#line 1 "a.cpp"
#line 2 "/home/nok0/documents/programming/library/template/header.hpp"
#include <bits/stdc++.h>
#line 3 "/home/nok0/documents/programming/library/template/def_const.hpp"

const int inf = 1000000000;
const long long INF = 1000000000000000000ll;
#line 4 "/home/nok0/documents/programming/library/template/debug.hpp"

namespace viewer {
void view(const long long &e) {
	if(e == INF)
		std::cerr << "INF";
	else if(e == -INF)
		std::cerr << "-INF";
	else
		std::cerr << e;
}

void view(const int &e) {
	if(e == inf)
		std::cerr << "inf";
	else if(e == -inf)
		std::cerr << "-inf";
	else
		std::cerr << e;
}

template <typename T>
void view(const T &e) {
	std::cerr << e;
}

template <typename T, typename U>
void view(const std::pair<T, U> &p) {
	std::cerr << "(";
	view(p.first);
	std::cerr << ", ";
	view(p.second);
	std::cerr << ")";
}

template <class T0, class T1, class T2>
void view(const std::tuple<T0, T1, T2> &p) {
	std::cerr << "(";
	view(std::get<0>(p));
	std::cerr << ", ";
	view(std::get<1>(p));
	std::cerr << ", ";
	view(std::get<2>(p));
	std::cerr << ")";
}

template <class T0, class T1, class T2, class T3>
void view(const std::tuple<T0, T1, T2, T3> &p) {
	std::cerr << "(";
	view(std::get<0>(p));
	std::cerr << ", ";
	view(std::get<1>(p));
	std::cerr << ", ";
	view(std::get<2>(p));
	std::cerr << ", ";
	view(std::get<3>(p));
	std::cerr << ")";
}

template <typename T>
void view(const std::set<T> &s) {
	if(s.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << "{ ";
	for(auto &t : s) {
		view(t);
		std::cerr << ", ";
	}
	std::cerr << "\b\b }";
}

template <typename T>
void view(const std::unordered_set<T> &s) {
	if(s.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << "{ ";
	for(auto &t : s) {
		view(t);
		std::cerr << ", ";
	}
	std::cerr << "\b\b }";
}

template <typename T>
void view(const std::multiset<T> &s) {
	if(s.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << "{ ";
	for(auto &t : s) {
		view(t);
		std::cerr << ", ";
	}
	std::cerr << "\b\b }";
}

template <typename T>
void view(const std::unordered_multiset<T> &s) {
	if(s.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << "{ ";
	for(auto &t : s) {
		view(t);
		std::cerr << ", ";
	}
	std::cerr << "\b\b }";
}

template <typename T>
void view(const std::vector<T> &v) {
	if(v.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << "{ ";
	for(const auto &e : v) {
		view(e);
		std::cerr << ", ";
	}
	std::cerr << "\b\b }";
}

template <typename T, std::size_t ary_size>
void view(const std::array<T, ary_size> &v) {
	if(v.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << "{ ";
	for(const auto &e : v) {
		view(e);
		std::cerr << ", ";
	}
	std::cerr << "\b\b }";
}

template <typename T>
void view(const std::vector<std::vector<T>> &vv) {
	std::cerr << "{\n";
	for(const auto &v : vv) {
		std::cerr << "\t";
		view(v);
		std::cerr << '\n';
	}
	std::cerr << "}";
}

template <typename T, typename U>
void view(const std::vector<std::pair<T, U>> &v) {
	std::cerr << "{\n";
	for(const auto &c : v) {
		std::cerr << "\t(";
		view(c.first);
		std::cerr << ", ";
		view(c.second);
		std::cerr << ")\n";
	}
	std::cerr << "}";
}

template <class T0, class T1, class T2>
void view(const std::vector<std::tuple<T0, T1, T2>> &v) {
	if(v.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << '{';
	for(const auto &t : v) {
		std::cerr << "\n\t";
		view(t);
		std::cerr << ",";
	}
	std::cerr << "\n}";
}

template <class T0, class T1, class T2, class T3>
void view(const std::vector<std::tuple<T0, T1, T2, T3>> &v) {
	if(v.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << '{';
	for(const auto &t : v) {
		std::cerr << "\n\t";
		view(t);
		std::cerr << ",";
	}
	std::cerr << "\n}";
}

