z - x * _m);
    if (_m <= v) v += _m;
    return v;
  }
};

// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
  if (m == 1) return 0;
  unsigned int _m = (unsigned int)(m);
  unsigned long long r = 1;
  unsigned long long y = safe_mod(x, m);
  while (n) {
    if (n & 1) r = (r * y) % _m;
    y = (y * y) % _m;
    n >>= 1;
  }
  return r;
}

// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
  if (n <= 1) return false;
  if (n == 2 || n == 7 || n == 61) return true;
  if (n % 2 == 0) return false;
  long long d = n - 1;
  while (d % 2 == 0) d /= 2;
  constexpr long long bases[3] = {2, 7, 61};
  for (long long a : bases) {
    long long t = d;
    long long y = pow_mod_constexpr(a, t, n);
    while (t != n - 1 && y != 1 && y != n - 1) {
      y = y * y % n;
      t <<= 1;
    }
    if (y != n - 1 && t % 2 == 0) {
      return false;
    }
  }
  return true;
}
template <int n>
constexpr bool is_prime = is_prime_constexpr(n);

// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
  a = safe_mod(a, b);
  if (a == 0) return {b, 0};

  // Contracts:
  // [1] s - m0 * a = 0 (mod b)
  // [2] t - m1 * a = 0 (mod b)
  // [3] s * |m1| + t * |m0| <= b
  long long s = b, t = a;
  long long m0 = 0, m1 = 1;

  while (t) {
    long long u = s / t;
    s -= t * u;
    m0 -= m1 * u;  // |m1 * u| <= |m1| * s <= b

    // [3]:
    // (s - t * u) * |m1| + t * |m0 - m1 * u|
    // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
    // = s * |m1| + t * |m0| <= b

    auto tmp = s;
    s = t;
    t = tmp;
    tmp = m0;
    m0 = m1;
    m1 = tmp;
  }
  // by [3]: |m0| <= b/g
  // by g != b: |m0| < b/g
  if (m0 < 0) m0 += b / s;
  return {s, m0};
}

// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
  if (m == 2) return 1;
  if (m == 167772161) return 3;
  if (m == 469762049) return 3;
  if (m == 754974721) return 11;
  if (m == 998244353) return 3;
  int divs[20] = {};
  divs[0] = 2;
  int cnt = 1;
  int x = (m - 1) / 2;
  while (x % 2 == 0) x /= 2;
  for (int i = 3; (long long)(i)*i <= x; i += 2) {
    if (x % i == 0) {
      divs[cnt++] = i;
      while (x % i == 0) {
        x /= i;
      }
    }
  }
  if (x > 1) {
    divs[cnt++] = x;
  }
  for (int g = 2;; g++) {
    bool ok = true;
    for (int i = 0; i < cnt; i++) {
      if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
        ok = false;
        break;
      }
    }
    if (ok) return g;
  }
}
template <int m>
constexpr int primitive_root = primitive_root_constexpr(m);

// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
unsigned long long floor_sum_unsigned(unsigned long long n,
                                      unsigned long long m,
                                      unsigned long long a,
                                      unsigned long long b) {
  unsigned long long ans = 0;
  while (true) {
    if (a >= m) {
      ans += n * (n - 1) / 2 * (a / m);
      a %= m;
    }
    if (b >= m) {
      ans += n * (b / m);
      b %= m;
    }

    unsigned long long y_max = a * n + b;
    if (y_max < m) break;
    // y_max < m * (n + 1)
    // floor(y_max / m) <= n
    n = (unsigned long long)(y_max / m);
    b = (unsigned long long)(y_max % m);
    std::swap(m, a);
  }
  return ans;
}

}  // namespace internal

namespace internal {

#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value ||
                                  std::is_same<T, __int128>::value,
                              std::true_type, std::false_type>::type;

template <class T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                  std::is_same<T, unsigned __int128>::value,
                              std::true_type, std::false_type>::type;

template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value, __uint128_t,
                              unsigned __int128>;

template <class T>
using is_integral =
    typename std::conditional<std::is_integral<T>::value ||
                                  is_signed_int128<T>::value ||
                                  is_unsigned_int128<T>::value,
                              std::true_type, std::false_type>::type;

template <class T>
using is_signed_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_signed<T>::value) ||
                                  is_signed_int128<T>::value,
                              std::true_type, std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type, std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value, make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value, std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;

#else

template <class T>
using is_integral = typename std::is_integral<T>;

template <class T>
using is_signed_int =
    typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
                              std::true_type, std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<is_integral<T>::value &&
                                  std::is_unsigned<T>::value,
                              std::true_type, std::false_type>::type;

template <class T>
using to_unsigned =
    typename std::conditional<is_signed_int<T>::value, std::make_unsigned<T>,
                              std::common_type<T>>::type;

#endif

template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

template <class T>
using to_unsigned_t = typename to_unsigned<T>::type;

}  // namespace internal

namespace internal {

struct modint_base {};
struct static_modint_base : modint_base {};

template <class T>
using is_modint = std::is_base_of<modint_base, T>;
template <class T>
using is_modint_t = std::enable_if_t<is_modint<T>::value>;

