#line 1 "main.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/2627"

#line 1 "library/my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else

// https://codeforces.com/blog/entry/96344
#pragma GCC optimize("Ofast,unroll-loops")
// いまの CF だとこれ入れると動かない？
// #pragma GCC target("avx2,popcnt")

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;

template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'010'000'000;
template <>
constexpr ll infty<ll> = 2'020'000'000'000'000'000;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;

using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;

#define vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) vector<vector<vector<type>>> name(h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) \
  vector<vector<vector<vector<type>>>> name(a, vector<vector<vector<type>>>(b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)

#define FOR_subset(t, s) for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if

#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second

#define stoi stoll

int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

template <typename T>
T floor(T a, T b) {
  return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
  return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
  return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

template <typename T, typename U>
T SUM(const vector<U> &A) {
  T sm = 0;
  for (auto &&a: A) sm += a;
  return sm;
}

#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()

template <typename T>
T POP(deque<T> &que) {
  T a = que.front();
  que.pop_front();
  return a;
}
template <typename T>
T POP(pq<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(pqg<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(vc<T> &que) {
  T a = que.back();
  que.pop_back();
  return a;
}

template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
  if (check_ok) assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    (check(x) ? ok : ng) = x;
  }
  return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
  FOR(iter) {
    double x = (ok + ng) / 2;
    (check(x) ? ok : ng) = x;
  }
  return (ok + ng) / 2;
}

template <class T, class S>
inline bool chmax(T &a, const S &b) {
  return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
  return (a > b ? a = b, 1 : 0);
}

// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
  vc<int> A(S.size());
  FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
  return A;
}

template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
  int N = A.size();
  vector<T> B(N + 1);
  FOR(i, N) { B[i + 1] = B[i] + A[i]; }
  if (off == 0) B.erase(B.begin());
  return B;
}

// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
  vector<int> ids(len(A));
  iota(all(ids), 0);
  sort(all(ids), [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
  return ids;
}

// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
  vc<T> B(len(I));
  FOR(i, len(I)) B[i] = A[I[i]];
  return B;
}

template <typename T, typename... Vectors>
void concat(vc<T> &first, const Vectors &... others) {
  vc<T> &res = first;
  (res.insert(res.end(), others.begin(), others.end()), ...);
}
#endif
#line 1 "library/other/io.hpp"
#define FASTIO
#include <unistd.h>

// https://judge.yosupo.jp/submission/21623
namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf
uint32_t pil = 0, pir = 0, por = 0;

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

inline void load() {
  memcpy(ibuf, ibuf + pil, pir - pil);
  pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
  pil = 0;
  if (pir < SZ) ibuf[pir++] = '\n';
}

inline void flush() {
  fwrite(obuf, 1, por, stdout);
  por = 0;
}

void rd(char &c) {
  do {
    if (pil + 1 > pir) load();
    c = ibuf[pil++];
  } while (isspace(c));
}

void rd(string &x) {
  x.clear();
  char c;
  do {
    if (pil + 1 > pir) load();
    c = ibuf[pil++];
  } while (isspace(c));
  do {
    x += c;
    if (pil == pir) load();
    c = ibuf[pil++];
  } while (!isspace(c));
}

template <typename T>
void rd_real(T &x) {
  string s;
  rd(s);
  x = stod(s);
}

template <typename T>
void rd_integer(T &x) {
  if (pil + 100 > pir) load();
  char c;
  do
    c = ibuf[pil++];
  while (c < '-');
  bool minus = 0;
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (c == '-') { minus = 1, c = ibuf[pil++]; }
  }
  x = 0;
  while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; }
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (minus) x = -x;
  }
}

void rd(int &x) { rd_integer(x); }
void rd(ll &x) { rd_integer(x); }
void rd(i128 &x) { rd_integer(x); }
void rd(u32 &x) { rd_integer(x); }
void rd(u64 &x) { rd_integer(x); }
void rd(u128 &x) { rd_integer(x); }
void rd(double &x) { rd_real(x); }
void rd(long double &x) { rd_real(x); }
void rd(f128 &x) { rd_real(x); }

