// Begin include: "../../template/template.hpp"
using namespace std;

// intrinstic
#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// Begin include: "util.hpp"
namespace yamada {
using ll = long long;
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 V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
template <typename T>
using VVV = vector<vector<vector<T>>>;
template <typename T>
using VVVV = vector<vector<vector<vector<T>>>>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<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 P : pair<T, U> {
	template <typename... Args>
	P(Args... args) : pair<T, U>(args...) {}

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

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

using pl = P<ll, ll>;
using vp = V<pl>;
using vvp = VV<pl>;

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>
inline T Max(const vector<T> &v) { return *max_element(begin(v), end(v)); }
template <typename T>
inline T Min(const vector<T> &v) { return *min_element(begin(v), end(v)); }
template <typename T>
inline long long Sum(const vector<T> &v) { return accumulate(begin(v), end(v), T(0)); }

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

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, 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);
	sort(ret.begin(), ret.end());
	ret.erase(unique(ret.begin(), ret.end()), ret.end());
	return ret;
}

template <typename F>
vector<int> mkord(int N, F f) {
	vector<int> ord(N);
	iota(begin(ord), end(ord), 0);
	sort(begin(ord), end(ord), f);
	return ord;
}

template <typename T>
vector<int> mkinv(vector<T> &v) {
	int max_val = *max_element(begin(v), end(v));
	vector<int> inv(max_val + 1, -1);
	for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
	return inv;
}

vector<int> mkiota(int n) {
	vector<int> ret(n);
	iota(begin(ret), end(ret), 0);
	return ret;
}

template <typename T>
T mkrev(const T &v) {
	T w{v};
	reverse(begin(w), end(w));
	return w;
}

template <typename T>
bool nxp(T &v) { return next_permutation(begin(v), end(v)); }

// 返り値の型は入力の T に依存
// i 要素目 : [0, a[i])
template <typename T>
vector<vector<T>> product(const vector<T> &a) {
	vector<vector<T>> ret;
	vector<T> v;
	auto dfs = [&](auto rc, int i) -> void {
		if (i == (int)a.size()) {
			ret.push_back(v);
			return;
		}
		for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back();
	};
	dfs(dfs, 0);
	return ret;
}

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) while ((int)ret.size() < siz) ret.emplace_back(0);
	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>
T Rev(const T &v) {
	T res = v;
	reverse(begin(res), end(res));
	return res;
}

template <typename T>
vector<T> Transpose(const vector<T> &v) {
	using U = typename T::value_type;
	if(v.empty()) return {};
	int H = v.size(), W = v[0].size();
	vector res(W, T(H, U{}));
	for (int i = 0; i < H; i++) for (int j = 0; j < W; j++) res[j][i] = v[i][j];
	return res;
}

template <typename T>
vector<T> Rotate(const vector<T> &v, int clockwise = true) {
	using U = typename T::value_type;
	int H = v.size(), W = v[0].size();
	vector res(W, T(H, U{}));
	for (int i = 0; i < H; i++) for (int j = 0; j < W; j++) {
		if (clockwise) res[W - 1 - j][i] = v[i][j];
		else res[j][H - 1 - i] = v[i][j];
	}
	return res;
}

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 T>
bool inLR(T L, T x, T R){ return (L <= x && x < R); }
bool YESNO(bool b) { std::cout << (b ? "YES\n" : "NO\n"); return b; }
bool YesNo(bool b) { std::cout << (b ? "Yes\n" : "No\n"); return b; }

template <typename mint>
std::string toFraction(mint a, int M) {
	for (int deno = 1; deno <= M; deno++) {
		mint inv = ((mint)deno).inverse();
		for (int nume = -M; nume <= M; nume++) {
			mint val = inv * nume;
			if (val == a) {
				if (deno == 1) return std::to_string(nume);
				return std::to_string(nume) + "/" + std::to_string(deno);
			}
		}
	}
	return "NF";
}

template <typename mint>
void mout(mint a, int M = 100) { std::cout << toFraction(a, M) << "\n"; }
template <typename mint>
void mout(std::vector<mint> A, int M = 100) {
	for (int i = 0; i < (int)A.size(); i++) {
		std::cout << toFraction(A[i], M) << (i == (int)A.size() - 1 ? "\n" : " ");
	}
}

bool is_square(uint64_t n) {
	if (n < 2) return true;
	uint64_t r = static_cast<uint64_t>(sqrtl(static_cast<long double>(n)));
	if (r * r == n) return true;
	++r;
	return r * r == n;
}

