// 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 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 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 = vector<double>;
using vs = vector<string>;
using vb = vector<bool>;
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 pl = pr<ll, ll>;
using vp = vc<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(ret.begin(), ret.end(), 0);
	return ret;
}

// g o f
vector<int> p_mrg(vector<int> f, const vector<int> &g) {
	for (int i = 0; i < (int)f.size(); i++) f[i]=g[f[i]];
	return f;
}

// f: old_idx -> new_idx
template <typename T>
vector<T> p_shf(const vector<int>& f, const vector<T>& A, 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) {
	T w{v};
	reverse(begin(w), end(w));
	return w;
}

template <typename T>
bool nxp(T &v) { return std::next_permutation(begin(v), end(v)); }
template <typename F>
void nxp(int n, F f) {
	vector<int> a(n);
	iota(begin(a), end(a), 0);
	do { f(a); } while (nxp(a));
}

// 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 = long long>
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; }
bool yesno(bool b) { std::cout << (b ? "yes\n" : "no\n"); return b; }

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); }
	T query() { return S.back(); }
	inline T operator()(int l, int r) { return query(l, r); }
	inline T operator()() { return query(); }
};

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 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, size_t K> ostream &operator<<(ostream &os, const array<T, K> &v);
template <typename T, size_t K> istream &operator>>(istream &is, array<T, K> &v);
template <typename T> ostream &operator<<(ostream &os, const vector<T> &v);
template <typename T> istream &operator>>(istream &is, vector<T> &v);
template <typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &p);
template <typename T, typename U> istream &operator>>(istream &is, pair<T, U> &p);

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;
}

template <typename T, size_t K>
ostream &operator<<(ostream &os, const array<T, K> &v) {
	for (int i = 0; i < K; i++) os << (i ? " " : "") << v[i];
	return os;
}

template <typename T, size_t K>
istream &operator>>(istream &is, array<T, K> &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 <char sep = ' ', typename T, class... U>
void out(const T &t, const U &...u) {
	cout << t;
	if constexpr (sizeof...(u)) {
		cout << sep;
		out<sep>(u...);
	}
	else out();
}

void fout() { cout << endl; }
template <char sep = ' ', typename T, class... U>
void fout(const T &t, const U &...u) {
	cout << t;
	if constexpr (sizeof...(u)) {
		cout << sep;
		fout<sep>(u...);
	}
	else fout();
}

void wout() {}
template <char sep = ' ', typename T, class... U>
void wout(const T &t, const U &...u) {
	cout << t;
	if constexpr (sizeof...(u)) {
		cout << sep;
		wout<sep>(u...);
	}
	else wout();
}

template <size_t iter = 1000, typename mint>
std::string toFraction(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 std::to_string(nume);
				return std::to_string(nume) + "/" + std::to_string(deno);
			}
			else if (-val == a) {
				if (deno == 1) return std::to_string(-nume);
				return std::to_string(-nume) + "/" + std::to_string(deno);
			}
		}
	}
	return "NF";
}

void mout() { cout << endl; }
template <size_t iter = 1000, char sep = ' ', typename mint, class... U>
void mout(const mint &a, const U &...u) {
	std::cout << toFraction<iter, mint>(a);
	if constexpr (sizeof...(u)) {
		cout << sep;
		mout<iter, sep>(u...);
	}
	else mout();
}

template <size_t iter = 1000, typename mint>
void mout(std::vector<mint> &A) {
	for (int i = 0; i < (int)A.size(); i++) {
		std::cout << toFraction(A[i], iter) << (i == (int)A.size() - 1 ? "\n" : " ");
	}
}

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 each4(x, y, z, w, v) for (auto&& [x, y, z, w] : 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: "../../segment-tree/rollback-segment-tree.hpp"

// Begin include: "../data-structure/rollback-array.hpp"

template <typename T>
struct RollbackArray {
	int N;
	std::vector<T> dat;
	std::vector<pair<int, T>> history;

	RollbackArray() {}
	RollbackArray(std::vector<T> x) : N(x.size()), dat(x) {}
	RollbackArray(int N) : N(N), dat(N) {}
	template <typename F>
	RollbackArray(int N, F f) : N(N) {
		dat.reserve(N);
		for (int i = 0; i < N; i++) dat.emplace_back(f(i));
	}

	int time() { return history.size(); }
	void rollback(int t) {
		for (int i = time() - 1; i >= t; i--) {
			auto& [idx, v] = history[i];
			dat[idx] = v;
		}
		history.resize(t);
	}
	T get(int idx) { return dat[idx]; }
	void set(int idx, T x) {
		history.eb(idx, dat[idx]);
		dat[idx] = x;
	}

	std::vector<T> get_all() {
		std::vector<T> res(N);
		for (int i = 0; i < N; i++) res[i] = get(i);
		return res;
	}
};
// End include: "../data-structure/rollback-array.hpp"

template <typename ActedMonoid>
struct RollbackLazySegmentTree {
	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;
	RollbackArray<X> dat;
	RollbackArray<A> laz;