template <class T, class U>
void rd(pair<T, U> &p) {
  return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T>
void rd_tuple(T &t) {
  if constexpr (N < std::tuple_size<T>::value) {
    auto &x = std::get<N>(t);
    rd(x);
    rd_tuple<N + 1>(t);
  }
}
template <class... T>
void rd(tuple<T...> &tpl) {
  rd_tuple(tpl);
}

template <size_t N = 0, typename T>
void rd(array<T, N> &x) {
  for (auto &d: x) rd(d);
}
template <class T>
void rd(vc<T> &x) {
  for (auto &d: x) rd(d);
}

void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
  rd(h), read(t...);
}

void wt(const char c) {
  if (por == SZ) flush();
  obuf[por++] = c;
}
void wt(const string s) {
  for (char c: s) wt(c);
}
void wt(const char *s) {
  size_t len = strlen(s);
  for (size_t i = 0; i < len; i++) wt(s[i]);
}

template <typename T>
void wt_integer(T x) {
  if (por > SZ - 100) flush();
  if (x < 0) { obuf[por++] = '-', x = -x; }
  int outi;
  for (outi = 96; x >= 10000; outi -= 4) {
    memcpy(out + outi, pre.num[x % 10000], 4);
    x /= 10000;
  }
  if (x >= 1000) {
    memcpy(obuf + por, pre.num[x], 4);
    por += 4;
  } else if (x >= 100) {
    memcpy(obuf + por, pre.num[x] + 1, 3);
    por += 3;
  } else if (x >= 10) {
    int q = (x * 103) >> 10;
    obuf[por] = q | '0';
    obuf[por + 1] = (x - q * 10) | '0';
    por += 2;
  } else
    obuf[por++] = x | '0';
  memcpy(obuf + por, out + outi + 4, 96 - outi);
  por += 96 - outi;
}

template <typename T>
void wt_real(T x) {
  ostringstream oss;
  oss << fixed << setprecision(15) << double(x);
  string s = oss.str();
  wt(s);
}

void wt(int x) { wt_integer(x); }
void wt(ll x) { wt_integer(x); }
void wt(i128 x) { wt_integer(x); }
void wt(u32 x) { wt_integer(x); }
void wt(u64 x) { wt_integer(x); }
void wt(u128 x) { wt_integer(x); }
void wt(double x) { wt_real(x); }
void wt(long double x) { wt_real(x); }
void wt(f128 x) { wt_real(x); }

template <class T, class U>
void wt(const pair<T, U> val) {
  wt(val.first);
  wt(' ');
  wt(val.second);
}
template <size_t N = 0, typename T>
void wt_tuple(const T t) {
  if constexpr (N < std::tuple_size<T>::value) {
    if constexpr (N > 0) { wt(' '); }
    const auto x = std::get<N>(t);
    wt(x);
    wt_tuple<N + 1>(t);
  }
}
template <class... T>
void wt(tuple<T...> tpl) {
  wt_tuple(tpl);
}
template <class T, size_t S>
void wt(const array<T, S> val) {
  auto n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}
template <class T>
void wt(const vector<T> val) {
  auto n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}

void print() { wt('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
  wt(head);
  if (sizeof...(Tail)) wt(' ');
  print(forward<Tail>(tail)...);
}

// gcc expansion. called automaticall after main.
void __attribute__((destructor)) _d() { flush(); }
} // namespace fastio
using fastio::read;
using fastio::print;
using fastio::flush;

#if defined(LOCAL)
#define SHOW(...) SHOW_IMPL(__VA_ARGS__, SHOW6, SHOW5, SHOW4, SHOW3, SHOW2, SHOW1)(__VA_ARGS__)
#define SHOW_IMPL(_1, _2, _3, _4, _5, _6, NAME, ...) NAME
#define SHOW1(x) print(#x, "=", (x)), flush()
#define SHOW2(x, y) print(#x, "=", (x), #y, "=", (y)), flush()
#define SHOW3(x, y, z) print(#x, "=", (x), #y, "=", (y), #z, "=", (z)), flush()
#define SHOW4(x, y, z, w) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w)), flush()
#define SHOW5(x, y, z, w, v) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v)), flush()
#define SHOW6(x, y, z, w, v, u) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v), #u, "=", (u)), flush()
#else
#define SHOW(...)
#endif