template <typename T, typename U>
void view(const std::map<T, U> &m) {
	std::cerr << "{\n";
	for(const auto &t : m) {
		std::cerr << "\t[";
		view(t.first);
		std::cerr << "] : ";
		view(t.second);
		std::cerr << '\n';
	}
	std::cerr << "}";
}

template <typename T, typename U>
void view(const std::unordered_map<T, U> &m) {
	std::cerr << "{\n";
	for(const auto &t : m) {
		std::cerr << "\t[";
		view(t.first);
		std::cerr << "] : ";
		view(t.second);
		std::cerr << '\n';
	}
	std::cerr << "}";
}
}  // namespace viewer

// when compiling : g++ foo.cpp -DLOCAL
#ifdef LOCAL
void debug_out() {}
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
	viewer::view(H);
	std::cerr << ", ";
	debug_out(T...);
}
#define debug(...)                                                \
	do {                                                          \
		std::cerr << __LINE__ << " [" << #__VA_ARGS__ << "] : ["; \
		debug_out(__VA_ARGS__);                                   \
		std::cerr << "\b\b]\n";                                   \
	} while(0)
#define dump(x)                                      \
	do {                                             \
		std::cerr << __LINE__ << " " << #x << " : "; \
		viewer::view(x);                             \
		std::cerr << '\n';                           \
	} while(0)

#else
#define debug(...) (void(0))
#define dump(x)    (void(0))
#endif
#line 3 "/home/nok0/documents/programming/library/template/def_name.hpp"

#define pb        push_back
#define eb        emplace_back
#define fi        first
#define se        second
#define SZ(x)     ((int)(x).size())
#define all(x)    (x).begin(), (x).end()
#define rall(x)   (x).rbegin(), (x).rend()
#define popcnt(x) __builtin_popcountll(x)
template <class T = int>
using V = std::vector<T>;
template <class T = int>
using VV = std::vector<std::vector<T>>;
template <class T>
using pqup = std::priority_queue<T, std::vector<T>, std::greater<T>>;
using ll = long long;
using ld = long double;
using int128 = __int128_t;
using pii = std::pair<int, int>;
using pll = std::pair<long long, long long>;
#line 3 "/home/nok0/documents/programming/library/template/fast_io.hpp"

struct fast_io {
	fast_io() {
		std::ios::sync_with_stdio(false);
		std::cin.tie(nullptr);
		std::cout << std::fixed << std::setprecision(15);
	}
} fast_io_;
#line 3 "/home/nok0/documents/programming/library/template/input.hpp"

template <class T, class U>
std::istream &operator>>(std::istream &is, std::pair<T, U> &p) {
	is >> p.first >> p.second;
	return is;
}
template <class T>
std::istream &operator>>(std::istream &is, std::vector<T> &v) {
	for(T &i : v) is >> i;
	return is;
}
std::istream &operator>>(std::istream &is, __int128_t &a) {
	std::string s;
	is >> s;
	__int128_t ret = 0;
	for(int i = 0; i < (int)s.length(); i++)
		if('0' <= s[i] and s[i] <= '9')
			ret = 10 * ret + s[i] - '0';
	a = ret * (s[0] == '-' ? -1 : 1);
	return is;
}
namespace scanner {
void scan(int &a) { std::cin >> a; }
void scan(long long &a) { std::cin >> a; }
void scan(std::string &a) { std::cin >> a; }
void scan(char &a) { std::cin >> a; }
void scan(char a[]) { std::ignore = std::scanf("%s", a); }
void scan(double &a) { std::cin >> a; }
void scan(long double &a) { std::cin >> a; }
template <class T, class U>
void scan(std::pair<T, U> &p) { std::cin >> p; }
template <class T>
void scan(std::vector<T> &a) { std::cin >> a; }
void INPUT() {}
template <class Head, class... Tail>
void INPUT(Head &head, Tail &...tail) {
	scan(head);
	INPUT(tail...);
}
}  // namespace scanner
#define VEC(type, name, size)     \
	std::vector<type> name(size); \
	scanner::INPUT(name)
#define VVEC(type, name, h, w)                                    \
	std::vector<std::vector<type>> name(h, std::vector<type>(w)); \
	scanner::INPUT(name)
#define INT(...)     \
	int __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define LL(...)            \
	long long __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define STR(...)             \
	std::string __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define CHAR(...)     \
	char __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define DOUBLE(...)     \
	double __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define LD(...)              \
	long double __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#line 3 "/home/nok0/documents/programming/library/template/math.hpp"