}  // namespace internal

template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
  using mint = static_modint;

 public:
  static constexpr int mod() { return m; }
  static mint raw(int v) {
    mint x;
    x._v = v;
    return x;
  }

  static_modint() : _v(0) {}
  template <class T, internal::is_signed_int_t<T>* = nullptr>
  static_modint(T v) {
    long long x = (long long)(v % (long long)(umod()));
    if (x < 0) x += umod();
    _v = (unsigned int)(x);
  }
  template <class T, internal::is_unsigned_int_t<T>* = nullptr>
  static_modint(T v) {
    _v = (unsigned int)(v % umod());
  }

  unsigned int val() const { return _v; }

  mint& operator++() {
    _v++;
    if (_v == umod()) _v = 0;
    return *this;
  }
  mint& operator--() {
    if (_v == 0) _v = umod();
    _v--;
    return *this;
  }
  mint operator++(int) {
    mint result = *this;
    ++*this;
    return result;
  }
  mint operator--(int) {
    mint result = *this;
    --*this;
    return result;
  }

  mint& operator+=(const mint& rhs) {
    _v += rhs._v;
    if (_v >= umod()) _v -= umod();
    return *this;
  }
  mint& operator-=(const mint& rhs) {
    _v -= rhs._v;
    if (_v >= umod()) _v += umod();
    return *this;
  }
  mint& operator*=(const mint& rhs) {
    unsigned long long z = _v;
    z *= rhs._v;
    _v = (unsigned int)(z % umod());
    return *this;
  }
  mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

  mint operator+() const { return *this; }
  mint operator-() const { return mint() - *this; }

  mint pow(long long n) const {
    assert(0 <= n);
    mint x = *this, r = 1;
    while (n) {
      if (n & 1) r *= x;
      x *= x;
      n >>= 1;
    }
    return r;
  }
  mint inv() const {
    if (prime) {
      assert(_v);
      return pow(umod() - 2);
    } else {
      auto eg = internal::inv_gcd(_v, m);
      assert(eg.first == 1);
      return eg.second;
    }
  }

  friend mint operator+(const mint& lhs, const mint& rhs) {
    return mint(lhs) += rhs;
  }
  friend mint operator-(const mint& lhs, const mint& rhs) {
    return mint(lhs) -= rhs;
  }
  friend mint operator*(const mint& lhs, const mint& rhs) {
    return mint(lhs) *= rhs;
  }
  friend mint operator/(const mint& lhs, const mint& rhs) {
    return mint(lhs) /= rhs;
  }
  friend bool operator==(const mint& lhs, const mint& rhs) {
    return lhs._v == rhs._v;
  }
  friend bool operator!=(const mint& lhs, const mint& rhs) {
    return lhs._v != rhs._v;
  }

 private:
  unsigned int _v;
  static constexpr unsigned int umod() { return m; }
  static constexpr bool prime = internal::is_prime<m>;
};

template <int id>
struct dynamic_modint : internal::modint_base {
  using mint = dynamic_modint;

 public:
  static int mod() { return (int)(bt.umod()); }
  static void set_mod(int m) {
    assert(1 <= m);
    bt = internal::barrett(m);
  }
  static mint raw(int v) {
    mint x;
    x._v = v;
    return x;
  }

  dynamic_modint() : _v(0) {}
  template <class T, internal::is_signed_int_t<T>* = nullptr>
  dynamic_modint(T v) {
    long long x = (long long)(v % (long long)(mod()));
    if (x < 0) x += mod();
    _v = (unsigned int)(x);
  }
  template <class T, internal::is_unsigned_int_t<T>* = nullptr>
  dynamic_modint(T v) {
    _v = (unsigned int)(v % mod());
  }

  unsigned int val() const { return _v; }

  mint& operator++() {
    _v++;
    if (_v == umod()) _v = 0;
    return *this;
  }
  mint& operator--() {
    if (_v == 0) _v = umod();
    _v--;
    return *this;
  }
  mint operator++(int) {
    mint result = *this;
    ++*this;
    return result;
  }
  mint operator--(int) {
    mint result = *this;
    --*this;
    return result;
  }

  mint& operator+=(const mint& rhs) {
    _v += rhs._v;
    if (_v >= umod()) _v -= umod();
    return *this;
  }
  mint& operator-=(const mint& rhs) {
    _v += mod() - rhs._v;
    if (_v >= umod()) _v -= umod();
    return *this;
  }
  mint& operator*=(const mint& rhs) {
    _v = bt.mul(_v, rhs._v);
    return *this;
  }
  mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

  mint operator+() const { return *this; }
  mint operator-() const { return mint() - *this; }

  mint pow(long long n) const {
    assert(0 <= n);
    mint x = *this, r = 1;
    while (n) {
      if (n & 1) r *= x;
      x *= x;
      n >>= 1;
    }
    return r;
  }
  mint inv() const {
    auto eg = internal::inv_gcd(_v, mod());
    assert(eg.first == 1);
    return eg.second;
  }

