/**
 * date   : 2026-10-09 22:34:51
 * author : yamadanull
 */

// ===== BEGIN INCLUDE: ../../template/template.hpp =====

#include <bits/stdc++.h>
using namespace std;

// ===== BEGIN INCLUDE: util.hpp =====
namespace yamada {
using ll = long long;
using i32 = int;
using u32 = unsigned int;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
using lld = long double;

template <typename T>
using vc = vector<T>;
template <typename T>
using vvc = vector<vector<T>>;
template <typename T>
using vvvc = vector<vector<vector<T>>>;
template <typename T>
using vvvvc = vector<vector<vector<vector<T>>>>;
using vint = vector<int>;
using vl = vector<long long>;
using vd = vector<double>;
using vs = vector<string>;
using vvl = vector<vector<long long>>;
using vvvl = vector<vector<vector<long long>>>;
using vvvvl = vector<vector<vector<vector<long long>>>>;
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;
template <typename T>
using maxpq = priority_queue<T, vector<T>, less<T>>;

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

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

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

using pint = pr<int, int>;
using pl = pr<ll, ll>;
using vp = vc<pl>;
using vvp = vvc<pl>;

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

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

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, typename U>
pair<T, U> mkp(const T &t, const U &u) { return make_pair(t, u); }
template <typename... Args>
tuple<Args...> mkt(const Args&... args) { return make_tuple(args...); }

template <typename T>
inline long long Sum(const vector<T> &v) { return accumulate(v.begin(), v.end(), T(0)); }

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

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>
vector<T> mkrui(const vector<T> &v, const 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);
	ranges::sort(ret);
	ret.erase(ranges::unique(ret).begin(), ret.end());
	return ret;
}

template <typename F>
vector<int> mkord(int N, const F &f) {
	vector<int> ord = views::iota(0, N) | ranges::to<vector>();
	ranges::sort(ord, f);
	return ord;
}

template <typename T>
vector<int> mkinv(const vector<T> &v) {
	vector<int> inv(ranges::max(v) + 1, -1);
	for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
	return inv;
}

vector<int> mkiota(int N) { return views::iota(0, N) | ranges::to<vector>(); }

vector<int> p_mrg(const vector<int> &f, const vector<int> &g) { // g o f
	return f | views::transform([&](auto a) { return g[a]; }) | ranges::to<vector>();
}

template <typename T> // f: old_idx -> new_idx
vector<T> p_shf(const vector<T>& A, const vector<int>& f, const bool inv = false) {
	int n = A.size();
	vector<T> ret(n);
	if (!inv) for (int i = 0; i < n; i++) ret[f[i]] = A[i];
	else for (int i = 0; i < n; i++) ret[i] = A[f[i]];
	return ret;
}

template <typename T>
T mkrev(const T &v) { return v | views::reverse | ranges::to<vector>(); }

template <typename C>
bool nxp(C &v) { return ranges::next_permutation(v).found; }
template <typename F>
void nxp(int N, F f) {
	auto a = views::iota(0, N) | ranges::to<vector>();
	do { f(a); } while (nxp(a));
}

// i 要素目 : [0, A[i])
template <typename F>
void Product(const vector<int> &A, const F& f) {
	vector<int> cur;
	auto dfs = [&](this auto dfs, int i) -> void {
		if (i == (int)A.size()) { f(cur); return; }
		for (int j = 0; j < A[i]; j++) cur.emplace_back(j), dfs(i + 1), cur.pop_back();
	}; dfs(0);
}
// i 要素目 : [0, M)
template <typename F>
void Product(const int N, const int M, const F& f) { vector<int> A(N, M); Product(A, f); }

template <typename T, typename U>
vector<U> Digit(T a, const U &x, int siz = -1) {
	vector<U> ret;
	while (a > 0) {
		ret.emplace_back(a % x);
		a /= x;
	}
	if (siz >= 0) ret.resize(siz);
	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>
vector<T> Transpose(const vector<T> &A) {
	if (A.empty()) return {};
	return views::iota(0, (int)A[0].size()) | views::transform([&](auto j) {
		return A | views::transform([&](auto&& a) { return a[j]; }) | ranges::to<T>();
	}) | ranges::to<vector<T>>();
}

template <typename T>
vector<T> RotateGrid(const vector<T> &A) {
	if (A.empty()) return {};
	return views::iota(0, (int)A[0].size()) | views::transform([&](auto j) {
		return A | views::transform([&](auto&& a) { return a[j]; }) | ranges::to<T>();
	}) | views::reverse | ranges::to<vector<T>>();
}