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

long long floor(long long a, long long b) {
	assert(b != 0);
	if (b < 0) a = -a, b = -b;
	return a / b - (a % b < 0);
}
long long under(long long a, long long b) {
	assert(b != 0);
	if (b < 0) a = -a, b = -b;
	return a / b - (a % b <= 0);
}
long long ceil(long long a, long long b) {
	assert(b != 0);
	if (b < 0) a = -a, b = -b;
	return a / b + (a % b > 0);
}
long long over(long long a, long long b) {
	assert(b != 0);
	if (b < 0) a = -a, b = -b;
	return a / b + (a % b >= 0);
}
long long modulo(long long a, long long b) {
	assert(b > 0);
	long long c = a % b;
	return c < 0 ? c + b : c;
}

} // 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 ctz(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; }
}  // namespace yamada
// End include: "bitop.hpp"
// Begin include: "inout.hpp"
namespace yamada {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
	os << p.first << " " << p.second;
	return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
	is >> p.first >> p.second;
	return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
	int s = (int)v.size();
	for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
	return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
	for (auto &x : v) is >> x;
	return is;
}

istream &operator>>(istream &is, __int128_t &x) {
	string S;
	is >> S;
	x = 0;
	int flag = 0;
	for (auto &c : S) {
		if (c == '-') {
			flag = true;
			continue;
		}
		x *= 10;
		x += c - '0';
	}
	if (flag) 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;
	reverse(begin(S), end(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;
	reverse(begin(S), end(S));
	return os << S;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
	cin >> t;
	in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
	cout << t;
	if (sizeof...(u)) cout << sep;
	out(u...);
}

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

}  // namespace yamada
// End include: "inout.hpp"
// Begin include: "macro.hpp"
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define each3(x, y, z, v) for (auto&& [x, y, z] : v)
#define all(v) (v).begin(), (v).end()

#define rep1(a) for (long long _ = 0; _ < (long long)(a); ++_)
#define rep2(i, a) for (long long i = 0; i < (long long)(a); ++i)
#define rep3(i, a, b) for (long long i = a; i < (long long)(b); ++i)
#define rep4(i, a, b, c) for (long long i = a; i < (long long)(b); i += c)
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)

#define rep1r(a) for (long long i = (long long)(a)-1; i >= 0LL; --i)
#define rep2r(i, a) for (long long i = (long long)(a)-1; i >= 0LL; --i)
#define rep3r(i, a, b) for (long long i = (long long)(b)-1; i >= (long long)(a); --i)
#define overload3(a, b, c, d, ...) d
#define repr(...) overload3(__VA_ARGS__, rep3r, rep2r, rep1r)(__VA_ARGS__)

#define eb emplace_back
#define mkp make_pair
#define mkt make_tuple
#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 ini(...)   \
	int __VA_ARGS__; \
	in(__VA_ARGS__)
#define inl(...)         \
	long long __VA_ARGS__; \
	in(__VA_ARGS__)
#define ins(...)      \
	string __VA_ARGS__; \
	in(__VA_ARGS__)
#define in2(s, t)                           \
	for (int i = 0; i < (int)s.size(); i++) { \
		in(s[i], t[i]);                         \
	}
#define in3(s, t, u)                        \
	for (int i = 0; i < (int)s.size(); i++) { \
		in(s[i], t[i], u[i]);                   \
	}
#define in4(s, t, u, v)                     \
	for (int i = 0; i < (int)s.size(); i++) { \
		in(s[i], t[i], u[i], v[i]);             \
	}
#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: "../../rbst/lazy-reversible-rbst.hpp"

// Begin include: "rbst-base.hpp"

// Begin include: "../data-structure/node-pool.hpp"