  friend mint operator+(const mint& lhs, const mint& rhs) {
    return mint(lhs) += rhs;
  }
  friend mint operator-(const mint& lhs, const mint& rhs) {
    return mint(lhs) -= rhs;
  }
  friend mint operator*(const mint& lhs, const mint& rhs) {
    return mint(lhs) *= rhs;
  }
  friend mint operator/(const mint& lhs, const mint& rhs) {
    return mint(lhs) /= rhs;
  }
  friend bool operator==(const mint& lhs, const mint& rhs) {
    return lhs._v == rhs._v;
  }
  friend bool operator!=(const mint& lhs, const mint& rhs) {
    return lhs._v != rhs._v;
  }

 private:
  unsigned int _v;
  static internal::barrett bt;
  static unsigned int umod() { return bt.umod(); }
};
template <int id>
internal::barrett dynamic_modint<id>::bt(998244353);

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;

namespace internal {

template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;

template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;

template <class>
struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};

template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;

}  // namespace internal
using mint = modint998244353;
/*
g++ -std=c++23 -O2 -Wall -Wextra A.cpp -o A
./A < input.in > output.out

*/
template <typename CostType>
struct Edge {
  CostType cost;
  int src, dst;

  explicit Edge(const int src, const int dst, const CostType cost = 0)
      : cost(cost), src(src), dst(dst) {}

  auto operator<=>(const Edge& x) const = default;
};

template <typename CostType>
struct HeavyLightDecomposition {
  std::vector<int> parent, subtree, id, inv, head;
  std::vector<CostType> cost;

  explicit HeavyLightDecomposition(
      const std::vector<std::vector<Edge<CostType>>>& graph, const int root = 0)
      : graph(graph) {
    const int n = graph.size();
    parent.assign(n, -1);
    subtree.assign(n, 1);
    dfs1(root);
    id.resize(n);
    inv.resize(n);
    head.assign(n, root);
    int cur_id = 0;
    dfs2(root, &cur_id);
  }

  template <typename Fn>
  void update_v(int u, int v, const Fn f) const {
    while (true) {
      if (id[u] > id[v]) std::swap(u, v);
      f(std::max(id[head[v]], id[u]), id[v] + 1);
      if (head[u] == head[v]) break;
      v = parent[head[v]];
    }
  }
  template <typename F, typename G, typename T>
  T query_v(int u, int v, const F f, const G g, const T id_t) const {
    T left = id_t, right = id_t;
    while (true) {
      if (id[u] > id[v]) {
        std::swap(u, v);
        std::swap(left, right);
      }
      // 在 v 这一侧的链上，查询 [max(id[head[v]], id[u]), id[v]] 这些点
      left = g(left, f(std::max(id[head[v]], id[u]), id[v] + 1));
      if (head[u] == head[v]) break;
      v = parent[head[v]];
    }
    return g(left, right);
  }

  template <typename Fn>
  void update_subtree_v(const int ver, const Fn f) const {
    f(id[ver], id[ver] + subtree[ver]);
  }

  template <typename T, typename Fn>
  T query_subtree_v(const int ver, const Fn f) const {
    return f(id[ver], id[ver] + subtree[ver]);
  }

  template <typename Fn>
  void update_e(int u, int v, const Fn f) const {
    while (true) {
      if (id[u] > id[v]) std::swap(u, v);
      if (head[u] == head[v]) {
        f(id[u], id[v]);
        break;
      } else {
        f(id[head[v]] - 1, id[v]);
        v = parent[head[v]];
      }
    }
  }

  template <typename F, typename G, typename T>
  T query_e(int u, int v, const F f, const G g, const T id_t) const {
    T left = id_t, right = id_t;
    while (true) {
      if (id[u] > id[v]) {
        std::swap(u, v);
        std::swap(left, right);
      }
      if (head[u] == head[v]) {
        left = g(left, f(id[u], id[v]));
        break;
      } else {
        left = g(left, f(id[head[v]] - 1, id[v]));
        v = parent[head[v]];
      }
    }
    return g(left, right);
  }

  template <typename Fn>
  void update_subtree_e(const int ver, const Fn f) const {
    f(id[ver], id[ver] + subtree[ver] - 1);
  }

  template <typename T, typename Fn>
  T query_subtree_e(const int ver, const Fn f) const {
    return f(id[ver], id[ver] + subtree[ver] - 1);
  }