template <typename T, typename F>
T bisect(T ok, T bad, F pred) {
	if (ok == bad) return ok;
	while (bad - ok > 1) { T mid = ok + (bad - ok) / 2; (pred(mid) ? ok : bad) = mid; } 
	return bad;
}

template <typename T, typename F>
T bisect_double(T ok, T bad, F pred, int iter = 100) {
	if (ok == bad) return ok;
	while (iter--) { T mid = ok + (bad - ok) / 2; (pred(mid) ? ok : bad) = mid; } 
	return bad;
}

template <typename T0, typename T1, typename T2>
bool inLR(T0 L, T1 x, T2 R){ return L <= x && x < R; }
bool YESNO(bool b) { cout << (b ? "YES\n" : "NO\n"); return b; }
bool YesNo(bool b) { cout << (b ? "Yes\n" : "No\n"); return b; }
bool yesno(bool b) { cout << (b ? "yes\n" : "no\n"); return b; }

long long Isqrt(long long n) {
	if (n <= 0) return 0;
	long long x = sqrt(n);
	while ((x + 1) * (x + 1) <= n) x++;
	while (x * x > n) x--;
	return x;
}

template <typename T>
struct CumulativeSum {
	vector<T> S;
	CumulativeSum(vector<T> &A) : S(A.size() + 1) {
		for (int i = 0; i < (int)A.size(); i++) S[i + 1] = S[i] + A[i];
	}
	T query(int l, int r) { return (l <= r ? S[r] - S[l] : T(0)); }
	T query() { return S.back(); }
	inline T operator()(int l, int r) { return query(l, r); }
	inline T operator()() { return query(); }
};

// 速度よりオーバーフロー対策優先
template <typename T>
T Floor(T a, T b) { assert(b != 0); if (b < 0) a = -a, b = -b; return a / b - (a % b < 0); }
template <typename T>
T Under(T a, T b) { assert(b != 0); if (b < 0) a = -a, b = -b; return a / b - (a % b <= 0); }
template <typename T>
T Ceil (T a, T b) { assert(b != 0); if (b < 0) a = -a, b = -b; return a / b + (a % b > 0); }
template <typename T>
T Over (T a, T b) { assert(b != 0); if (b < 0) a = -a, b = -b; return a / b + (a % b >= 0); }
template <typename T>
T Modulo(T a, T b) { assert(b > 0); T c = a % b; return c < 0 ? c + b : c; }

template <typename T>
pair<T, T> DivMod(T a, T b) {
	assert(b > 0);
	T q = a / b, r = a % b;
	if (r < 0) --q, r += b;
	return {q, r};
}

string rds() { string S; cin >> S; return S; }
int rdi() { int x; cin >> x; return x; }
char rdc() { char c; cin >> c; return c; }
long long rdl() { long long x; cin >> x; return x; }

template <typename mint, int iter = 1000>
string tof(const mint &a) {
	for (int deno = 1; deno <= iter; deno++) {
		mint inv = ((mint)deno).inverse();
		for (int nume = 0; nume <= iter; nume++) {
			mint val = inv * nume;
			if (val == a) {
				if (deno == 1) return to_string(nume);
				return to_string(nume) + "/" + to_string(deno);
			}
			else if (-val == a) {
				if (deno == 1) return to_string(-nume);
				return to_string(-nume) + "/" + to_string(deno);
			}
		}
	}
	return "!NF";
}

} // namespace yamada
// ===== END INCLUDE: util.hpp =====
// ===== BEGIN INCLUDE: bitop.hpp =====
namespace yamada {
__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 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; }

string tog(int msk, int N) {
	return views::iota(0, N) | views::transform([&](auto i) {
		return msk >> i & 1 ? '#' : '.';
	}) | ranges::to<string>();
}
}  // namespace yamada
// ===== END INCLUDE: bitop.hpp =====
// ===== BEGIN INCLUDE: io.hpp =====
namespace yamada {
istream &operator>>(istream &is, __int128_t &x) {
	string S; is >> S;
	x = 0;
	bool f{};
	for (auto &c : S) {
		if (c == '-') { f = 1; continue; }
		x *= 10;
		x += c - '0';
	}
	if (f) 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;
	ranges::reverse(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;
	ranges::reverse(S);
	return os << S;
}

template <class T> // tuple / pair / array
concept TupleLike = requires { tuple_size<remove_cvref_t<T>>::value; };
template <class R> // vector / set / ranges::view など（set は入力不可）
concept ListLike = ranges::input_range<R> && !convertible_to<R, string_view> && !TupleLike<R>;

template <TupleLike T> ostream& operator<<(ostream&, const T&);
template <TupleLike T> istream& operator>>(istream&, T&&);
template <ListLike  R> ostream& operator<<(ostream&, const R&);
template <ListLike  R> istream& operator>>(istream&, R&&);

