#include namespace { #pragma GCC diagnostic ignored "-Wunused-function" #include #pragma GCC diagnostic warning "-Wunused-function" using namespace std; using namespace atcoder; #define rep(i,n) for(int i = 0; i < (int)(n); i++) #define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--) #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) template bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; } using ll = long long; using P = pair; using VI = vector; using VVI = vector; using VL = vector; using VVL = vector; auto floor_div(signed_integral auto x, signed_integral auto y) { return x / y - ((x ^ y) < 0 && x % y != 0); } template T floor_div(T x, unsigned_integral auto y) { return x >= 0 ? T(x / y) : -T(-x / y + (-x % y != 0)); } auto ceil_div(signed_integral auto x, signed_integral auto y) { return x / y + ((x ^ y) >= 0 && x % y != 0); } template T ceil_div(T x, unsigned_integral auto y) { return x >= 0 ? T(x / y + (x % y != 0)) : -T(-x / y); } template > struct erasable_priority_queue { priority_queue, Comp> q, q_erase; void push(T x) { q.push(move(x)); } template void emplace(Args&&... args) { q.emplace(forward(args)...); } void erase(T x) { q_erase.push(move(x)); } decltype(auto) top() { assert(!empty()); expose_top(); return q.top(); } void pop() { assert(!empty()); expose_top(); q.pop(); } int size() { return int(q.size()) - int(q_erase.size()); } bool empty() { return !size(); } void expose_top() { while (!q_erase.empty() && q_erase.top() == q.top()) { q_erase.pop(); q.pop(); } } }; template , class PQMin = priority_queue, greater>> struct SlopeTrick { static constexpr T INF = numeric_limits::max() / 3; T min_f = 0; // acutual value of x in L is ADD_add_L(x) = x + add_L T add_L = 0, add_R = 0; PQMax L; PQMin R; T top_L() { return L.empty() ? -INF : L.top() + add_L; } T top_R() { return R.empty() ? +INF : R.top() + add_R; } void push_L(T x) { L.push(x - add_L); } void push_R(T x) { R.push(x - add_R); } T pushpop_L(T x) { T L_max = top_L(); if (x >= L_max) return x; L.pop(); push_L(x); return L_max; } T pushpop_R(T x) { T R_min = top_R(); if (x <= R_min) return x; R.pop(); push_R(x); return R_min; } // f(x) += c void add_constant(T c) { min_f += c; } // f(x) += max(x - a, 0) void add_right_slope(T a) { min_f += max(top_L() - a, 0); push_R(pushpop_L(a)); } // f(x) += max(a - x, 0) void add_left_slope(T a) { min_f += max(a - top_R(), 0); push_L(pushpop_R(a)); } // f(x) += abs(x - a) void add_v(T a) { add_right_slope(a); add_left_slope(a); } void shift(T a, T b) { assert(a <= b); add_L += a; add_R += b; } void shift(T a) { shift(a, a); } // f(x) -= max(x - a, 0) void erase_right_slope(T a) { if (top_R() <= a) { R.erase(a - add_R); } else { min_f -= top_R() - a; L.erase(a - add_L); push_L(top_R()); R.pop(); } } // f(x) -= max(a - x, 0) void erase_left_slope(T a) { if (a <= top_L()) { L.erase(a - add_L); } else { min_f -= a - top_L(); R.erase(a - add_R); push_R(top_L()); L.pop(); } } // f(x) -= abs(x - a) void erase_v(T a) { erase_right_slope(a); erase_left_slope(a); } }; template using ErasableSlopeTrick = SlopeTrick < T, erasable_priority_queue, erasable_priority_queue>>; } int main() { ios::sync_with_stdio(false); cin.tie(0); int n, k; ll l, r; cin >> n >> k >> l >> r; r++; ErasableSlopeTrick st; vector> shift_slope; rep(_, n) { ll a; cin >> a; ll la = l - a, ra = r - a; auto lc = ceil_div(la, k); auto rc = ceil_div(ra, k) - 1; st.add_left_slope(lc); st.add_right_slope(rc); int nxt_l = la % k; if (nxt_l < 0) nxt_l += k; int nxt_r = ra % k; if (nxt_r < 0) nxt_r += k; if (nxt_l) shift_slope.emplace_back(nxt_l, 0, lc); if (nxt_r) shift_slope.emplace_back(nxt_r, 1, rc); } ll ans = st.min_f; sort(all(shift_slope), [](const auto& x, const auto& y) { return get<0>(x) > get<0>(y); }); rep(r, k) { if (shift_slope.empty()) break; r = get<0>(shift_slope.back()); while (shift_slope.size() && get<0>(shift_slope.back()) == r) { auto [_, t, a] = shift_slope.back(); shift_slope.pop_back(); if (!t) st.erase_left_slope(a), st.add_left_slope(a - 1); else st.erase_right_slope(a), st.add_right_slope(a - 1); } chmin(ans, st.min_f); } assert(shift_slope.empty()); cout << ans << '\n'; }