  // 对树边 (u, v) 做一次单边更新：调用 f(pos)
  // 其中 pos 是该边在“边序列”里的唯一位置（本实现为 id[child] - 1）。
  template <typename Fn>
  void update_single_edge(int u, int v, const Fn& f) const {
    if (parent[u] == v) std::swap(u, v);
    const int pos = id[v] - 1;
    f(pos);
  }

  int lowest_common_ancestor(int u, int v) const {
    while (true) {
      if (id[u] > id[v]) std::swap(u, v);
      if (head[u] == head[v]) break;
      v = parent[head[v]];
    }
    return u;
  }

 private:
  std::vector<std::vector<Edge<CostType>>> graph;

  void dfs1(const int ver) {
    for (int i = 0; std::cmp_less(i, graph[ver].size()); ++i) {
      Edge<CostType>& e = graph[ver][i];
      if (e.dst != parent[ver]) {
        parent[e.dst] = ver;
        dfs1(e.dst);
        subtree[ver] += subtree[e.dst];
        if (subtree[e.dst] > subtree[graph[ver].front().dst]) {
          std::swap(e, graph[ver].front());
        }
      }
    }
  }

  void dfs2(const int ver, int* cur_id) {
    id[ver] = (*cur_id)++;
    inv[id[ver]] = ver;
    for (const Edge<CostType>& e : graph[ver]) {
      if (e.dst != parent[ver]) {
        head[e.dst] = (e.dst == graph[ver].front().dst ? head[ver] : e.dst);
        cost.emplace_back(e.cost);
        dfs2(e.dst, cur_id);
      }
    }
  }
};

struct BitRank {
  // block: bit 列を管理, count: block ごとに立っている 1 の数を管理
  std::vector<unsigned long long> block;
  std::vector<unsigned int> count;
  BitRank() {}
  void resize(const unsigned int num) {
    block.resize(((num + 1) >> 6) + 1, 0);
    count.resize(block.size(), 0);
  }
  // i ビット目を val(0,1) にセット
  void set(const unsigned int i, const unsigned long long val) {
    block[i >> 6] |= (val << (i & 63));
  }
  void build() {
    for (unsigned int i = 1; i < block.size(); i++) {
      count[i] = count[i - 1] + __builtin_popcountll(block[i - 1]);
    }
  }
  // [0, i) ビットの 1 の数
  unsigned int rank1(const unsigned int i) const {
    return count[i >> 6] +
           __builtin_popcountll(block[i >> 6] & ((1ULL << (i & 63)) - 1ULL));
  }
  // [i, j) ビットの 1 の数
  unsigned int rank1(const unsigned int i, const unsigned int j) const {
    return rank1(j) - rank1(i);
  }
  // [0, i) ビットの 0 の数
  unsigned int rank0(const unsigned int i) const { return i - rank1(i); }
  // [i, j) ビットの 0 の数
  unsigned int rank0(const unsigned int i, const unsigned int j) const {
    return rank0(j) - rank0(i);
  }
};

class WaveletMatrix {
 private:
  unsigned int height;
  std::vector<BitRank> B;
  std::vector<int> pos;
  std::vector<std::vector<long long>> rui;

 public:
  WaveletMatrix() {}
  WaveletMatrix(std::vector<int> vec)
      : WaveletMatrix(vec, *std::max_element(vec.begin(), vec.end()) + 1) {}
  // sigma:文字の種類数
  WaveletMatrix(std::vector<int> vec, const unsigned int sigma) {
    init(vec, sigma);
  }
  void init(std::vector<int>& vec, const unsigned int sigma) {
    height = (sigma == 1) ? 1 : (64 - __builtin_clzll(sigma - 1));
    B.resize(height), pos.resize(height);
    std::vector<int> A = vec;
    rui.resize(height + 1);
    for (unsigned int i = 0; i < height; ++i) {
      B[i].resize(vec.size());
      for (unsigned int j = 0; j < vec.size(); ++j) {
        B[i].set(j, get(vec[j], height - i - 1));
      }
      B[i].build();
      auto it = stable_partition(vec.begin(), vec.end(), [&](int c) {
        return !get(c, height - i - 1);
      });
      pos[i] = it - vec.begin();
    }

    for (unsigned int i = 0; i <= height; ++i) {
      rui[i].resize(A.size() + 1);
      for (int j = 1; j <= A.size(); j++) {
        rui[i][j] = rui[i][j - 1] + A[j - 1];
      }
      if (i == height) break;
      std::stable_partition(A.begin(), A.end(),
                            [&](int c) { return !get(c, height - i - 1); });
    }
  }
  // val の i ビット目の値を返す(0,1)
  int get(const int val, const int i) { return val >> i & 1; }
  // [l, r) の間に現れる値 val の数
  int rank(const int val, const int l, const int r) {
    return rank(val, r) - rank(val, l);
  }
  // [0, i) の間に現れる値 val の数
  int rank(int val, int i) {
    int p = 0;
    for (unsigned int j = 0; j < height; ++j) {
      if (get(val, height - j - 1)) {
        p = pos[j] + B[j].rank1(p);
        i = pos[j] + B[j].rank1(i);
      } else {
        p = B[j].rank0(p);
        i = B[j].rank0(i);
      }
    }
    return i - p;
  }
  // [l, r) の k(0,1,2...) 番目に小さい値を返す
  int quantile(int k, int l, int r) {
    int res = 0;
    for (unsigned int i = 0; i < height; ++i) {
      const int j = B[i].rank0(l, r);
      if (j > k) {
        l = B[i].rank0(l);
        r = B[i].rank0(r);
      } else {
        l = pos[i] + B[i].rank1(l);
        r = pos[i] + B[i].rank1(r);
        k -= j;
        res |= (1 << (height - i - 1));
      }
    }
    return res;
  }
  long long topKsum(int k, int l, int r) {
    if (l == r) return 0LL;
    long long res = 0;
    int atai = 0;
    for (unsigned int i = 0; i < height; ++i) {
      const int j = B[i].rank0(l, r);
      if (j > k) {
        l = B[i].rank0(l);
        r = B[i].rank0(r);
      } else {
        int l2 = B[i].rank0(l);
        int r2 = B[i].rank0(r);
        res += rui[i + 1][r2] - rui[i + 1][l2];