template <TupleLike T>
ostream& operator<<(ostream& os, const T& t) {
	bool f{};
	apply([&](const auto&... x) {
		(..., (os << (exchange(f, 1) ? " " : "") << x));
	}, t);
	return os;
}
template <TupleLike T>
istream& operator>>(istream& is, T&& t) {
	apply([&](auto&... x) { (..., (is >> x)); }, t);
	return is;
}
template <ListLike R>
ostream& operator<<(ostream& os, const R& a) {
	bool f{};
	for (const auto& x : a) os << (exchange(f, 1) ? " " : "") << x;
	return os;
}
template <ListLike R>
istream& operator>>(istream& is, R&& a) {
	for (auto&& x : a) is >> x;
	return is;
}

template <class... T>
void IN(T&&... x) { (cin >> ... >> x); }
template <class... T>
void OUT (const T&... x) { bool f{}; (..., (cout << (exchange(f, 1) ? " " : "") << x)); cout << '\n'; }
template <class... T> // "Flush after OUT"
void FOUT(const T&... x) { bool f{}; (..., (cout << (exchange(f, 1) ? " " : "") << x)); cout << endl; }
template <class... T> // "WithOUT ln"
void WOUT(const T&... x) { bool f{}; (..., (cout << (exchange(f, 1) ? " " : "") << x)); }

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

namespace DebugImpl {

void dump(const char&   t) { cerr << t; }
void dump(const string& t) { cerr << t; }
void dump(const bool&   t) { cerr << (t ? "true" : "false"); }
void dump(__int128_t    t) { cerr << t; }
void dump(__uint128_t   t) { cerr << t; }

template <integral T>
void dump(const T& t) {
	string res;
	if (t == yamada::inf) res = "inf";
	if constexpr (is_signed<T>::value) {
		if (t == -yamada::inf) res = "-inf";
	}
	if constexpr (sizeof(T) == 8) {
		if (t == yamada::infLL) res = "inf";
		if constexpr (is_signed<T>::value) {
			if (t == -yamada::infLL) res = "-inf";
		}
	}
	if (res.empty()) res = to_string(t);
	cerr << res;
}

template <typename T>
requires (!ListLike<T> && !TupleLike<T> && !integral<T>)
void dump(const T& t) { cerr << t; }

template <ListLike  R> void dump(const R&);
template <TupleLike T> void dump(const T&);

template <ListLike R>
void dump(const R& a) {
	bool f{};
	for (const auto& x : a) {
		cerr << (exchange(f, 1) ? ", " : "[ ");
		dump(x);
	}
	cerr << " ]";
}

template <TupleLike T>
void dump(const T& t) {
	bool f{};
	apply([&](const auto&... x) {
		(..., (cerr << (exchange(f, 1) ? ", " : "( "), dump(x)));
	}, t);
	cerr << " )";
}

template <class... T>
void trace(const T&... x) {
	bool f{};
	(..., (cerr << (exchange(f, 1) ? ", " : " "), dump(x)));
	cerr << endl;
}

}  // namespace DebugImpl

}  // namespace yamada


#ifdef yamadaDebug
#define ERR(...) \
	do { \
		std::cerr << "## " << #__VA_ARGS__ << " = "; \
		yamada::DebugImpl::trace(__VA_ARGS__); \
	} while (0)
#else
#define ERR(...) (void(0))
#endif
// ===== END INCLUDE: io.hpp =====
// ===== BEGIN INCLUDE: ranges.hpp =====
namespace yamada {
constexpr auto All = ranges::all_of; // of なし (Python に合わせている）
constexpr auto Any = ranges::any_of; // 同上
constexpr auto BinarySearch = ranges::binary_search;
constexpr auto Contains = ranges::contains;
constexpr auto Copy = ranges::copy;
constexpr auto Count = ranges::count;
constexpr auto CountIf = ranges::count_if;
constexpr auto Fill = ranges::fill;
constexpr auto Find = ranges::find;
constexpr auto FindIf = ranges::find_if;
constexpr auto FoldLeft = ranges::fold_left;
constexpr auto FoldRight = ranges::fold_right;
constexpr auto IsSorted = ranges::is_sorted;
constexpr auto IsSortedUntil = ranges::is_sorted_until;
constexpr auto LowerBound = ranges::lower_bound;
constexpr auto Max = ranges::max;
constexpr auto MaxElement = ranges::max_element;
constexpr auto Min = ranges::min;
constexpr auto MinElement = ranges::min_element;
constexpr auto MinMax = ranges::minmax;
constexpr auto MinMaxElement = ranges::minmax_element;
constexpr auto Reverse = ranges::reverse;
constexpr auto Rotate = ranges::rotate;
constexpr auto Sort = ranges::sort;
constexpr auto UpperBound = ranges::upper_bound;