template <class T, class U>
inline bool chmin(T &a, const U &b) { return a > b ? a = b, true : false; }
template <class T, class U>
inline bool chmax(T &a, const U &b) { return a < b ? a = b, true : false; }
template <class T>
T divup(T x, T y) { return (x + y - 1) / y; }
template <class T>
T POW(T a, long long n) {
	T ret = 1;
	while(n) {
		if(n & 1) ret *= a;
		a *= a;
		n >>= 1;
	}
	return ret;
}
long long POW(long long a, long long n, const int mod) {
	long long ret = 1;
	a = (a % mod + mod) % mod;
	while(n) {
		if(n & 1) (ret *= a) %= mod;
		(a *= a) %= mod;
		n >>= 1;
	}
	return ret;
}
template <class T, class F>
T bin_search(T ok, T ng, const F &f) {
	while(abs(ok - ng) > 1) {
		T mid = (ok + ng) >> 1;
		(f(mid) ? ok : ng) = mid;
	}
	return ok;
}
template <class T, class F>
T bin_search(T ok, T ng, const F &f, int loop) {
	for(int i = 0; i < loop; i++) {
		T mid = (ok + ng) / 2;
		(f(mid) ? ok : ng) = mid;
	}
	return ok;
}
#line 3 "/home/nok0/documents/programming/library/template/output.hpp"


template <class T, class U>
std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &p) {
	os << p.first << " " << p.second;
	return os;
}
template <class T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &a) {
	for(int i = 0; i < int(a.size()); ++i) {
		if(i) os << " ";
		os << a[i];
	}
	return os;
}
std::ostream &operator<<(std::ostream &dest, __int128_t &value) {
	std::ostream::sentry s(dest);
	if(s) {
		__uint128_t tmp = value < 0 ? -value : value;
		char buffer[128];
		char *d = std::end(buffer);
		do {
			--d;
			*d = "0123456789"[tmp % 10];
			tmp /= 10;
		} while(tmp != 0);
		if(value < 0) {
			--d;
			*d = '-';
		}
		int len = std::end(buffer) - d;
		if(dest.rdbuf()->sputn(d, len) != len) {
			dest.setstate(std::ios_base::badbit);
		}
	}
	return dest;
}
template <class T>
void print(const T a) { std::cout << a << '\n'; }
template <class Head, class... Tail>
void print(Head H, Tail... T) {
	std::cout << H << ' ';
	print(T...);
}
template <class T>
void println(const T a) { std::cout << a << '\n'; }
template <class T>
void println(const std::vector<T> &a) {
	for(const auto &v : a)
		std::cout << v << '\n';
}
template <class Head, class... Tail>
void println(Head H, Tail... T) {
	std::cout << H << '\n';
	println(T...);
}
void Yes(const bool b = true) { std::cout << (b ? "Yes\n" : "No\n"); }
void No() { std::cout << "No\n"; }
void YES(const bool b = true) { std::cout << (b ? "YES\n" : "NO\n"); }
void NO() { std::cout << "NO\n"; }
#line 2 "/home/nok0/documents/programming/library/template/rep.hpp"

#define foa(v, a)                   for(auto &v : a)
#define repname(a, b, c, d, e, ...) e
#define rep(...)                    repname(__VA_ARGS__, rep3, rep2, rep1, rep0)(__VA_ARGS__)
#define rep0(x)                     for(int rep_counter = 0; rep_counter < (x); ++rep_counter)
#define rep1(i, x)                  for(int i = 0; i < (x); ++i)
#define rep2(i, l, r)               for(int i = (l); i < (r); ++i)
#define rep3(i, l, r, c)            for(int i = (l); i < (r); i += (c))

#define repsname(a, b, c, ...) c
#define reps(...)              repsname(__VA_ARGS__, reps1, reps0)(__VA_ARGS__)
#define reps0(x)               for(int reps_counter = 1; reps_counter <= (x); ++reps_counter)
#define reps1(i, x)            for(int i = 1; i <= (x); ++i)