        l = pos[i] + B[i].rank1(l);
        r = pos[i] + B[i].rank1(r);
        k -= j;

        atai |= (1 << (height - i - 1));
      }
    }
    res += (long long)atai * k;
    return res;
  }
  int rangefreq(const int i, const int j, const int a, const int b, const int l,
                const int r, const int x) {
    if (i == j || r <= a || b <= l) return 0;
    const int mid = (l + r) >> 1;
    if (a <= l && r <= b) {
      return j - i;
    } else {
      const int left =
          rangefreq(B[x].rank0(i), B[x].rank0(j), a, b, l, mid, x + 1);
      const int right = rangefreq(pos[x] + B[x].rank1(i),
                                  pos[x] + B[x].rank1(j), a, b, mid, r, x + 1);
      return left + right;
    }
  }
  // [l,r) で値が [a,b) 内に含まれる数を返す
  int rangefreq(const int l, const int r, const int a, const int b) {
    return rangefreq(l, r, a, b, 0, 1 << height, 0);
  }
  int rangemin(const int i, const int j, const int a, const int b, const int l,
               const int r, const int x, const int val) {
    if (i == j || r <= a || b <= l) return -1;
    if (r - l == 1) return val;
    const int mid = (l + r) >> 1;
    const int res =
        rangemin(B[x].rank0(i), B[x].rank0(j), a, b, l, mid, x + 1, val);
    if (res < 0)
      return rangemin(pos[x] + B[x].rank1(i), pos[x] + B[x].rank1(j), a, b, mid,
                      r, x + 1, val + (1 << (height - x - 1)));
    else
      return res;
  }
  // [l,r) で値が [a,b) 内に最小の数を返す(数が存在しない場合は -1 を返す)
  int rangemin(int l, int r, int a, int b) {
    return rangemin(l, r, a, b, 0, 1 << height, 0, 0);
  }
};

template <typename T>
struct LazySegmentTree {
  using Monoid = typename T::Monoid;
  using LazyMonoid = typename T::LazyMonoid;

  explicit LazySegmentTree(const int n)
      : LazySegmentTree(std::vector<Monoid>(n, T::m_id())) {}

  explicit LazySegmentTree(const std::vector<Monoid>& a)
      : n(a.size()), height(0) {
    while ((1 << height) < n) ++height;
    sz = 1 << height;
    lazy.assign(sz, T::lazy_id());
    data.assign(sz << 1, T::m_id());
    std::copy(a.begin(), a.end(), data.begin() + sz);
    for (int i = sz - 1; i > 0; --i) {
      data[i] = T::m_merge(data[i << 1], data[(i << 1) + 1]);
    }
  }

  void set(int idx, const Monoid val) {
    idx += sz;
    for (int i = height; i > 0; --i) {
      propagate(idx >> i);
    }
    data[idx] = val;
    for (int i = 1; i <= height; ++i) {
      const int current_idx = idx >> i;
      data[current_idx] =
          T::m_merge(data[current_idx << 1], data[(current_idx << 1) + 1]);
    }
  }

  void apply(int idx, const LazyMonoid val) {
    idx += sz;
    for (int i = height; i > 0; --i) {
      propagate(idx >> i);
    }
    data[idx] = T::apply(data[idx], val);
    for (int i = 1; i <= height; ++i) {
      const int current_idx = idx >> i;
      data[current_idx] =
          T::m_merge(data[current_idx << 1], data[(current_idx << 1) + 1]);
    }
  }

  void apply(int left, int right, const LazyMonoid val) {
    if (right <= left) return;
    left += sz;
    right += sz;
    const int ctz_left = __builtin_ctz(left);
    for (int i = height; i > ctz_left; --i) {
      propagate(left >> i);
    }
    const int ctz_right = __builtin_ctz(right);
    for (int i = height; i > ctz_right; --i) {
      propagate(right >> i);
    }
    for (int l = left, r = right; l < r; l >>= 1, r >>= 1) {
      if (l & 1) apply_sub(l++, val);
      if (r & 1) apply_sub(--r, val);
    }
    for (int i = left >> (ctz_left + 1); i > 0; i >>= 1) {
      data[i] = T::m_merge(data[i << 1], data[(i << 1) + 1]);
    }
    for (int i = right >> (ctz_right + 1); i > 0; i >>= 1) {
      data[i] = T::m_merge(data[i << 1], data[(i << 1) + 1]);
    }
  }