#define INT(...)   \
  int __VA_ARGS__; \
  read(__VA_ARGS__)
#define LL(...)   \
  ll __VA_ARGS__; \
  read(__VA_ARGS__)
#define U32(...)   \
  u32 __VA_ARGS__; \
  read(__VA_ARGS__)
#define U64(...)   \
  u64 __VA_ARGS__; \
  read(__VA_ARGS__)
#define STR(...)      \
  string __VA_ARGS__; \
  read(__VA_ARGS__)
#define CHAR(...)   \
  char __VA_ARGS__; \
  read(__VA_ARGS__)
#define DBL(...)      \
  double __VA_ARGS__; \
  read(__VA_ARGS__)

#define VEC(type, name, size) \
  vector<type> name(size);    \
  read(name)
#define VV(type, name, h, w)                     \
  vector<vector<type>> name(h, vector<type>(w)); \
  read(name)

void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 5 "main.cpp"

#line 2 "library/ds/segtree/dynamic_segtree_sparse.hpp"

// 常にほとんどの要素が unit であることが保証されるような動的セグ木
// したがって、default_prod の類は持たせられず、acted monoid も一般には扱えない
// 追加 N 回のときノード数 N 以下が保証される
template <typename Monoid, bool PERSISTENT>
struct Dynamic_SegTree_Sparse {
  using MX = Monoid;
  using X = typename MX::value_type;

  struct Node {
    ll idx;
    Node *l, *r;
    X prod, x;
  };
  const int NODES;
  const ll L0, R0;
  Node *pool;
  int pid;
  using np = Node *;
  vc<np> FREE;

  Dynamic_SegTree_Sparse(int NODES, ll L0, ll R0) : NODES(NODES), L0(L0), R0(R0), pid(0) { pool = new Node[NODES]; }
  ~Dynamic_SegTree_Sparse() { delete[] pool; }

  // 木 dp のマージのときなどに使用すると MLE 回避できることがある
  // https://codeforces.com/problemset/problem/671/D
  void free_subtree(np c) {
    auto dfs = [&](auto &dfs, np c) -> void {
      if (c->l) dfs(dfs, c->l);
      if (c->r) dfs(dfs, c->r);
      FREE.eb(c);
    };
    dfs(dfs, c);
  }

  np new_root() { return nullptr; }

  np new_node(ll idx, const X x) {
    if (!FREE.empty()) {
      np c = POP(FREE);
      c->idx = idx, c->l = c->r = nullptr;
      c->prod = c->x = x;
      return c;
    }
    assert(pid < NODES);
    pool[pid].idx = idx;
    pool[pid].l = pool[pid].r = nullptr;
    pool[pid].x = pool[pid].prod = x;
    return &(pool[pid++]);
  }

  X prod(np root, ll l, ll r) {
    assert(L0 <= l && l <= r && r <= R0);
    if (l == r) return MX::unit();
    X x = MX::unit();
    prod_rec(root, L0, R0, l, r, x);
    return x;
  }

  X prod_all(np root) { return prod(root, L0, R0); }

  np set(np root, ll i, const X &x) {
    assert(L0 <= i && i < R0);
    return set_rec(root, L0, R0, i, x);
  }

  np multiply(np root, ll i, const X &x) {
    assert(L0 <= i && i < R0);
    return multiply_rec(root, L0, R0, i, x);
  }

  template <typename F>
  ll max_right(np root, F check, ll L) {
    assert(L0 <= L && L <= R0 && check(MX::unit()));
    X x = MX::unit();
    return max_right_rec(root, check, L0, R0, L, x);
  }

  template <typename F>
  ll min_left(np root, F check, ll R) {
    assert(L0 <= R && R <= R0 && check(MX::unit()));
    X x = MX::unit();
    return min_left_rec(root, check, L0, R0, R, x);
  }

  void reset() {
    pid = 0;
    FREE.clear();
  }

  vc<pair<ll, X>> get_all(np root) {
    vc<pair<ll, X>> res;
    auto dfs = [&](auto &dfs, np c) -> void {
      if (!c) return;
      dfs(dfs, c->l);
      res.eb(c->idx, c->x);
      dfs(dfs, c->r);
    };
    dfs(dfs, root);
    return res;
  }