// マルチテストケースに弱いので static で確保すること
template <typename Node>
struct NodePool {
	struct Slot {
		union alignas(Node) {
			Slot* next;
			unsigned char storage[sizeof(Node)];
		};
	};
	using Ptr = Node*;

	static constexpr int CHUNK_SIZE = 1 << 12;

	std::vector<std::unique_ptr<Slot[]>> chunks;
	Slot* cur = nullptr;
	int cur_used = 0;
	Slot* free_head = nullptr;

	NodePool() { alloc_chunk(); }

	template <typename... Args>
	Ptr create(Args&&... args) {
		Slot* s = new_slot();
		return ::new (s) Node(std::forward<Args>(args)...);
	}

	Ptr clone(const Ptr x) {
		assert(x);
		Slot* s = new_slot();
		return ::new (s) Node(*x);  // コピーコンストラクタ呼び出し
	}

	void destroy(Ptr x) {
		if (!x) return;
		x->~Node();
		auto s = reinterpret_cast<Slot*>(x);
		s->next = free_head;
		free_head = s;
	}

	void reset() {
		free_head = nullptr;
		if (!chunks.empty()) {
			cur = chunks[0].get();
			cur_used = 0;
		}
	}

	private:
	void alloc_chunk() {
		chunks.emplace_back(std::make_unique<Slot[]>(CHUNK_SIZE));
		cur = chunks.back().get();
		cur_used = 0;
	}

	Slot* new_slot() {
		if (free_head) {
			Slot* s = free_head;
			free_head = free_head->next;
			return s;
		}
		if (cur_used == CHUNK_SIZE) alloc_chunk();
		return &cur[cur_used++];
	}
};
// End include: "../data-structure/node-pool.hpp"

// RBSTそのものではなく、RBSTを操作する関数の集合体
template <typename Node>
struct RBSTBase {
	using Ptr = Node *;
	NodePool<Node> pool;
	template <typename... Args>
	Ptr my_new(Args... args) {
		Ptr c = pool.create();
		*c = Node(args...);
		return c;
	}
	void reset() { pool.reset(); }
	inline void my_del(Ptr t) { pool.destroy(t); }
	inline Ptr make_tree() const { return nullptr; }
	int size(Ptr t) const { return count(t); }

	Ptr merge(Ptr l, Ptr r) {
		if (!l || !r) return l ? l : r;
		if (int((rng() * (l->cnt + r->cnt)) >> 32) < l->cnt) {
			push(l);
			l = clone(l);
			l->r = merge(l->r, r);
			return update(l);
		}
		else {
			push(r);
			r = clone(r);
			r->l = merge(l, r->l);
			return update(r);
		}
	}
	Ptr merge3(Ptr x, Ptr y, Ptr z) { return merge(merge(x, y), z); }

	std::pair<Ptr, Ptr> split(Ptr root, int k) {
		if (!root) return {nullptr, nullptr};
		push(root);
		if (k <= count(root->l)) { // decompose left
			auto [x, y] = split(root->l, k);
			root = clone(root);
			root->l = y;
			return {x, update(root)};
		}
		else { // decompose right
			auto [x, y] = split(root->r, k - count(root->l) - 1);
			root = clone(root);
			root->r = x;
			return {update(root), y};
		}
	}

	std::tuple<Ptr, Ptr, Ptr> split3(Ptr root, int L, int R) {
		Ptr nm, nr;
		std::tie(root, nr) = split(root, R);
		std::tie(root, nm) = split(root, L);
		return {root, nm, nr};
	}

	Ptr build(int l, int r, const std::vector<decltype(Node::key)> &init) {
		if (l + 1 == r) return my_new(init[l]);
		int m = (l + r) >> 1;
		Ptr pm = my_new(init[m]);
		if (l < m) pm->l = build(l, m, init);
		if (m + 1 < r) pm->r = build(m + 1, r, init);
		return update(pm);
	}
	Ptr build(const std::vector<decltype(Node::key)> &init) { return build(0, (int)init.size(), init); }

	template <typename... Args>
	Ptr insert(Ptr root, int k, const Args &... args) {
		auto [x, y] = split(root, k);
		return merge3(x, my_new(args...), y);
	}