  Monoid get(int left, int right) {
    if (right <= left) return T::m_id();
    left += sz;
    right += sz;
    const int ctz_left = __builtin_ctz(left);
    for (int i = height; i > ctz_left; --i) {
      propagate(left >> i);
    }
    const int ctz_right = __builtin_ctz(right);
    for (int i = height; i > ctz_right; --i) {
      propagate(right >> i);
    }
    Monoid res_l = T::m_id(), res_r = T::m_id();
    for (; left < right; left >>= 1, right >>= 1) {
      if (left & 1) res_l = T::m_merge(res_l, data[left++]);
      if (right & 1) res_r = T::m_merge(data[--right], res_r);
    }
    return T::m_merge(res_l, res_r);
  }

  Monoid operator[](const int idx) {
    const int node = idx + sz;
    for (int i = height; i > 0; --i) {
      propagate(node >> i);
    }
    return data[node];
  }

  template <typename G>
  int find_right(int left, const G g) {
    if (left >= n) return n;
    left += sz;
    for (int i = height; i > 0; --i) {
      propagate(left >> i);
    }
    Monoid val = T::m_id();
    do {
      while (!(left & 1)) left >>= 1;
      Monoid nxt = T::m_merge(val, data[left]);
      if (!g(nxt)) {
        while (left < sz) {
          propagate(left);
          left <<= 1;
          nxt = T::m_merge(val, data[left]);
          if (g(nxt)) {
            val = nxt;
            ++left;
          }
        }
        return left - sz;
      }
      val = nxt;
      ++left;
    } while (__builtin_popcount(left) > 1);
    return n;
  }

  template <typename G>
  int find_left(int right, const G g) {
    if (right <= 0) return -1;
    right += sz;
    for (int i = height; i > 0; --i) {
      propagate((right - 1) >> i);
    }
    Monoid val = T::m_id();
    do {
      --right;
      while (right > 1 && (right & 1)) right >>= 1;
      Monoid nxt = T::m_merge(data[right], val);
      if (!g(nxt)) {
        while (right < sz) {
          propagate(right);
          right = (right << 1) + 1;
          nxt = T::m_merge(data[right], val);
          if (g(nxt)) {
            val = nxt;
            --right;
          }
        }
        return right - sz;
      }
      val = nxt;
    } while (__builtin_popcount(right) > 1);
    return -1;
  }

  const int n;
  int sz, height;
  std::vector<Monoid> data;
  std::vector<LazyMonoid> lazy;

  void apply_sub(const int idx, const LazyMonoid& val) {
    data[idx] = T::apply(data[idx], val);
    if (idx < sz) lazy[idx] = T::lazy_merge(lazy[idx], val);
  }

  void propagate(const int idx) {
    apply_sub(idx << 1, lazy[idx]);
    apply_sub((idx << 1) + 1, lazy[idx]);
    lazy[idx] = T::lazy_id();
  }
};

namespace monoid {

template <typename T>
struct RangeMinimumAndUpdateQuery {
  using Monoid = T;
  using LazyMonoid = T;
  static constexpr Monoid m_id() { return std::numeric_limits<Monoid>::max(); }
  static constexpr LazyMonoid lazy_id() {
    return std::numeric_limits<LazyMonoid>::max();
  }
  static Monoid m_merge(const Monoid& a, const Monoid& b) {
    return std::min(a, b);
  }
  static LazyMonoid lazy_merge(const LazyMonoid& a, const LazyMonoid& b) {
    return b == lazy_id() ? a : b;
  }
  static Monoid apply(const Monoid& a, const LazyMonoid& b) {
    return b == lazy_id() ? a : b;
  }
};

template <typename T>
struct RangeMaximumAndUpdateQuery {
  using Monoid = T;
  using LazyMonoid = T;
  static constexpr Monoid m_id() {
    return std::numeric_limits<Monoid>::lowest();
  }
  static constexpr LazyMonoid lazy_id() {
    return std::numeric_limits<LazyMonoid>::lowest();
  }
  static Monoid m_merge(const Monoid& a, const Monoid& b) {
    return std::max(a, b);
  }
  static LazyMonoid lazy_merge(const LazyMonoid& a, const LazyMonoid& b) {
    return b == lazy_id() ? a : b;
  }
  static Monoid apply(const Monoid& a, const LazyMonoid& b) {
    return b == lazy_id() ? a : b;
  }
};

template <typename T, T Inf>
struct RangeMinimumAndAddQuery {
  using Monoid = T;
  using LazyMonoid = T;
  static constexpr Monoid m_id() { return Inf; }
  static constexpr LazyMonoid lazy_id() { return 0; }
  static Monoid m_merge(const Monoid& a, const Monoid& b) {
    return std::min(a, b);
  }
  static LazyMonoid lazy_merge(const LazyMonoid& a, const LazyMonoid& b) {
    return a + b;
  }
  static Monoid apply(const Monoid& a, const LazyMonoid& b) { return a + b; }
};