template <int K>
constexpr auto Adjacent = views::adjacent<K>;
constexpr auto Chunk = views::chunk;
constexpr auto Drop = views::drop;
constexpr auto DropWhile = views::drop_while;
constexpr auto Enumerate = views::enumerate;
constexpr auto Filter = views::filter;
constexpr auto Join = views::join;
constexpr auto Slide = views::slide;
constexpr auto Stride = views::stride;
constexpr auto Take = views::take;
constexpr auto TakeWhile = views::take_while;
constexpr auto Zip = views::zip;

constexpr auto Rev = views::reverse; // ranges の方と混同しない
constexpr auto Transform = views::transform; // ranges の方は多分使わない
constexpr auto Iota = views::iota; // ranges の方は多分使わない

constexpr auto rtov = ranges::to<vector>();
constexpr auto rtos = ranges::to<string>();

namespace rg = ranges;
namespace vw = views;
using namespace placeholders;
} // namespace yamada
// ===== END INCLUDE: ranges.hpp =====
// ===== BEGIN INCLUDE: macro.hpp =====
#define FOR_E1(x, v) for (auto&& x : v)
#define FOR_E2(x, y, v) for (auto&& [x, y] : v)
#define FOR_E3(x, y, z, v) for (auto&& [x, y, z] : v)
#define FOR_E4(x, y, z, w, v) for (auto&& [x, y, z, w] : v)
#define OVERLOAD5(a, b, c, d, e, f, ...) f
#define FOR_E(...) OVERLOAD5(__VA_ARGS__, FOR_E4, FOR_E3, FOR_E2, FOR_E1)(__VA_ARGS__)

#define FOR1(a) for (long long _ = 0; _ < (long long)(a); ++_)
#define FOR2(i, a) for (long long i = 0; i < (long long)(a); ++i)
#define FOR3(i, a, b) for (long long i = a; i < (long long)(b); ++i)
#define FOR4(i, a, b, c) for (long long i = a; i < (long long)(b); i += c)
#define OVERLOAD4(a, b, c, d, e, ...) e
#define FOR(...) OVERLOAD4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)

#define FOR_R1(a) for (long long i = (long long)(a)-1; i >= 0LL; --i)
#define FOR_R2(i, a) for (long long i = (long long)(a)-1; i >= 0LL; --i)
#define FOR_R3(i, a, b) for (long long i = (long long)(b)-1; i >= (long long)(a); --i)
#define OVERLOAD3(a, b, c, d, ...) d
#define FOR_R(...) OVERLOAD3(__VA_ARGS__, FOR_R3, FOR_R2, FOR_R1)(__VA_ARGS__)

#define eb emplace_back
#define pb push_back
#define fi first
#define se second

#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__))))

#define CHAR(...) char __VA_ARGS__; IN(__VA_ARGS__)
#define INT(...) int __VA_ARGS__; IN(__VA_ARGS__)
#define LL(...) long long __VA_ARGS__; IN(__VA_ARGS__)
#define STR(...) std::string __VA_ARGS__; IN(__VA_ARGS__)
#define ZIN(...) for (auto&& [__VA_ARGS__] : std::views::zip(__VA_ARGS__)) IN(__VA_ARGS__)
#define DIE(...) do { yamada::OUT(__VA_ARGS__); return; } while (0)
// ===== END INCLUDE: macro.hpp =====

namespace yamada {
void solve();
}
int main() { yamada::solve(); }
// ===== END INCLUDE: ../../template/template.hpp =====
// ===== BEGIN INCLUDE: ../../segment-tree/lazy-segment-tree-utility.hpp =====

// ===== BEGIN INCLUDE: ../monoid/add-max.hpp =====

// ===== BEGIN INCLUDE: add.hpp =====

namespace MONOID {

template <typename E>
struct Add {
	using value_type = E;
	static constexpr value_type O(const value_type& x, const value_type& y) noexcept { return x + y; }
	static constexpr value_type inverse(const value_type &x) noexcept { return -x; }
	static constexpr value_type power(const value_type& x, long long n) noexcept { return value_type(n) * x; }
	static constexpr value_type I() { return value_type(0); }
	static constexpr bool COMMUTATIVE = true;
};

} // namespace monoid
// ===== END INCLUDE: add.hpp =====
// ===== BEGIN INCLUDE: max.hpp =====

