#include <bits/stdc++.h>
namespace suisen {
    template <class T> bool chmin(T& x, const T& y) { return y >= x ? false : (x = y, true); }
    template <class T> bool chmax(T& x, const T& y) { return y <= x ? false : (x = y, true); }
    template <class T> constexpr int pow_m1(T n) { return -(n & 1) | 1; }
    template <class T> constexpr T fld(const T x, const T y) { T q = x / y, r = x % y; return q - ((x ^ y) < 0 and (r != 0)); }
    template <class T> constexpr T cld(const T x, const T y) { T q = x / y, r = x % y; return q + ((x ^ y) > 0 and (r != 0)); }
}
namespace suisen::macro {
#define IMPL_REPITER(cond) auto& begin() { return *this; } auto end() { return nullptr; } auto& operator*() { return _val; } auto& operator++() { return _val += _step, *this; } bool operator!=(std::nullptr_t) { return cond; }
    template <class Int, class IntL = Int, class IntStep = Int, std::enable_if_t<(std::is_signed_v<Int> == std::is_signed_v<IntL>), std::nullptr_t> = nullptr> struct rep_impl {
        Int _val; const Int _end, _step;
        rep_impl(Int n) : rep_impl(0, n) {}
        rep_impl(IntL l, Int r, IntStep step = 1) : _val(l), _end(r), _step(step) {}
        IMPL_REPITER((_val < _end))
    };
    template <class Int, class IntL = Int, class IntStep = Int, std::enable_if_t<(std::is_signed_v<Int> == std::is_signed_v<IntL>), std::nullptr_t> = nullptr> struct rrep_impl {
        Int _val; const Int _end, _step;
        rrep_impl(Int n) : rrep_impl(0, n) {}
        rrep_impl(IntL l, Int r) : _val(r - 1), _end(l), _step(-1) {}
        rrep_impl(IntL l, Int r, IntStep step) : _val(l + fld<Int>(r - l - 1, step) * step), _end(l), _step(-step) {}
        IMPL_REPITER((_val >= _end))
    };
    template <class Int, class IntStep = Int> struct repinf_impl {
        Int _val; const Int _step;
        repinf_impl(Int l, IntStep step = 1) : _val(l), _step(step) {}
        IMPL_REPITER((true))
    };
#undef IMPL_REPITER
}

#include <iostream>

#include <limits>
#include <type_traits>

namespace suisen {
    template <typename ...Constraints> using constraints_t = std::enable_if_t<std::conjunction_v<Constraints...>, std::nullptr_t>;

    template <typename T, typename = std::nullptr_t> struct bitnum { static constexpr int value = 0; };
    template <typename T> struct bitnum<T, constraints_t<std::is_integral<T>>> { static constexpr int value = std::numeric_limits<std::make_unsigned_t<T>>::digits; };
    template <typename T> static constexpr int bitnum_v = bitnum<T>::value;
    template <typename T, size_t n> struct is_nbit { static constexpr bool value = bitnum_v<T> == n; };
    template <typename T, size_t n> static constexpr bool is_nbit_v = is_nbit<T, n>::value;

    template <typename T, typename = std::nullptr_t> struct safely_multipliable { using type = T; };
    template <typename T> struct safely_multipliable<T, constraints_t<std::is_signed<T>, is_nbit<T, 32>>> { using type = long long; };
    template <typename T> struct safely_multipliable<T, constraints_t<std::is_signed<T>, is_nbit<T, 64>>> { using type = __int128_t; };
    template <typename T> struct safely_multipliable<T, constraints_t<std::is_unsigned<T>, is_nbit<T, 32>>> { using type = unsigned long long; };
    template <typename T> struct safely_multipliable<T, constraints_t<std::is_unsigned<T>, is_nbit<T, 64>>> { using type = __uint128_t; };
    template <typename T> using safely_multipliable_t = typename safely_multipliable<T>::type;

    template <typename T, typename = void> struct rec_value_type { using type = T; };
    template <typename T> struct rec_value_type<T, std::void_t<typename T::value_type>> {
        using type = typename rec_value_type<typename T::value_type>::type;
    };
    template <typename T> using rec_value_type_t = typename rec_value_type<T>::type;