	Ptr erase(Ptr root, int k) {
		auto [x, y, z] = split3(root, k, k + 1);
		my_del(y);
		return merge(x, z);
	}

	template <typename F>
	Ptr max_ok(Ptr root, const F &check) {
		if (!root) return nullptr;
		push(root);
		if (!check(root)) return max_ok(root->l, check);
		auto res = max_ok(root->r, check);
		return res ? res : root;
	}

	template <typename F>
	Ptr min_ng(Ptr root, const F &check) {
		if (!root) return nullptr;
		push(root);
		if (check(root)) return min_ng(root->r, check);
		auto res = min_ng(root->l, check);
		return res ? res : root;
	}

	template <typename F>
	int count_ok(Ptr root, const F &check) {
		if (!root) return 0;
		push(root);
		if (!check(root)) return count_ok(root->l, check);
		int ans = 1;
		if (root->l) ans += root->l->cnt;
		ans += count_ok(root->r, check);
		return ans;
	}

	// 最後に check(s) が成り立つところまでを左としてsplit
	template <typename F>
	std::pair<Ptr, Ptr> split_max_right(Ptr& root, const F &check) {
		if (!root) return {nullptr, nullptr};
		push(root);
		root = clone(root);
		if (check(root)) {
			auto [u0, u1] = split_max_right(root->r, check);
			root->r = u0;
			return {update(root), u1};
		}
		else {
			auto [u0, u1] = split_max_right(root->l, check);
			root->l = u1;
			return {u0, update(root)};
		}
	}

	std::vector<Ptr> enumerate(Ptr& root) {
		if (!root) return std::vector<Ptr>();
		std::vector<Ptr> ans(root->cnt);
		int ansi = 0;
		auto dfs = [&](auto&& self, Ptr u)->void{
			if (!u) return;
			push(u);
			self(self, u->l);
			ans[ansi++] = u;
			self(self, u->r);
		}; dfs(dfs, root);
		return ans;
	}

	Ptr kth_element(Ptr u, int k) {
		assert(u);
		while (u) {
			push(u);
			if (u->l && u->l->cnt > k) u = u->l;
			else {
				if (u->l) k -= u->l->cnt;
				if (k == 0) return u;
				k -= 1;
				u = u->r;
			}
		}
		return nullptr;
	}

	Ptr extract(Ptr root, int ql, int qr) { // DO NOT USE when NOT PERSISTENT!!!
		if (!root) return nullptr;
		push(root);
		ql = std::max(0, ql);
		qr = std::min(count(root), qr);
		if (ql >= qr) return nullptr;
		if (ql == 0 && qr == root->cnt) return root;

		int l_siz = count(root->l);
		if (qr <= l_siz) return extract(root->l, ql, qr);
		int offset = l_siz + 1;
		if (offset <= ql) return extract(root->r, ql - offset, qr - offset);

		root = clone(root);
		root->l = extract(root->l, ql, qr);
		root->r = extract(root->r, ql - offset, qr - offset);
		return update(root);
	}

	static uint64_t rng() { // https://ja.wikipedia.org/wiki/Xorshift
		static uint64_t x_ = 88172645463325252ULL;
		return x_ ^= x_ << 7, x_ ^= x_ >> 9, x_ & 0xFFFFFFFFull;
	}
	inline int count(const Ptr t) const { return t ? t->cnt : 0; }
	virtual void push(Ptr) = 0;
	virtual Ptr update(Ptr) = 0;
	virtual Ptr clone(Ptr) = 0;
};
// End include: "rbst-base.hpp"

template <typename T, typename E>
struct LazyReversibleRBSTNode {
	typename RBSTBase<LazyReversibleRBSTNode>::Ptr l, r;
	T key, sum; // 頂点内のlaz, rev反映済
	E laz;
	int cnt;
	bool rev;

	LazyReversibleRBSTNode(const T &t = T(), const E &e = E())
		: l(), r(), key(t), sum(t), laz(e), cnt(1), rev(false) {}
};

// 疑問点: E (*es)(E)が必要になる問題は存在するのか？
template <typename T, typename E, T (*f)(T, T), T (*g)(T, E), E (*h)(E, E),
		 T (*ti)(), E (*ei)(), T (*ts)(T), bool PERSISTENT = false>
struct LazyReversibleRBST : RBSTBase<LazyReversibleRBSTNode<T, E>> {
	using Node = LazyReversibleRBSTNode<T, E>;
	using base = RBSTBase<LazyReversibleRBSTNode<T, E>>;
	using base::merge;
	using base::split;
	using base::merge3;
	using base::split3;
	using base::clone;
	using base::count;
	using base::extract;
	using typename base::Ptr;