#include <algorithm>
#include <limits>

namespace MONOID {

template <typename E, E MNF = std::numeric_limits<E>::min()>
struct Max {
	using value_type = E;
	static constexpr value_type O(const value_type& x, const value_type& y) { return std::max(x, y); }
	static constexpr value_type I() { return MNF; }
	static constexpr bool COMMUTATIVE = true;
};

} // namespace monoid
// ===== END INCLUDE: max.hpp =====

namespace ACTED_MONOID {

template <typename E, E MNF = std::numeric_limits<E>::min()>
struct Add_Max {
	using Monoid_X = MONOID::Max<E, MNF>;
	using Monoid_A = MONOID::Add<E>;
	using X = typename Monoid_X::value_type; // E
	using A = typename Monoid_A::value_type; // E
	static constexpr X O(const X& x, const A& a, const long long) {
		return x == MNF ? x : x + a;
	}
};

} // namespace ACTED_MONOID

// ===== END INCLUDE: ../monoid/add-max.hpp =====
// ===== BEGIN INCLUDE: ../monoid/add-min.hpp =====

// ===== BEGIN INCLUDE: min.hpp =====

#include <algorithm>
#include <limits>

namespace MONOID {

template <typename E, E INF = std::numeric_limits<E>::max()>
struct Min {
	using value_type = E;
	static constexpr value_type O(const value_type& x, const value_type& y) { return std::min(x, y); }
	static constexpr value_type I() { return INF; }
	static constexpr bool COMMUTATIVE = true;
};

} // namespace monoid
// ===== END INCLUDE: min.hpp =====

namespace ACTED_MONOID {

template <typename E, E INF = std::numeric_limits<E>::max()>
struct Add_Min {
	using Monoid_X = MONOID::Min<E, INF>;
	using Monoid_A = MONOID::Add<E>;
	using X = typename Monoid_X::value_type; // E
	using A = typename Monoid_A::value_type; // E
	static constexpr X O(const X& x, const A& a, const long long) { return x + a; }
};

} // namespace ACTED_MONOID

// ===== END INCLUDE: ../monoid/add-min.hpp =====
// ===== BEGIN INCLUDE: ../monoid/add-sum.hpp =====


namespace ACTED_MONOID {

template <typename E>
struct Add_Sum {
	using Monoid_X = MONOID::Add<E>;
	using Monoid_A = MONOID::Add<E>;
	using X = typename Monoid_X::value_type; // E
	using A = typename Monoid_A::value_type; // E
	static constexpr X O(const X& x, const A& a, const long long &size) {
		return x + a * E(size);
	}
};

} // namespace ACTED_MONOID

// ===== END INCLUDE: ../monoid/add-sum.hpp =====
// ===== BEGIN INCLUDE: ../monoid/update-max.hpp =====

// ===== BEGIN INCLUDE: update.hpp =====

#include <optional>

namespace MONOID {

template <typename T>
struct Update {
	using value_type = std::optional<T>;
	static constexpr value_type O(const value_type& x, const value_type& y) { return y.has_value() ? y : x; }
	static constexpr value_type I() { return std::nullopt; }
	static constexpr bool COMMUTATIVE = false;
};

} // namespace monoid
// ===== END INCLUDE: update.hpp =====

namespace ACTED_MONOID {

template <typename E, E MNF = std::numeric_limits<E>::min()>
struct Update_Max {
	using Monoid_X = MONOID::Max<E, MNF>;
	using Monoid_A = MONOID::Update<E>;
	using X = typename Monoid_X::value_type; // E
	using A = typename Monoid_A::value_type; // optional<E>
	static constexpr X O(const X& x, A& a, const long long) {
		return a.has_value() ? a.value() : x;
	}
};

} // namespace ACTED_MONOID

// ===== END INCLUDE: ../monoid/update-max.hpp =====
// ===== BEGIN INCLUDE: ../monoid/update-min.hpp =====


namespace ACTED_MONOID {

template <typename E, E INF = std::numeric_limits<E>::max()>
struct Update_Min {
	using Monoid_X = MONOID::Min<E, INF>;
	using Monoid_A = MONOID::Update<E>;
	using X = typename Monoid_X::value_type; // E
	using A = typename Monoid_A::value_type; // optional<E>
	static constexpr X O(const X& x, const A& a, const long long) {
		return a.has_value() ? a : x;
	}
};

} // namespace ACTED_MONOID

// ===== END INCLUDE: ../monoid/update-min.hpp =====
// ===== BEGIN INCLUDE: ../monoid/update-sum.hpp =====


namespace ACTED_MONOID {

template <typename E>
struct Update_Sum {
	using Monoid_X = MONOID::Add<E>;
	using Monoid_A = MONOID::Update<E>;
	using X = typename Monoid_X::value_type; // E
	using A = typename Monoid_A::value_type; // optional<E>
	static constexpr X O(const X& x, const A& a, const long long &size) {
		return a.has_value() ? a.value() * E(size) : x;
	}
};