    template <typename T> class is_iterable {
        template <typename T_> static auto test(T_ e) -> decltype(e.begin(), e.end(), std::true_type{});
        static std::false_type test(...);
    public:
        static constexpr bool value = decltype(test(std::declval<T>()))::value;
    };
    template <typename T> static constexpr bool is_iterable_v = is_iterable<T>::value;
    template <typename T> class is_writable {
        template <typename T_> static auto test(T_ e) -> decltype(std::declval<std::ostream&>() << e, std::true_type{});
        static std::false_type test(...);
    public:
        static constexpr bool value = decltype(test(std::declval<T>()))::value;
    };
    template <typename T> static constexpr bool is_writable_v = is_writable<T>::value;
    template <typename T> class is_readable {
        template <typename T_> static auto test(T_ e) -> decltype(std::declval<std::istream&>() >> e, std::true_type{});
        static std::false_type test(...);
    public:
        static constexpr bool value = decltype(test(std::declval<T>()))::value;
    };
    template <typename T> static constexpr bool is_readable_v = is_readable<T>::value;
} // namespace suisen
namespace suisen::io {
    template <typename IStream, std::enable_if_t<std::conjunction_v<std::is_base_of<std::istream, std::remove_reference_t<IStream>>, std::negation<std::is_const<std::remove_reference_t<IStream>>>>, std::nullptr_t> = nullptr>
    struct InputStream {
    private:
        using istream_type = std::remove_reference_t<IStream>;
        IStream is;
        struct { InputStream* is; template <typename T> operator T() { T e; *is >> e; return e; } } _reader{ this };
    public:
        template <typename IStream_> InputStream(IStream_ &&is) : is(std::move(is)) {}
        template <typename IStream_> InputStream(IStream_ &is) : is(is) {}
        template <typename T> InputStream& operator>>(T& e) {
            if constexpr (suisen::is_readable_v<T>) is >> e; else _read(e);
            return *this;
        }
        auto read() { return _reader; }
        template <typename Head, typename... Tail>
        void read(Head& head, Tail &...tails) { ((*this >> head) >> ... >> tails); }
        istream_type& get_stream() { return is; }
    private:
        static __uint128_t _stou128(const std::string& s) {
            __uint128_t ret = 0;
            for (char c : s) if ('0' <= c and c <= '9') ret = 10 * ret + c - '0';
            return ret;
        }
        static __int128_t _stoi128(const std::string& s) { return (s[0] == '-' ? -1 : +1) * _stou128(s); }

        void _read(__uint128_t& v) { v = _stou128(std::string(_reader)); }
        void _read(__int128_t& v) { v = _stoi128(std::string(_reader)); }
        template <typename T, typename U>
        void _read(std::pair<T, U>& a) { *this >> a.first >> a.second; }
        template <size_t N = 0, typename ...Args>
        void _read(std::tuple<Args...>& a) { if constexpr (N < sizeof...(Args)) *this >> std::get<N>(a), _read<N + 1>(a); }
        template <typename Iterable, std::enable_if_t<suisen::is_iterable_v<Iterable>, std::nullptr_t> = nullptr>
        void _read(Iterable& a) { for (auto& e : a) *this >> e; }
    };
    template <typename IStream>
    InputStream(IStream &&) -> InputStream<IStream>;
    template <typename IStream>
    InputStream(IStream &) -> InputStream<IStream&>;

    InputStream cin{ std::cin };

    auto read() { return cin.read(); }
    template <typename Head, typename... Tail>
    void read(Head& head, Tail &...tails) { cin.read(head, tails...); }
} // namespace suisen::io
namespace suisen { using io::read; } // namespace suisen