template <typename T, T Inf>
struct RangeMaximumAndAddQuery {
  using Monoid = T;
  using LazyMonoid = T;
  static constexpr Monoid m_id() { return -Inf; }
  static constexpr LazyMonoid lazy_id() { return 0; }
  static Monoid m_merge(const Monoid& a, const Monoid& b) {
    return std::max(a, b);
  }
  static LazyMonoid lazy_merge(const LazyMonoid& a, const LazyMonoid& b) {
    return a + b;
  }
  static Monoid apply(const Monoid& a, const LazyMonoid& b) { return a + b; }
};

template <typename T>
struct RangeSumAndUpdateQuery {
  using Monoid = struct {
    T sum;
    int len;
  };
  using LazyMonoid = T;
  static std::vector<Monoid> init(const int n) {
    return std::vector<Monoid>(n, Monoid{0, 1});
  }
  static constexpr Monoid m_id() { return {0, 0}; }
  static constexpr LazyMonoid lazy_id() {
    return std::numeric_limits<LazyMonoid>::max();
  }
  static Monoid m_merge(const Monoid& a, const Monoid& b) {
    return Monoid{a.sum + b.sum, a.len + b.len};
  }
  static LazyMonoid lazy_merge(const LazyMonoid& a, const LazyMonoid& b) {
    return b == lazy_id() ? a : b;
  }
  static Monoid apply(const Monoid& a, const LazyMonoid& b) {
    return Monoid{b == lazy_id() ? a.sum : b * a.len, a.len};
  }
};

template <typename T>
struct RangeSumAndAddQuery {
  using Monoid = struct {
    T sum;
    int len;
  };
  using LazyMonoid = T;
  static std::vector<Monoid> init(const int n) {
    return std::vector<Monoid>(n, Monoid{0, 1});
  }
  static constexpr Monoid m_id() { return {0, 0}; }
  static constexpr LazyMonoid lazy_id() { return 0; }
  static Monoid m_merge(const Monoid& a, const Monoid& b) {
    return Monoid{a.sum + b.sum, a.len + b.len};
  }
  static LazyMonoid lazy_merge(const LazyMonoid& a, const LazyMonoid& b) {
    return a + b;
  }
  static Monoid apply(const Monoid& a, const LazyMonoid& b) {
    return Monoid{a.sum + b * a.len, a.len};
  }
};

}  // namespace monoid

#pragma once
// credit emthrm.github.io/library
template <typename T>
struct SegmentTree {
  using Monoid = typename T::Monoid;

  explicit SegmentTree(int n) : SegmentTree(std::vector<Monoid>(n, T::id())) {}

  explicit SegmentTree(const std::vector<Monoid>& a) : n(a.size()), sz(1) {
    while (sz < n) sz <<= 1;
    data.assign(sz << 1, T::id());
    std::copy(a.begin(), a.end(), data.begin() + sz);
    for (int i = sz - 1; i > 0; --i) {
      data[i] = T::merge(data[i << 1], data[(i << 1) + 1]);
    }
  }

  void set(int idx, const Monoid val) {
    idx += sz;
    data[idx] = val;
    while (idx >>= 1)
      data[idx] = T::merge(data[idx << 1], data[(idx << 1) + 1]);
  }

  Monoid get(int left, int right) const {
    Monoid res_l = T::id(), res_r = T::id();
    for (left += sz, right += sz; left < right; left >>= 1, right >>= 1) {
      if (left & 1) res_l = T::merge(res_l, data[left++]);
      if (right & 1) res_r = T::merge(data[--right], res_r);
    }
    return T::merge(res_l, res_r);
  }

  Monoid operator[](const int idx) const { return data[idx + sz]; }

 private:
  const int n;
  int sz;  // sz + 原数组坐标 = 线段树里的编号，1 based
  std::vector<Monoid> data;
};

namespace monoid {

template <typename T>
struct RangeMinimumQuery {
  using Monoid = T;
  static constexpr Monoid id() { return std::numeric_limits<Monoid>::max(); }
  static Monoid merge(const Monoid& a, const Monoid& b) {
    return std::min(a, b);
  }
};

template <typename T>
struct RangeMaximumQuery {
  using Monoid = T;
  static constexpr Monoid id() { return std::numeric_limits<Monoid>::lowest(); }
  static Monoid merge(const Monoid& a, const Monoid& b) {
    return std::max(a, b);
  }
};

template <typename T>
struct RangeSumQuery {
  using Monoid = T;
  static constexpr Monoid id() { return 0; }
  static Monoid merge(const Monoid& a, const Monoid& b) { return a + b; }
};

template <typename T>
struct RangeXorQuery {
  using Monoid = T;
  static constexpr Monoid id() { return 0; }
  static Monoid merge(const Monoid& a, const Monoid& b) { return a ^ b; }
};

}  // namespace monoid

struct TupleHash {
  template <class T>
  static void hash_combine(std::size_t& seed, const T& v) {
    seed ^= std::hash<T>{}(v) + 0x9e3779b9 + (seed << 6) + (seed >> 2);
  }

  template <class... Ts>
  std::size_t operator()(const std::tuple<Ts...>& t) const noexcept {
    std::size_t seed = 0;
    std::apply([&](const auto&... xs) { (hash_combine(seed, xs), ...); }, t);
    return seed;
  }
};