} // namespace ACTED_MONOID

// ===== END INCLUDE: ../monoid/update-sum.hpp =====
// ===== BEGIN INCLUDE: segment-tree.hpp =====
#include <algorithm>
#include <cassert>
#include <vector>

template <typename Monoid>
struct SegmentTree {
	using X = typename Monoid::value_type;
	std::vector<X> dat;
	int N, LOG, size;

	SegmentTree() {}
	SegmentTree(int N) { build(N); }
	template <typename F>
	SegmentTree(int N, F init) { build(N, init); }
	template <std::ranges::input_range R>
	SegmentTree(const R& v) { build(v); }

	void build(int m) {
		build(m, [](int i) -> X { return Monoid::I(); });
	}
	template <std::ranges::input_range R>
	void build(const R& v) {
		build(v.size(), [&](int i) -> X { return v[i]; });
	}
	template <typename F>
	void build(int m, F init) {
		N = m, LOG = 1;
		while ((1 << LOG) < N) ++LOG;
		size = 1 << LOG;
		dat.assign(size << 1, Monoid::I());
		for (int i = 0; i < N; i++) dat[size + i] = init(i);
		for (int i = size - 1; i >= 1; i--) update(i);
	}

	X get(int i) const { return dat[size + i]; }
	std::vector<X> get() const { return {dat.begin() + size, dat.begin() + size + N}; }

	void update(int i) { dat[i] = Monoid::O(dat[2 * i], dat[2 * i + 1]); }
	void set(int i, const X x) {
		assert(i < N);
		dat[i += size] = x;
		while (i >>= 1) update(i);
	}

	void multiply(int i, const X x) {
		assert(i < N);
		i += size;
		dat[i] = Monoid::O(dat[i], x);
		while (i >>= 1) update(i);
	}

	X prod(int L, int R) const {
		assert(0 <= L && L <= R && R <= N);
		X vl = Monoid::I(), vr = Monoid::I();
		L += size, R += size;
		while (L < R) {
			if (L & 1) vl = Monoid::O(vl, dat[L++]);
			if (R & 1) vr = Monoid::O(dat[--R], vr);
			L >>= 1, R >>= 1;
		}
		return Monoid::O(vl, vr);
	}

	std::vector<int> prod_ids(int L, int R) const {
		assert(0 <= L && L <= R && R <= N);
		std::vector<int> I, J;
		L += size, R += size;
		while (L < R) {
			if (L & 1) I.emplace_back(L++);
			if (R & 1) J.emplace_back(--R);
			L >>= 1, R >>= 1;
		}
		std::ranges::reverse(J);
		I.resize(I.size() + J.size());
		for (int j = 0; j < (int)J.size(); j++) I[(int)I.size() - (int)J.size() + j] = J[j];
		return I;
	}

	X prod() const { return dat[1]; }
	template <typename... Args>
	X operator()(Args... args) { return prod(args...); }
	template <typename... Args>
	X operator[](Args... args) { return get(args...); }

	template <typename F>
	int max_right(int L, F check) const {
		assert(0 <= L && L <= N && check(Monoid::I()));
		if (L == N) return N;
		L += size;
		X sm = Monoid::I();
		do {
			while (L % 2 == 0) L >>= 1;
			if (!check(Monoid::O(sm, dat[L]))) {
				while (L < size) {
					L = 2 * L;
					if (check(Monoid::O(sm, dat[L]))) {
						sm = Monoid::O(sm, dat[L++]);
					}
				}
				return L - size;
			}
			sm = Monoid::O(sm, dat[L++]);
		} while ((L & -L) != L);
		return N;
	}

	template <typename F>
	int min_left(int R, F check) const {
		assert(0 <= R && R <= N && check(Monoid::I()));
		if (R == 0) return 0;
		R += size;
		X sm = Monoid::I();
		do {
			--R;
			while (R > 1 && (R % 2)) R >>= 1;
			if (!check(Monoid::O(dat[R], sm))) {
				while (R < size) {
					R = 2 * R + 1;
					if (check(Monoid::O(dat[R], sm))) {
						sm = Monoid::O(dat[R--], sm);
					}
				}
				return R + 1 - size;
			}
			sm = Monoid::O(dat[R], sm);
		} while ((R & -R) != R);
		return 0;
	}