#define rrepname(a, b, c, ...) c
#define rrep(...)              rrepname(__VA_ARGS__, rrep1, rrep0)(__VA_ARGS__)
#define rrep0(x)               for(int rrep_counter = (x)-1; rrep_counter >= 0; --rrep_counter)
#define rrep1(i, x)            for(int i = (x)-1; i >= 0; --i)
#line 3 "/home/nok0/documents/programming/library/template/string_converter.hpp"

struct string_converter {
	char start = 0;
	char type(const char &c) const { return (islower(c) ? 'a' : isupper(c) ? 'A' :
		                                                    isdigit(c)     ? '0' :
		                                                                     0); }
	int convert(const char &c) {
		if(!start) start = type(c);
		return c - start;
	}
	int convert(const char &c, const std::string &chars) { return chars.find(c); }
	template <typename T>
	auto convert(const T &v) {
		std::vector<decltype(convert(v[0]))> ret;
		ret.reserve(size(v));
		for(auto &&e : v) ret.emplace_back(convert(e));
		return ret;
	}
	template <typename T>
	auto convert(const T &v, const std::string &chars) {
		std::vector<decltype(convert(v[0], chars))> ret;
		ret.reserve(size(v));
		for(auto &&e : v) ret.emplace_back(convert(e, chars));
		return ret;
	}
	int operator()(const char &v, char s = 0) {
		start = s;
		return convert(v);
	}
	int operator()(const char &v, const std::string &chars) { return convert(v, chars); }
	template <typename T>
	auto operator()(const T &v, char s = 0) {
		start = s;
		return convert(v);
	}
	template <typename T>
	auto operator()(const T &v, const std::string &chars) { return convert(v, chars); }
} toint;
#line 3 "/home/nok0/documents/programming/library/template/vector.hpp"

template <class T>
int lb(const std::vector<T> &a, const T x) { return std::distance((a).begin(), std::lower_bound((a).begin(), (a).end(), (x))); }
template <class T>
int ub(const std::vector<T> &a, const T x) { return std::distance((a).begin(), std::upper_bound((a).begin(), (a).end(), (x))); }
template <class T>
void UNIQUE(std::vector<T> &a) {
	std::sort(a.begin(), a.end());
	a.erase(std::unique(a.begin(), a.end()), a.end());
}
template <class T>
std::vector<T> press(std::vector<T> &a) {
	auto res = a;
	UNIQUE(res);
	for(auto &v : a)
		v = lb(res, v);
	return res;
}
#define SORTname(a, b, c, ...) c
#define SORT(...)              SORTname(__VA_ARGS__, SORT1, SORT0, ...)(__VA_ARGS__)
#define SORT0(a)               std::sort((a).begin(), (a).end())
#define SORT1(a, c)            std::sort((a).begin(), (a).end(), [](const auto x, const auto y) { return x c y; })
template <class T>
void ADD(std::vector<T> &a, const T x = 1) {
	for(auto &v : a) v += x;
}
template <class T>
void SUB(std::vector<T> &a, const T x = 1) {
	for(auto &v : a) v -= x;
}
template <class T>
struct cum_vector {
   public:
	cum_vector() = default;
	template <class U>
	cum_vector(const std::vector<U> &vec) : cum((int)vec.size() + 1) {
		for(int i = 0; i < (int)vec.size(); i++)
			cum[i + 1] = cum[i] + vec[i];
	}
	T prod(int l, int r) {
		return cum[r] - cum[l];
	}

   private:
	std::vector<T> cum;
};
std::vector<std::pair<char, int>> rle(const std::string &s) {
	const int n = s.size();
	std::vector<std::pair<char, int>> ret;
	ret.reserve(n);
	for(int l = 0; l < n;) {
		int r = l + 1;
		for(; r < n and s[l] == s[r]; r++) {}
		ret.emplace_back(s[l], r - l);
		l = r;
	}
	return ret;
}
template <class T>
std::vector<std::pair<T, int>> rle(const std::vector<T> &v) {
	const int n = v.size();
	std::vector<std::pair<T, int>> ret;
	ret.reserve(n);
	for(int l = 0; l < n;) {
		int r = l + 1;
		for(; r < n and v[l] == v[r]; r++) {}
		ret.emplace_back(v[l], r - l);
		l = r;
	}
	return ret;
}
std::vector<int> iota(int n) {
	std::vector<int> p(n);
	std::iota(p.begin(), p.end(), 0);
	return p;
}
#line 12 "/home/nok0/documents/programming/library/template/all"
using namespace std;
#line 2 "a.cpp"