	RollbackLazySegmentTree() {}
	RollbackLazySegmentTree(int N) { build(N); }
	template <typename F>
	RollbackLazySegmentTree(int N, F init) { build(N, init); }
	template <typename T>
	RollbackLazySegmentTree(const std::vector<T>& v) { build(v); }

	void build(int m) {
		build(m, [](int) -> X { return MX::I(); });
	}
	template <typename T>
	void build(const std::vector<T>& 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 = RollbackArray<X>(std::vector<X>(size << 1, MX::I()));
		laz = RollbackArray<A>(std::vector<A>(size, MA::I()));
		for (int i = 0; i < N; i++) dat.set(size + i, init(i));
		for (int i = size - 1; i >= 1; i--) update(i);
	}

	void update(int k) { dat.set(k, MX::O(dat.get(2 * k), dat.get(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.set(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.set(p, MX::O(dat.get(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.get(p);
	}

	std::vector<X> get() {
		for (int k = 1; k < size; k++) push(k);
		auto tmp = dat.get_all();
		return {tmp.begin() + size, tmp.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.get(l++));
			if (r & 1) xr = MX::O(dat.get(--r), xr);
			l >>= 1, r >>= 1;
		}
		return MX::O(xl, xr);
	}

	X prod() { return dat.get(1); }
	template <typename... Args>
	X operator()(Args... args) { return prod(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(const F check, int l) {
		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.get(l)))) {
				while (l < size) {
					push(l);
					l = (2 * l);
					if (check(MX::O(sm, dat.get(l)))) {
						sm = MX::O(sm, dat.get(l++));
					}
				}
				return l - size;
			}
			sm = MX::O(sm, dat.get(l++));
		} while ((l & -l) != l);
		return N;
	}

	template <typename F>
	int min_left(const F check, int r) {
		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.get(r), sm))) {
				while (r < size) {
					push(r);
					r = (2 * r + 1);
					if (check(MX::O(dat.get(r), sm))) {
						sm = MX::O(dat.get(r--), sm);
					}
				}
				return r + 1 - size;
			}
			sm = MX::O(dat.get(r), sm);
		} while ((r & -r) != r);
		return 0;
	}

	pair<int, int> time() { return {dat.time(), laz.time()}; }
	void rollback(pair<int, int> t) { dat.rollback(t.fi), laz.rollback(t.se); }

	void push(int k) {
		if (laz.get(k) == MA::I()) return;
		apply_at(2 * k, laz.get(k)), apply_at(2 * k + 1, laz.get(k));
		laz.set(k, MA::I());
	}

	private:
	int topbit(int x) { return x == 0 ? -1 : 31 - __builtin_clz(x); }
	void apply_at(int k, A a) {
		long long sz = 1 << (LOG - topbit(k));
		dat.set(k, ActedMonoid::O(dat.get(k), a, sz));
		if (k < size) laz.set(k, MA::O(laz.get(k), a));
	}
};
// End include: "../../segment-tree/rollback-segment-tree.hpp"
// Begin include: "../../monoid/update-sum.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: "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>
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"

const int LG=30;
void yamada::solve()
{
	using AM=ACTED_MONOID::Update_Sum<int>;
	using SEG=RollbackLazySegmentTree<AM>;
	ini(N,M);
	array<SEG,LG> seg;
	{
		vc<int> A(N); in(A);
		vv(int,init,LG,N+1);
		rep(t,LG){
			rep(i,N)init[t][i]=A[i]>>t&1;
			seg[t]=SEG(init[t]);
		}
	}

	vc<pr<int,int>> initime(LG);
	rep(t,LG)initime[t]=seg[t].time();
	auto seginit=[&](){ rep(t,LG)seg[t].rollback(initime[t]); };

	vc<array<int,5>> lrxLR(M);
	for(auto&&[l,r,x,L,R]:lrxLR)in(l);
	for(auto&&[l,r,x,L,R]:lrxLR)in(r);
	for(auto&&[l,r,x,L,R]:lrxLR)in(x);
	for(auto&&[l,r,x,L,R]:lrxLR)in(L);
	for(auto&&[l,r,x,L,R]:lrxLR)in(R);

	ini(Q);
	rep(qi,1,Q+1){
		if(qi>=2)seginit();
		int y=qi;
		ini(s,q);
		rep(j,1,q+1){
			int z=(s+j)%M+1;
			auto[l,r,x,L,R]=lrxLR[z-1];
			int u=min<int>(N,max<int>(1,l^y));
			int v=min<int>(N,max<int>(1,r^y));
			int U=min<int>(N,max<int>(1,L^y));
			int V=min<int>(N,max<int>(1,R^y));

			int l_=min(u,v);
			int r_=max(u,v);
			int L_=min(U,V);
			int R_=max(U,V);

			--l_; --L_;
			if(z%2==0){
				rep(t,LG)if((x^y)>>t&1){
					seg[t].apply(l_,r_,1);
				}
			}
			else{
				rep(t,LG)if(!((x^y)>>t&1)){
					seg[t].apply(l_,r_,0);
				}
			}

			ll ny=0;
			rep(t,LG)ny+=(1LL<<t)*seg[t](L_,R_);
			y=ny&MSK(LG);
		}
		out(y);
	}
}