	// prod_{l<=i<r} A[i xor x]
	X xor_prod(int l, int r, int xor_val) const {
		static_assert(Monoid::COMMUTATIVE);
		X x = Monoid::I();
		for (int k = 0; k < LOG + 1; ++k) {
			if (l >= r) break;
			if (l & 1) {
				x = Monoid::O(x, dat[(size >> k) + ((l++) ^ xor_val)]);
			}
			if (r & 1) {
				x = Monoid::O(x, dat[(size >> k) + ((--r) ^ xor_val)]);
			}
			l /= 2, r /= 2, xor_val /= 2;
		}
		return x;
	}
};
// ===== END INCLUDE: segment-tree.hpp =====
// ===== BEGIN INCLUDE: lazy-segment-tree.hpp =====
#include <vector>
#include <cassert>

template <typename ActedMonoid>
struct LazySegmentTree {
	using MX = typename ActedMonoid::Monoid_X;
	using MA = typename ActedMonoid::Monoid_A;
	using X = typename MX::value_type;
	using A = typename MA::value_type;
	int N, LOG, size;
	std::vector<X> dat;
	std::vector<A> laz;
	std::vector<bool> has_laz;

	LazySegmentTree() {}
	LazySegmentTree(int N) { build(N); }
	template <typename F>
	LazySegmentTree(int N, F init) { build(N, init); }
	template <std::ranges::input_range R>
	LazySegmentTree(const R& v) { build(v); }

	void build(int m) {
		build(m, [](int i) -> X { return MX::I(); });
	}
	template <std::ranges::input_range R>
	void build(const R& v) {
		build(v.size(), [&](int i) -> X { return v[i]; });
	}
	template <typename F>
	void build(int m, F init) {
		N = m, LOG = 1;
		while ((1 << LOG) < N) ++LOG;
		size = 1 << LOG;
		dat.assign(size << 1, MX::I());
		laz.assign(size, MA::I());
		has_laz.assign(size, false);
		for (int i = 0; i < N; i++) dat[size + i] = init(i);
		for (int i = size - 1; i >= 1; i--) update(i);
	}

	void update(int k) { dat[k] = MX::O(dat[2 * k], dat[2 * k + 1]); }
	void set(int p, X x) {
		assert(0 <= p && p < N);
		p += size;
		for (int i = LOG; i >= 1; i--) push(p >> i);
		dat[p] = x;
		for (int i = 1; i <= LOG; i++) update(p >> i);
	}
	void multiply(int p, const X& x) {
		assert(0 <= p && p < N);
		p += size;
		for (int i = LOG; i >= 1; i--) push(p >> i);
		dat[p] = MX::O(dat[p], x);
		for (int i = 1; i <= LOG; i++) update(p >> i);
	}

	X get(int p) {
		assert(0 <= p && p < N);
		p += size;
		for (int i = LOG; i >= 1; i--) push(p >> i);
		return dat[p];
	}

	std::vector<X> get() {
		for (int k = 0; k < size; k++) push(k);
		return {dat.begin() + size, dat.begin() + size + N};
	}

	X prod(int l, int r) {
		assert(0 <= l && l <= r && r <= N);
		if (l == r) return MX::I();
		l += size, r += size;
		for (int i = LOG; i >= 1; i--) {
			if (((l >> i) << i) != l) push(l >> i);
			if (((r >> i) << i) != r) push((r - 1) >> i);
		}
		X xl = MX::I(), xr = MX::I();
		while (l < r) {
			if (l & 1) xl = MX::O(xl, dat[l++]);
			if (r & 1) xr = MX::O(dat[--r], xr);
			l >>= 1, r >>= 1;
		}
		return MX::O(xl, xr);
	}

	X prod() { return dat[1]; }
	template <typename... Args>
	X operator()(Args... args) { return prod(args...); }
	template <typename... Args>
	X operator[](Args... args) { return get(args...); }

	void apply(int l, int r, A a) {
		assert(0 <= l && l <= r && r <= N);
		if (l == r) return;
		l += size, r += size;
		for (int i = LOG; i >= 1; i--) {
			if (((l >> i) << i) != l) push(l >> i);
			if (((r >> i) << i) != r) push((r - 1) >> i);
		}
		int l2 = l, r2 = r;
		while (l < r) {
			if (l & 1) apply_at(l++, a);
			if (r & 1) apply_at(--r, a);
			l >>= 1, r >>= 1;
		}
		l = l2, r = r2;
		for (int i = 1; i <= LOG; i++) {
			if (((l >> i) << i) != l) update(l >> i);
			if (((r >> i) << i) != r) update((r - 1) >> i);
		}
	}