namespace suisen::io {
    template <typename OStream, std::enable_if_t<std::conjunction_v<std::is_base_of<std::ostream, std::remove_reference_t<OStream>>, std::negation<std::is_const<std::remove_reference_t<OStream>>>>, std::nullptr_t> = nullptr>
    struct OutputStream {
    private:
        using ostream_type = std::remove_reference_t<OStream>;
        OStream os;
    public:
        template <typename OStream_> OutputStream(OStream_ &&os) : os(std::move(os)) {}
        template <typename OStream_> OutputStream(OStream_ &os) : os(os) {}
        template <typename T> OutputStream& operator<<(const T& e) {
            if constexpr (suisen::is_writable_v<T>) os << e; else _print(e);
            return *this;
        }
        void print() { *this << '\n'; }
        template <typename Head, typename... Tail>
        void print(const Head& head, const Tail &...tails) { *this << head, ((*this << ' ' << tails), ...), *this << '\n'; }
        template <typename Iterable, std::enable_if_t<suisen::is_iterable_v<Iterable>, std::nullptr_t> = nullptr>
        void print_all(const Iterable& v, std::string sep = " ", std::string end = "\n") {
            for (auto it = v.begin(); it != v.end();) if (*this << *it; ++it != v.end()) *this << sep;
            *this << end;
        }
        ostream_type& get_stream() { return os; }
    private:
        void _print(__uint128_t value) {
            char buffer[41], *d = std::end(buffer);
            do *--d = '0' + (value % 10), value /= 10; while (value);
            os.rdbuf()->sputn(d, std::end(buffer) - d);
        }
        void _print(__int128_t value) {
            if (value < 0) *this << '-';
            _print(__uint128_t(value < 0 ? -value : value));
        }
        template <typename T, typename U>
        void _print(const std::pair<T, U>& a) { *this << a.first << ' ' << a.second; }
        template <size_t N = 0, typename ...Args>
        void _print(const std::tuple<Args...>& a) {
            if constexpr (N < std::tuple_size_v<std::tuple<Args...>>) {
                if constexpr (N) *this << ' ';
                *this << std::get<N>(a), _print<N + 1>(a);
            }
        }
        template <typename Iterable, std::enable_if_t<suisen::is_iterable_v<Iterable>, std::nullptr_t> = nullptr>
        void _print(const Iterable& a) { print_all(a, " ", ""); }
    };
    template <typename OStream_>
    OutputStream(OStream_ &&) -> OutputStream<OStream_>;
    template <typename OStream_>
    OutputStream(OStream_ &) -> OutputStream<OStream_&>;

    OutputStream cout{ std::cout }, cerr{ std::cerr };

    template <typename... Args>
    void print(const Args &... args) { cout.print(args...); }
    template <typename Iterable, std::enable_if_t<suisen::is_iterable_v<Iterable>, std::nullptr_t> = nullptr>
    void print_all(const Iterable& v, const std::string& sep = " ", const std::string& end = "\n") { cout.print_all(v, sep, end); }
} // namespace suisen::io
namespace suisen { using io::print, io::print_all; } // namespace suisen

namespace suisen {
    template <class T, class ToKey, class CompKey = std::less<>, std::enable_if_t<std::conjunction_v<std::is_invocable<ToKey, T>, std::is_invocable_r<bool, CompKey, std::invoke_result_t<ToKey, T>, std::invoke_result_t<ToKey, T>>>, std::nullptr_t> = nullptr>
    auto comparator(const ToKey& to_key, const CompKey& comp_key = std::less<>()) {
        return [=](const T& x, const T& y) { return comp_key(to_key(x), to_key(y)); };
    }
    template <class Compare, std::enable_if_t<std::is_invocable_r_v<bool, Compare, int, int>, std::nullptr_t> = nullptr>
    std::vector<int> sorted_indices(int n, const Compare& compare) {
        std::vector<int> p(n);
        return std::iota(p.begin(), p.end(), 0), std::sort(p.begin(), p.end(), compare), p;
    }
    template <class ToKey, std::enable_if_t<std::is_invocable_v<ToKey, int>, std::nullptr_t> = nullptr>
    std::vector<int> sorted_indices(int n, const ToKey& to_key) { return sorted_indices(n, comparator<int>(to_key)); }
    template <class T, class Comparator>
    auto priority_queue_with_comparator(const Comparator& comparator) { return std::priority_queue<T, std::vector<T>, Comparator>{ comparator }; }
    template <class Iterable, std::enable_if_t<suisen::is_iterable_v<Iterable>, std::nullptr_t> = nullptr>
    void sort_unique_erase(Iterable& a) { std::sort(a.begin(), a.end()), a.erase(std::unique(a.begin(), a.end()), a.end()); }