  X get(np root, ll idx) {
    auto dfs = [&](auto &dfs, np c) -> X {
      if (!c) return Monoid::unit();
      if (idx == c->idx) return c->x;
      if (idx < (c->idx)) return dfs(dfs, c->l);
      return dfs(dfs, c->r);
    };
    return dfs(dfs, root);
  }

private:
  void update(np c) {
    c->prod = c->x;
    if (c->l) c->prod = MX::op(c->l->prod, c->prod);
    if (c->r) c->prod = MX::op(c->prod, c->r->prod);
  }

  np copy_node(np c) {
    if (!c || !PERSISTENT) return c;
    assert(pid < NODES);
    pool[pid].idx = c->idx;
    pool[pid].l = c->l;
    pool[pid].r = c->r;
    pool[pid].x = c->x;
    pool[pid].prod = c->prod;
    return &(pool[pid++]);
  }

  np set_rec(np c, ll l, ll r, ll i, X x) {
    if (!c) {
      c = new_node(i, x);
      return c;
    }
    c = copy_node(c);
    if (c->idx == i) {
      c->x = x;
      update(c);
      return c;
    }
    ll m = (l + r) / 2;
    if (i < m) {
      if (c->idx < i) swap(c->idx, i), swap(c->x, x);
      c->l = set_rec(c->l, l, m, i, x);
    }
    if (m <= i) {
      if (i < c->idx) swap(c->idx, i), swap(c->x, x);
      c->r = set_rec(c->r, m, r, i, x);
    }
    update(c);
    return c;
  }

  np multiply_rec(np c, ll l, ll r, ll i, X x) {
    if (!c) {
      c = new_node(i, x);
      return c;
    }
    c = copy_node(c);
    if (c->idx == i) {
      c->x = MX::op(c->x, x);
      update(c);
      return c;
    }
    ll m = (l + r) / 2;
    if (i < m) {
      if (c->idx < i) swap(c->idx, i), swap(c->x, x);
      c->l = multiply_rec(c->l, l, m, i, x);
    }
    if (m <= i) {
      if (i < c->idx) swap(c->idx, i), swap(c->x, x);
      c->r = multiply_rec(c->r, m, r, i, x);
    }
    update(c);
    return c;
  }

  void prod_rec(np c, ll l, ll r, ll ql, ll qr, X &x) {
    chmax(ql, l);
    chmin(qr, r);
    if (ql >= qr || !c) return;
    if (l == ql && r == qr) {
      x = MX::op(x, c->prod);
      return;
    }
    ll m = (l + r) / 2;
    prod_rec(c->l, l, m, ql, qr, x);
    if (ql <= (c->idx) && (c->idx) < qr) x = MX::op(x, c->x);
    prod_rec(c->r, m, r, ql, qr, x);
  }

  template <typename F>
  ll max_right_rec(np c, const F &check, ll l, ll r, ll ql, X &x) {
    if (!c || r <= ql) return R0;
    if (check(MX::op(x, c->prod))) {
      x = MX::op(x, c->prod);
      return R0;
    }
    ll m = (l + r) / 2;
    ll k = max_right_rec(c->l, check, l, m, ql, x);
    if (k != R0) return k;
    if (ql <= (c->idx)) {
      x = MX::op(x, c->x);
      if (!check(x)) return c->idx;
    }
    return max_right_rec(c->r, check, m, r, ql, x);
  }

  template <typename F>
  ll min_left_rec(np c, const F &check, ll l, ll r, ll qr, X &x) {
    if (!c || qr <= l) return L0;
    if (check(MX::op(c->prod, x))) {
      x = MX::op(c->prod, x);
      return L0;
    }
    ll m = (l + r) / 2;
    ll k = min_left_rec(c->r, check, m, r, qr, x);
    if (k != L0) return k;
    if (c->idx < qr) {
      x = MX::op(c->x, x);
      if (!check(x)) return c->idx + 1;
    }
    return min_left_rec(c->l, check, l, m, qr, x);
  }
};
#line 2 "library/alg/monoid/add_pair.hpp"