	template <typename F>
	int max_right(int l, const F check) {
		assert(0 <= l && l <= N);
		assert(check(MX::I()));
		if (l == N) return N;
		l += size;
		for (int i = LOG; i >= 1; i--) push(l >> i);
		X sm = MX::I();
		do {
			while (l % 2 == 0) l >>= 1;
			if (!check(MX::O(sm, dat[l]))) {
				while (l < size) {
					push(l);
					l = (2 * l);
					if (check(MX::O(sm, dat[l]))) {
						sm = MX::O(sm, dat[l++]);
					}
				}
				return l - size;
			}
			sm = MX::O(sm, dat[l++]);
		} while ((l & -l) != l);
		return N;
	}

	template <typename F>
	int min_left(int r, const F check) {
		assert(0 <= r && r <= N);
		assert(check(MX::I()));
		if (r == 0) return 0;
		r += size;
		for (int i = LOG; i >= 1; i--) push((r - 1) >> i);
		X sm = MX::I();
		do {
			r--;
			while (r > 1 && (r % 2)) r >>= 1;
			if (!check(MX::O(dat[r], sm))) {
				while (r < size) {
					push(r);
					r = (2 * r + 1);
					if (check(MX::O(dat[r], sm))) {
						sm = MX::O(dat[r--], sm);
					}
				}
				return r + 1 - size;
			}
			sm = MX::O(dat[r], sm);
		} while ((r & -r) != r);
		return 0;
	}

	// l <= i xor (xor_val) < r となる i 全体に apply
	void apply_xor_range(int l, int r, int xor_val, A a) {
		assert(!(N & (N - 1)));
		assert(0 <= xor_val && xor_val < N);
		assert(0 <= l && l <= r && r <= N);

		auto dfs = [&](auto& dfs, int idx, int seg_l, int seg_r) -> void {
			if (l <= seg_l && seg_r <= r) {
				return apply_at(idx, a);
			}
			if (r <= seg_l || seg_r <= l) return;
			push(idx);
			int seg_m = (seg_l + seg_r) / 2;
			int bit = (seg_r - seg_l) / 2;
			int left = 2 * idx + 0, right = 2 * idx + 1;
			if (xor_val & bit) std::swap(left, right);
			dfs(dfs, left, seg_l, seg_m);
			dfs(dfs, right, seg_m, seg_r);
			update(idx);
		};
		dfs(dfs, 1, 0, N);
	}

	private:
	inline int msb(const int &a) { return a ? 31 - __builtin_clz(a) : -1; }
	void apply_at(int k, A a) {
		long long sz = 1 << (LOG - msb(k));
		dat[k] = ActedMonoid::O(dat[k], a, sz);
		if (k < size) has_laz[k] = 1, laz[k] = MA::O(laz[k], a);
	}
	void push(int k) {
		if (!has_laz[k]) return;
		has_laz[k] = 0;
		apply_at(2 * k, laz[k]), apply_at(2 * k + 1, laz[k]);
		laz[k] = MA::I();
	}
};
// ===== END INCLUDE: lazy-segment-tree.hpp =====

template <typename T>
using sum_segtree = SegmentTree<MONOID::Add<T>>;
template <typename T>
using min_segtree = SegmentTree<MONOID::Min<T>>;
template <typename T>
using max_segtree = SegmentTree<MONOID::Max<T>>;

template <typename T>
using addmax_lazyseg = LazySegmentTree<ACTED_MONOID::Add_Max<T>>;
template <typename T>
using addmin_lazyseg = LazySegmentTree<ACTED_MONOID::Add_Min<T>>;
template <typename T>
using addsum_lazyseg = LazySegmentTree<ACTED_MONOID::Add_Sum<T>>;
template <typename T>
using updatemax_lazyseg = LazySegmentTree<ACTED_MONOID::Update_Max<T>>;
template <typename T>
using updatemin_lazyseg = LazySegmentTree<ACTED_MONOID::Update_Min<T>>;
template <typename T>
using updatesum_lazyseg = LazySegmentTree<ACTED_MONOID::Update_Sum<T>>;

// ===== END INCLUDE: ../../segment-tree/lazy-segment-tree-utility.hpp =====

void yamada::solve()
{
	LL(N,B,C);
	vl A(N); IN(A);
	if(C==N+1)DIE(Sum(A));
	auto D=mkrui(A);

	max_segtree<ll> seg(N); // dp[i] - D[i+1]
	FOR(i,N){
		ll d=(i<C? D[i]:-infLL); // 初めて休む場合
		ll L=max(0LL,i-C);
		ll R=(B==2?i-1:i);
		if(L<R){
			ERR(L,R);
			amax(d,seg(L,R)+D[i]);
		}
		ERR(i,L,R,d);
		seg.set(i,d-D[i+1]);
	}

	OUT(seg(max(0LL,N-C),N)+D[N]);
}