// unordered_map<tuple<int, long long>, int, TupleHash> cnt;

struct ChthollyNode {
  int l, r;
  mutable int v;
  ChthollyNode(int l, int r, int v) : l(l), r(r), v(v) {}
  bool operator<(const ChthollyNode& o) const { return l < o.l; }
};

std::set<ChthollyNode> tr;
std::set<ChthollyNode>::iterator split(int pos) {
  auto it = tr.lower_bound(ChthollyNode(pos, 0, 0));
  if (it != tr.end() && it->l == pos) return it;
  it--;
  int l = it->l, r = it->r, v = it->v;
  tr.erase(it);
  tr.insert(ChthollyNode(l, pos - 1, v));
  return tr.insert(ChthollyNode(pos, r, v)).first;
}

// range add
void add(int l, int r, int v) {  // [l, r]
  auto end = split(r + 1);
  for (auto it = split(l); it != end; it++) it->v += v;
}

// range assign
void assign(int l, int r, int v) {
  auto end = split(r + 1), begin = split(l);  // 顺序不能颠倒，否则可能RE
  tr.erase(begin, end);                       // 清除一系列节点
  tr.insert(ChthollyNode(l, r, v));           // 插入新的节点
}

// range kth
int kth(int l, int r, int k) {
  auto end = split(r + 1);
  std::vector<std::pair<int, int>> v;  // 这个pair里存节点的值和区间长度
  for (auto it = split(l); it != end; it++)
    v.emplace_back(it->v, it->r - it->l + 1);
  std::sort(v.begin(), v.end());      // 直接按节点的值的大小排下序
  for (int i = 0; i < v.size(); i++)  // 然后挨个丢出来，直到丢出k个元素为止
  {
    k -= v[i].second;
    if (k <= 0) return v[i].first;
  }
}
int ones = 0;  // 全局变量，记录当前数组中 1 的个数
void range_xor(int l, int r) {
  auto itR = split(r + 1);
  for (auto it = split(l); it != itR; ++it) {
    int len = it->r - it->l + 1;
    ones += (it->v ? -len : +len);
    it->v ^= 1;
  }
}

void paint_black(int l, int r) {
  auto itR = split(r + 1);
  auto itL = split(l);

  for (auto it = itL; it != itR; ++it) {
    if (it->v == 1) ones -= (it->r - it->l + 1);
  }

  tr.erase(itL, itR);
  tr.insert(ChthollyNode(l, r, 1));
  ones += (r - l + 1);
}

struct EulerianTrailInUndirectedGraph {
  std::vector<int> trail;

  explicit EulerianTrailInUndirectedGraph(const int n)
      : n(n), is_visited(n), graph(n) {}

  void add_edge(const int u, const int v) {
    graph[u].emplace_back(v, graph[v].size());
    graph[v].emplace_back(u, graph[u].size() - 1);
  }

  bool build(int s = -1) {
    trail.clear();
    int odd_deg = 0, edge_num = 0;
    for (int i = 0; i < n; ++i) {
      if (graph[i].size() & 1) {
        ++odd_deg;
        if (s == -1) s = i;
      }
      edge_num += graph[i].size();
    }
    edge_num >>= 1;
    if (edge_num == 0) {
      trail = {s == -1 ? 0 : s};
      return true;
    }
    if (odd_deg == 0) {
      if (s == -1) {
        s = std::distance(
            graph.begin(),
            std::find_if_not(graph.begin(), graph.end(),
                             [](const std::vector<Edge>& edges) -> bool {
                               return edges.empty();
                             }));
      }
    } else if (odd_deg != 2) {
      return false;
    }
    for (int i = 0; i < n; ++i) {
      is_visited[i].assign(graph[i].size(), false);
    }
    dfs(s);
    if (std::cmp_equal(trail.size(), edge_num + 1)) {
      std::reverse(trail.begin(), trail.end());
      return true;
    }
    trail.clear();
    return false;
  }

 private:
  struct Edge {
    int dst, rev;
    explicit Edge(const int dst, const int rev) : dst(dst), rev(rev) {}
  };

  const int n;
  std::vector<std::vector<bool>> is_visited;
  std::vector<std::vector<Edge>> graph;

  void dfs(const int ver) {
    const int deg = graph[ver].size();
    for (int i = 0; i < deg; ++i) {
      if (!is_visited[ver][i]) {
        const int dst = graph[ver][i].dst;
        is_visited[ver][i] = true;
        is_visited[dst][graph[ver][i].rev] = true;
        dfs(dst);
      }
    }
    trail.emplace_back(ver);
  }
};

int main() {
  int n, m;
  std::cin >> n >> m  ;
  EulerianTrailInUndirectedGraph g(n);
  for (int i = 0; i < m; ++i) {
    int u, v;
    std::cin >> u >> v;
    g.add_edge(u, v);
  }
  if (g.build()) {
    std::cout << "YES\n";
  } else {
    std::cout << "NO\n";
  }
}