    template <size_t D> struct Dim : std::array<int, D> {
        template <typename ...Ints> Dim(const Ints& ...ns) : std::array<int, D>::array{ static_cast<int>(ns)... } {}
    };
    template <typename ...Ints> Dim(const Ints& ...) -> Dim<sizeof...(Ints)>;
    template <class T, size_t D, size_t I = 0>
    auto ndvec(const Dim<D> &ns, const T& value = {}) {
        if constexpr (I + 1 < D) {
            return std::vector(ns[I], ndvec<T, D, I + 1>(ns, value));
        } else {
            return std::vector<T>(ns[I], value);
        }
    }
}
namespace suisen {
    using int128 = __int128_t;
    using uint128 = __uint128_t;
    template <class T> using min_priority_queue = std::priority_queue<T, std::vector<T>, std::greater<T>>;
    template <class T> using max_priority_queue = std::priority_queue<T, std::vector<T>, std::less<T>>;
}
namespace suisen { const std::string Yes = "Yes", No = "No", YES = "YES", NO = "NO"; }

#ifdef LOCAL
#  define debug(...) debug_impl(#__VA_ARGS__, __VA_ARGS__)
template <class H, class... Ts> void debug_impl(const char* s, const H& h, const Ts&... t) {
    suisen::io::cerr << "[\033[32mDEBUG\033[m] " << s << ": " << h, ((suisen::io::cerr << ", " << t), ..., (suisen::io::cerr << "\n"));
}
#else
#  define debug(...) void(0)
#endif
#define FOR(e, v) for (auto &&e : v)
#define CFOR(e, v) for (const auto &e : v)
#define REP(i, ...) CFOR(i, suisen::macro::rep_impl(__VA_ARGS__))
#define RREP(i, ...) CFOR(i, suisen::macro::rrep_impl(__VA_ARGS__))
#define REPINF(i, ...) CFOR(i, suisen::macro::repinf_impl(__VA_ARGS__))
#define LOOP(n) for ([[maybe_unused]] const auto& _ : suisen::macro::rep_impl(n))
#define ALL(iterable) std::begin(iterable), std::end(iterable)

using namespace suisen;
using namespace std;
struct io_setup {
    io_setup(int precision = 20) {
        std::ios::sync_with_stdio(false), std::cin.tie(nullptr);
        std::cout << std::fixed << std::setprecision(precision);
    }
} io_setup_ {};

constexpr int iinf = std::numeric_limits<int>::max() / 2;
constexpr long long linf = std::numeric_limits<long long>::max() / 2;

#include <cassert>
#include <cstdint>
#include <optional>
#include <tuple>
#include <utility>
#include <vector>

namespace suisen {
    struct FunctionalGraph {
        struct Doubling;
        template <typename T, T(*)(T, T), T(*)()>
        struct DoublingSum;
        friend struct Doubling;
        template <typename T, T(*op)(T, T), T(*e)()>
        friend struct DoublingSum;

        FunctionalGraph() : FunctionalGraph(0) {}
        FunctionalGraph(int n) : _n(n), _nxt(n) {}
        FunctionalGraph(const std::vector<int>& nxt) : _n(nxt.size()), _nxt(nxt) {}

        const int& operator[](int u) const {
            return _nxt[u];
        }
        int& operator[](int u) {
            return _nxt[u];
        }

        struct Doubling {
            friend struct FunctionalGraph;

            int query(int u, long long d) const {
                for (int l = _log; l >= 0; --l) if ((d >> l) & 1) u = _nxt[l][u];
                return u;
            }

            struct BinarySearchResult {
                int v;
                long long step;
                operator std::pair<int, long long>() const { return std::pair<int, long long>{ v, step }; }
            };

            template <typename Pred>
            auto max_step(int u, Pred &&f) const {
                assert(f(u));
                long long step = 0;
                for (int l = _log; l >= 0; --l) if (int nxt_u = _nxt[l][u]; f(nxt_u)) {
                    u = nxt_u, step |= 1LL << l;
                }
                return BinarySearchResult{ u, step };
            }

            template <typename Pred>
            std::optional<BinarySearchResult> step_until(int u, Pred &&f) const {
                if (f(u)) return BinarySearchResult { u, 0 };
                auto [v, step] = max_step(u, [&](int v) { return not f(v); });
                v = _nxt[0][v], ++step;
                if (not f(v)) return std::nullopt;
                return BinarySearchResult{ v, step };
            }

        private:
            int _n, _log;
            std::vector<std::vector<int>> _nxt;