struct bitvector {
	ll n = 0;
	vector<bool> a;
	vector<int> cm;
	bitvector() {}
	bitvector(ll n_) : n(n_), a(n), cm(n + 1) {}
	bool operator[](ll i) const { return a[i]; }
	void set(ll i, bool x) { a[i] = x; }
	void build() {
		for(ll i = 0; i < n; ++i) cm[i + 1] = cm[i] + a[i];
	}
	ll rank(bool x, ll k) {  // k個目(1-origin)までのxの個数
		return x ? cm[k] : k - cm[k];
	}
	ll num(bool x, ll l, ll r) {  //[l,r]のxの個数
		ll nm1 = cm[r + 1] - cm[l];
		return x ? nm1 : r - l + 1 - nm1;
	}
	// friend ostream &operator << (ostream &os,const bitvector &a){
	//	for (ll i=0;i<a.n;++i) os << a[i];
	//	return os << '\n';
	// }
};

struct waveletmatrix {
	ll n = 0;              //配列長
	ll h = 1;              // bit数
	vector<ll> a;          //元配列
	vector<bitvector> bs;  // bs[lv]:第lvビット列 lv=h-1(上)~0(下)
	vector<ll> mid;        // mid[lv]:第lvビット列の0の個数(=第lv-1ビット列の01境界位置)
	ll mxv = -INF;         //最大値
	waveletmatrix() {}
	waveletmatrix(const vector<ll> &a_) : n((ll)a_.size()), a(a_) {
		if(a.empty()) return;
		//最大値、bit数を得る
		ll mx = mxv = *max_element(a.begin(), a.end());
		while(mx > 1) mx >>= 1, ++h;
		//構築
		bs.resize(h, bitvector(n));
		mid.resize(h);
		vector<ll> s = a;
		for(ll lv = h - 1; lv >= 0; --lv) {
			bitvector &b = bs[lv];
			//ビット列作成
			for(ll i = 0; i < n; ++i) {
				b.set(i, (s[i] >> lv) & 1);
			}
			b.build();
			// 01境界位置記録
			mid[lv] = b.rank(0, n);
			//第lv-1ビット用に配列入れ替え
			vector<ll> tmp(n);
			ll l = 0, r = b.rank(0, n);
			for(ll i = 0; i < n; ++i) {
				if(b[i])
					tmp[r++] = s[i];
				else
					tmp[l++] = s[i];
			}
			s.swap(tmp);
		}
	}
	ll nthsmall(ll l, ll r, ll k) {  //[l,r]内昇順k番目の値 1-origin ない時-1
		if(r < l || n <= l || r < 0 || k < 1) return -1;
		chmax(l, 0LL), chmin(r, n - 1);
		if(r - l + 1 < k) return -1;