template <typename E>
struct Monoid_Add_Pair {
  using value_type = pair<E, E>;
  using X = value_type;
  static constexpr X op(const X &x, const X &y) {
    return {x.fi + y.fi, x.se + y.se};
  }
  static constexpr X inverse(const X &x) { return {-x.fi, -x.se}; }
  static constexpr X unit() { return {0, 0}; }
  static constexpr bool commute = true;
};
#line 1 "library/other/fibonacci_search.hpp"
// returns: {fx, x}
// [L, R) での極小値をひとつ求める、単峰は不要
template <typename T, bool MINIMIZE, typename F>
pair<T, ll> fibonacci_search(F f, ll L, ll R) {
  assert(L < R);
  --R;
  ll a = L, b = L + 1, c = L + 2, d = L + 3;
  int n = 0;
  while (d < R) { b = c, c = d, d = b + c - a, ++n; }
  auto get = [&](ll x) -> T {
    if (R < x) return infty<T>;
    return (MINIMIZE ? f(x) : -f(x));
  };
  T ya = get(a), yb = get(b), yc = get(c), yd = get(d);
  // この中で極小ならば全体でも極小、を維持する
  FOR(n) {
    if (yb <= yc) {
      d = c, c = b, b = a + d - c;
      yd = yc, yc = yb, yb = get(b);
    } else {
      a = b, b = c, c = a + d - b;
      ya = yb, yb = yc, yc = get(c);
    }
  }
  ll x = a;
  T y = ya;
  if (chmin(y, yb)) x = b;
  if (chmin(y, yc)) x = c;
  if (chmin(y, yd)) x = d;
  if (MINIMIZE) return {y, x};
  return {-y, x};
}
#line 9 "main.cpp"

/*
max - min を減らすということ
0 回操作するやつがあるとしてよい

width=Kq+r

商を持つ
最小値のあまりを決めると
[c,c+q] （r箇所）
[c,c+q) （K-r箇所）
これで c を最適化したいのだが
これは c について凸なので適当にやる

やりたいこと c を決めたときの計算ができればよい
セグ木でいいか
*/

void solve() {
  LL(N, K, L, U);
  VEC(ll, A, N);

  for (auto& x: A) x += K;

  vvc<ll> dat(K + K);
  FOR(i, N) {
    ll r = A[i] % K;
    dat[r].eb((A[i] - r) / K);
    dat[K + r].eb((A[i] - K - r) / K);
  }
  // FOR(k, K + K) print("dat", k, dat[k]);

  ll q, r;
  tie(q, r) = divmod(U - L + 1, K);
  ll LIM = ceil<ll>(1LL << 40, K);
  Dynamic_SegTree_Sparse<Monoid_Add_Pair<ll>, false> seg(K, 0, LIM);
  using np = decltype(seg)::np;

  np X = seg.new_root();
  np Y = seg.new_root();
  FOR(k, K) {
    if (k < r)
      for (auto& x: dat[k]) { X = seg.multiply(X, x, {1, x}); }
    if (k >= r)
      for (auto& x: dat[k]) { Y = seg.multiply(Y, x, {1, x}); }
  }

  auto eval = [&](i128 c) -> i128 {
    i128 ans = 0;
    if (0 <= c) {
      auto [cnt, sm] = seg.prod(X, 0, c);
      ans += i128(cnt) * c - sm;
      tie(cnt, sm) = seg.prod(Y, 0, c);
      ans += i128(cnt) * c - sm;
    }
    if (c + q + 1 < LIM) {
      auto [cnt, sm] = seg.prod(X, c + q + 1, LIM);
      ans += i128(sm) - i128(cnt) * (c + q);
      tie(cnt, sm) = seg.prod(Y, c + q, LIM);
      ans += i128(sm) - i128(cnt) * (c + q - 1);
    }
    return ans;
  };

  auto best = [&]() -> ll { return fibonacci_search<i128, true>(eval, 0, LIM).fi; };

  ll ANS = infty<ll>;
  FOR(L, K) {
    chmin(ANS, best());
    // L 削除
    // L+r Y->X
    // L+K Y
    for (auto& x: dat[L]) { X = seg.multiply(X, x, {-1, -x}); }
    for (auto& x: dat[L + r]) {
      X = seg.multiply(X, x, {1, x});
      Y = seg.multiply(Y, x, {-1, -x});
    }
    for (auto& x: dat[L + K]) { Y = seg.multiply(Y, x, {1, x}); }
  }
  print(ANS);
}

signed main() {
  int T = 1;
  // INT(T);
  FOR(T) solve();
  return 0;
}