	LazyReversibleRBST() = default;

	// doesn't use "split" in case PERSISTENT
	T fold(Ptr root, int L, int R, bool rev = false) { // DO NOT TOUCH "rev"
		assert(root);
		assert(0 <= L && L <= R && R <= root->cnt);
		if (L == 0 && R == root->cnt) return root->sum;
		Ptr l_ptr = (rev ? root->r : root->l);
		Ptr r_ptr = (rev ? root->l : root->r);
		int l_siz = count(l_ptr);
		T ans = ti();
		if (L < l_siz) { // see Left
			T bns = fold(l_ptr, L, std::min(R, l_siz), rev ^ root->rev);
			ans = f(ans, g(bns, root->laz));
		}
		if (L <= l_siz && l_siz < R) ans = f(ans, root->key); // see here
		int offset = l_siz + 1;
		if (offset < R) { // see Right
			T bns = fold(r_ptr, std::max(offset, L) - offset, R - offset, rev ^ root->rev);
			ans = f(ans, g(bns, root->laz));
		}
		return ans;
	}
	T fold(Ptr root) { return (root ? root->sum : ti()); }

	T get_val(Ptr root, int k, bool rev = false, E laz = ei()) { // DO NOT TOUCH "rev" or "laz"
		Ptr l_ptr = (rev ? root->r : root->l);
		Ptr r_ptr = (rev ? root->l : root->r);
		int l_siz = count(l_ptr);
		if (k == l_siz) return g(root->key, laz); // k is here
		laz = h(root->laz, laz);
		rev ^= root->rev;
		if (k < l_siz) return get_val(l_ptr, k, rev, laz); // k is in Left
		return get_val(r_ptr, k - (l_siz + 1), rev, laz); // k is in Right
	}

	std::vector<T> get_all(Ptr root) {
		std::vector<T> ans;
		auto dfs = [&](auto &dfs, Ptr root, bool rev, E laz) -> void {
			if (!root) return;
			T bns = g(root->key, laz);
			laz = h(root->laz, laz);
			dfs(dfs, (rev ? root->r : root->l), rev ^ root->rev, laz); // go Left
			ans.eb(bns);
			dfs(dfs, (rev ? root->l : root->r), rev ^ root->rev, laz); // go Right
		};
		dfs(dfs, root, 0, ei());
		return ans;
	}

	// doesn't use "split" in case PERSISTENT
	Ptr apply(Ptr root, int L, int R, const E laz) {
		assert(root);
		assert(0 <= L && L <= R && R <= root->cnt);
		push(root);
		root = clone(root);
		if (L == 0 && R == root->cnt) { // apply all
			root->key = g(root->key, laz);
			root->sum = g(root->sum, laz);
			root->laz = laz;
			return root;
		}
		int l_siz = count(root->l);
		if (L < l_siz) root->l = apply(root->l, L, std::min(R, l_siz), laz); // need to see Left
		if (L <= l_siz && l_siz < R) root->key = g(root->key, laz); // apply here
		int offset = l_siz + 1;
		if (offset < R) root->r = apply(root->r, std::max(0, L - offset), R - offset, laz); // need to see Right
		return update(root);
	}
	Ptr apply(Ptr root, const E laz) { return apply(root, 0, root->cnt, laz); }

	Ptr set_val(Ptr root, int k, const T &val) {
		if (!root) return root;
		push(root);
		int l_siz = count(root->l);
		if (k < l_siz) { // k is in Left
			root = clone(root);
			root->l = set_val(root->l, k, val);
			return update(root);
		}
		else if (k == l_siz) { // k is here
			root = clone(root);
			root->key = val;
			return update(root);
		}
		else { // k is in Right
			root = clone(root);
			root->r = set_val(root->r, k - (l_siz + 1), val);
			return update(root);
		}
	}

	Ptr reverse(Ptr root, int L, int R) {
		assert(root);
		assert(0 <= L && L <= R && R <= root->cnt);
		if (R - L <= 1) return root;
		auto [x, y, z] = split3(root, L, R);
		y->rev ^= 1;
		y->sum = ts(y->sum);
		std::swap(y->l, y->r);
		return merge3(x, y, z);
	}