		++r;
		ll ret = 0;
		for(ll lv = h - 1; lv >= 0; --lv) {
			bitvector &b = bs[lv];
			ll lznm = b.rank(0, l);
			ll rznm = b.rank(0, r);
			ll lonm = l - lznm;
			ll ronm = r - rznm;
			ll znm = rznm - lznm;
			if(k <= znm) {  //左
				l = lznm, r = rznm;
			} else {  //右
				ret |= 1ll << lv;
				l = mid[lv] + lonm;
				r = mid[lv] + ronm;
				k -= znm;
			}
		}
		return ret;
	}
	ll leftnumof(ll l, ll r, ll x) {  //[l,r]内x以下の個数
		auto [p, q] = rangefreq(l, r, x);
		return p + q;
	}
	ll rightnumof(ll l, ll r, ll x) {  //[l,r]内x以上の個数
		return r - l + 1 - rangefreq(l, r, x).first;
	}
	ll numof(ll l, ll r, ll x) {  //[l,r]内xの個数
		return rangefreq(l, r, x).second;
	}
	ll numof(ll l, ll r, ll x, ll y) {                         //[l,r]内x以上y以下の個数
		return leftnumof(l, r, y) - rangefreq(l, r, x).first;  // n(y以下)-n(x未満)
	}
	ll nthbig(ll l, ll r, ll k) {  //[l,r]内降順k番目の値 1-origin ない時-1
		if(r < l || n <= l || r < 0 || k < 1) return -1;
		chmax(l, 0LL), chmin(r, n - 1);
		return nthsmall(l, r, r - l + 2 - k);
	}
	ll floorval(ll l, ll r, ll x) {  //[l,r]内x以下最大の値 ない時-1
		ll k = leftnumof(l, r, x);
		return nthsmall(l, r, k);
	}
	ll ceilval(ll l, ll r, ll x) {  //[l,r]内x以上最小の値 ない時INF
		auto [k, _] = rangefreq(l, r, x);
		ll ret = nthsmall(l, r, k + 1);
		return ret == -1 ? INF : ret;
	}
	//---- utility
	ll down(ll lv, ll i, bool x) { return bs[lv].rank(x, i) + mid[lv] * x; }
	//!<                        ↑第lvビット列の境界i(i-1とiの間)のlv-1での位置
	//!<                        ↑  戻り値をretとすると位置ret-1とretの間が境界
	ll down(ll lv, ll i) { return down(lv, i, bs[lv][i]); }
	//!<                                    ↑第lvビット列の位置iのlv-1での位置
	pll succ(ll l, ll r, bool x, ll lv) { return {down(lv, l, x), down(lv, r, x)}; }
	//!<                                    ↑第lvビット列の[l,r)のlv-1での範囲
	pll rangefreq(ll l, ll r, ll x) {  //[l,r]内のx未満/x の個数
		if(r < l || n <= l || r < 0 || x < 0) return {0, 0};
		chmax(l, 0LL), chmin(r, n - 1);
		if(x > mxv) return {r - l + 1, 0};

		++r;
		ll ret = 0;
		for(ll lv = h - 1; lv >= 0; --lv) {
			ll len = r - l;
			bool xb = (x >> lv) & 1;
			tie(l, r) = succ(l, r, xb, lv);
			if(xb) ret += len - (r - l);
		}
		return {ret, r - l};
	}
};
/*
.               ↓vector<ll> 0以上
waveletmatrix wm(a);
ll nm=wm.leftnumof(l,r,x); //[l,r]内x以下の個数
ll nm=wm.rightnumof(l,r,x);//[l,r]内x以上の個数
ll nm=wm.numof(l,r,x);     //[l,r]内xの個数
ll nm=wm.numof(l,r,x,y);   //[l,r]内x以上y以下の個数
ll v=wm.nthsmall(l,r,k);   //[l,r]内小さい方からk番目の値 1-origin ない時-1
ll v=wm.nthbig(l,r,k);     //[l,r]内大きい方からk番目の値 1-origin ない時-1
ll v=wm.floorval(l,r,x);   //[l,r]内x以下最大の値 ない時-1
ll v=wm.ceilval(l,r,x);    //[l,r]内x以上最小の値 ない時INF
*/


template <class T, class S>
struct waveletmatrix2d {
	using Int = long long;
	using ll = long long;
	using TS = pair<T, S>;
	waveletmatrix wm;
	vector<TS> xys;  //全点昇順 uniqしない
	vector<S> ys;
	S none;
	/*---- コンストラクタ ----*/
	waveletmatrix2d() {}
	waveletmatrix2d(const vector<TS> &xys_, S none_ = -INF) : xys(xys_), none(none_) {
		for(auto &&[x, y] : xys) ys.push_back(y);
		init();
	}
	waveletmatrix2d(const vector<T> &xs, const vector<S> &ys_, S none_ = -INF) : ys(ys_), none(none_) {
		ll n = xs.size();
		assert(ys.size() == n);
		for(ll i = 0; i < n; ++i) xys.emplace_back(xs[i], ys[i]);
		init();
	}
	/*---- I/F ----*/
	Int size() const { return (Int)xys.size(); }
	// Int numof(T sx,T ex,S sy,S ey){ //矩形[sx,ex,sy,ey]内の個数 境界含む