	Ptr multiply(Ptr root, int k, const T &val) {
		if (!root) return root;
		push(root);
		int l_siz = count(root->l);
		root = clone(root);
		if (k < l_siz) { // k is in Left
			root->l = multiply(root->l, k, val);
			return update(root);
		}
		else if (k == l_siz) { // k is here
			root->key = f(root->key, val);
			return update(root);
		}
		else { // k is in Right
			root->r = multiply(root->r, k - (l_siz + 1), val);
			return update(root);
		}
	}

	// u[L:R) <- apply(v[L:R), laz)
	Ptr copy_interval(Ptr u, Ptr v, int L, int R, E laz = ei()) {
		assert(PERSISTENT);
		assert(u); assert(v);
		Ptr m = extract(v, L, R);
		propagate(m, laz);
		return merge3(extract(u, 0, L), m, extract(u, R, u->cnt));
	}

	inline T sum(const Ptr t) const { return t ? t->sum : ti(); }

	Ptr update(Ptr t) override { // doesn't change tree shape
		push(t);
		t->cnt = 1;
		t->sum = t->key;
		if (t->l) t->cnt += t->l->cnt, t->sum = f(t->l->sum, t->sum);
		if (t->r) t->cnt += t->r->cnt, t->sum = f(t->sum, t->r->sum);
		return t;
	}

	void push(Ptr t) override { // only copy child
		if (t->rev || t->laz != ei()) t->l = clone(t->l), t->r = clone(t->r);
		if (t->rev) {
			toggle(t->l);
			toggle(t->r);
			t->rev = false;
		}
		if (t->laz != ei()) {
			propagate(t->l, t->laz);
			propagate(t->r, t->laz);
			t->laz = ei();
		}
	}

	Ptr clone(Ptr n) override {
		if constexpr (!PERSISTENT) return n;
		if (!n) return n;
		return base::pool.clone(n);
	}

	void toggle(Ptr t) {
		if (!t) return;
		swap(t->l, t->r);
		t->sum = ts(t->sum);
		t->rev ^= true;
	}

	void propagate(Ptr t, const E &laz) {
		if (!t) return;
		t->laz = h(t->laz, laz);
		t->key = g(t->key, laz);
		t->sum = g(t->sum, laz);
	}
};

namespace ReversibleRBSTSumImpl {
template <typename T>
T g(T l, bool) { return l; }
bool h(bool, bool) { return false; }
bool ei() { return false; }

template <typename T, T (*f)(T, T), T (*ti)(), T (*ts)(T), bool PERSISTENT = false>
using ReversibleRBSTSum = LazyReversibleRBST<T, bool, f, g, h, ti, ei, ts, PERSISTENT>;
}  // namespace ReversibleRBSTSumImpl

namespace ReversibleDualRBSTImpl {
bool f(bool, bool) { return false; }
template <typename E>
bool g(bool, E e) { return e; }
bool ti() { return false; }
bool ts(bool a) { return a; }

template <typename E, E (*h)(E, E), E (*ei)(), bool PERSISTENT = false>
using ReversibleDualRBST = LazyReversibleRBST<bool, E, f, g, h, ti, ei, ts, PERSISTENT>;
} // namespace DualRBSTImpl

using ReversibleRBSTSumImpl::ReversibleRBSTSum;
using ReversibleDualRBSTImpl::ReversibleDualRBST;
// End include: "../../rbst/lazy-reversible-rbst.hpp"
using namespace yamada;

using T=ll;
T F(ll a,ll b){return a+b;}
T ti(){return 0;}
T ts(T a){return a;}

void yamada::solve()
{
	inl(N,Q);
	vl A(N); in(A);
	ReversibleRBSTSum<T,F,ti,ts> seg;
	auto root=seg.build(A);

	while(Q--){
		inl(i,x,l,r); --l;
		root=seg.insert(root,i,x);

		/* each(p,seg.enumerate(root)){ */
		/* 	cout<<p->key<<" "; */
		/* } */
		/* out(); */
		out(seg.fold(root,l,r));
	}
}