	//}
	// S nthsmall(T sx,T ex,Int k){ //[sx,ex]内、y座標小さい方からk番目 1-origin ない時none

	//}
	// S nthbig(T sx,T ex,Int k){ //[sx,ex]内、y座標大きい方からk番目 1-origin ない時none

	//}
	// S biggest(T sx,T ex,S ey){ //[sx,ex]内、ey以下で最大のy ない時none

	//}
	S smallest(T sx, T ex, S sy) {  //[sx,ex]内、sy以上で最小のy ない時NONE
		auto [l, r] = xrange2lr(sx, ex);
		ll sj = ceilIdxY(sy);
		ll j = wm.ceilval(l, r, sj);
		return j == INF ? none : ys[j];
	}
	/*---- utility ----*/
	void init() {
		sort(xys.begin(), xys.end());
		sort(ys.begin(), ys.end());
		ys.erase(unique(ys.begin(), ys.end()), ys.end());
		vector<ll> ini;
		for(auto &&[x, y] : xys) {
			ll j = lower_bound(ys.begin(), ys.end(), y) - ys.begin();
			ini.push_back(j);
		}
		wm = waveletmatrix(ini);
	}
	static bool cmpx(const TS &a, const TS &b) { return a.first < b.first; }
	ll floorIdxX(T x) {  // x以下最大に対応するi ない時-1
		return upper_bound(xys.begin(), xys.end(), TS{x, S()}, cmpx) - xys.begin() - 1;
	}
	ll ceilIdxX(T x) {  // x以上最小に対応するi ない時size()
		return lower_bound(xys.begin(), xys.end(), TS{x, S()}, cmpx) - xys.begin();
	}
	ll floorIdxY(S y) {  // y以下最大に対応するj ない時-1
		return upper_bound(ys.begin(), ys.end(), y) - ys.begin() - 1;
	}
	ll ceilIdxY(S y) {  // y以上最小に対応するj ない時ys.size()
		return lower_bound(ys.begin(), ys.end(), y) - ys.begin();
	}
	pair<ll, ll> xrange2lr(T sx, T ex) { return {ceilIdxX(sx), floorIdxX(ex)}; }
};
using wm2d = waveletmatrix2d<ll, ll>;
/*
- -------- 定義 --------
wm2d wm(xy);
.                               ↓無効値(smallest等の戻り値用)
waveletmatrix2d<dd,dd> wm(xy,-1e300);
- -------- アクセス --------
ll y=wm.smallest(sx,ex,sy);    //[sx,ex]内、sy以上で最小のy ない時wm.none
if (y==wm.none)  …            //ない時の判定法
*/
void main_();
int main() {
	int t = 1;
	while(t--) main_();
}

void main_() {
	LL(n, b, c, x);
	ll day = b + c;
	VEC(ll, a, n - 1);
	V<ll> cum(n);
	rep(i, n - 1) cum[i + 1] = cum[i] + a[i];
	vector<unordered_map<ll, ll>> dp(n);
	dp[0][0] = 0;
	auto is_safe = [&](ll ti) {
		return ti % day <= b;
	};
	auto nxt_good = [&](ll ti) {
		if(is_safe(ti))
			return ti;
		else
			return ti + day - ti % day;
	};
	auto mchmin = [&](int idx, ll j, ll val) {
		if(dp[idx].count(j))
			chmin(dp[idx][j], val);
		else
			dp[idx][j] = val;
	};
	V<pll> bis(n);
	rep(i, n) bis[i] = {cum[i] % day, i};
	wm2d wm(bis, INF);
	auto calc_k = [&](int i, ll t) -> ll {
		ll l = (b + 1 - t + cum[i]) % day;
		if(l < 0) l += day;
		ll r = (day - 1 - t + cum[i]) % day;
		if(r < 0) r += day;
		ll k = INF;
		if(l <= r) {
			chmin(k, wm.smallest(l, r, i + 1));
		} else {
			chmin(k, wm.smallest(0, r, i + 1));
			chmin(k, wm.smallest(l, day - 1, i + 1));
		}
		return k;
	};
	ll ans = INF;
	rep(i, n - 1) {
		for(auto [j, now] : dp[i]) {
			ll k = calc_k(i, j);
			if(k > n - 1 or cum.back() - (x - now) <= cum[k]) {
				chmin(ans, nxt_good(max(now, now + cum.back() - cum[i] - (x - now))));
				continue;
			}
			ll nxt_time = j + cum[k] - cum[i];
			mchmin(k, nxt_good(nxt_time), now);
			ll bef = nxt_time;
			if(bef % day > b) bef -= bef % day - b;
			assert(is_safe(bef) and bef <= nxt_time);
			ll nxt_used = now + nxt_time - bef;
			if(nxt_used <= x) {
				mchmin(k, bef, nxt_used);
			}
		}
	}
	print(ans);
}