            Doubling(const std::vector<int>& nxt, long long max_step) : _n(nxt.size()), _log(floor_log2(max_step)), _nxt(_log + 1, std::vector<int>(_n)) {
                _nxt[0] = nxt;
                for (int i = 1; i <= _log; ++i) for (int j = 0; j < _n; ++j) {
                    _nxt[i][j] = _nxt[i - 1][_nxt[i - 1][j]];
                }
            }
        };

        template <typename T, T(*op)(T, T), T(*e)()>
        struct DoublingSum : private Doubling {
            friend struct FunctionalGraph;

            struct Result {
                int v;
                T sum;
                operator std::pair<int, T>() const { return std::pair<int, T>{ v, sum }; }
            };

            auto query(int u, long long d) const {
                T sum = e();
                for (int l = _log; l >= 0; --l) if ((d >> l) & 1) sum = op(sum, _dat[l][std::exchange(u, _nxt[l][u])]);
                return Result{ u, sum };
            }

            struct BinarySearchResult {
                int v;
                T sum;
                long long step;
                operator std::tuple<int, T, long long>() const { return std::tuple<int, T, long long>{ v, sum, step }; }
            };

            template <typename Pred>
            auto max_step(int u, Pred &&f) const {
                assert(f(e()));
                long long step = 0;
                T sum = e();
                for (int l = _log; l >= 0; --l) {
                    if (T nxt_sum = op(sum, _dat[l][u]); f(nxt_sum)) {
                        sum = std::move(nxt_sum), u = _nxt[l][u], step |= 1LL << l;
                    }
                }
                return BinarySearchResult{ u, sum, step };
            }
            template <typename Pred>
            std::optional<BinarySearchResult> step_until(int u, Pred &&f) const {
                if (f(e())) return BinarySearchResult { u, e(), 0 };
                auto [v, sum, step] = max_step(u, [&](const T& v) { return not f(v); });
                sum = op(sum, _dat[0][v]), v = _nxt[0][v], ++step;
                if (not f(sum)) return std::nullopt;
                return BinarySearchResult{ v, sum, step };
            }

        private:
            std::vector<std::vector<T>> _dat;

            DoublingSum(const std::vector<int>& nxt, long long max_step, const std::vector<T>& dat) : Doubling(nxt, max_step), _dat(_log + 1, std::vector<T>(_n, e())) {
                _dat[0] = dat;
                for (int i = 1; i <= _log; ++i) for (int j = 0; j < _n; ++j) {
                    _dat[i][j] = op(_dat[i - 1][j], _dat[i - 1][_nxt[i - 1][j]]);
                }
            }
        };

        Doubling doubling(long long max_step) const {
            return Doubling(_nxt, max_step);
        }

        template <typename T, T(*op)(T, T), T(*e)()>
        DoublingSum<T, op, e> doubling(long long max_step, const std::vector<T>& dat) const {
            return DoublingSum<T, op, e>(_nxt, max_step, dat);
        }

        struct InfinitePath {
            int head_v;
            int head_len;
            int loop_v;
            int loop_len;
            InfinitePath() = default;
            InfinitePath(int head_v, int head_len, int loop_v, int loop_len) : head_v(head_v), head_len(head_len), loop_v(loop_v), loop_len(loop_len) {}
        };

        std::vector<InfinitePath> infinite_paths() const {
            std::vector<InfinitePath> res(_n);

            std::vector<int> vis(_n, _n);
            std::vector<int> dep(_n, 0);

            int time = 0;
            auto dfs = [&](auto dfs, int u) -> int {
                vis[u] = time;
                int v = _nxt[u];
                if (vis[v] == vis[u]) { // found cycle
                    int loop_len = dep[u] - dep[v] + 1;
                    res[u] = { u, 0, u, loop_len };
                    return loop_len - 1;
                } else if (vis[v] < vis[u]) {
                    res[u] = { u, res[v].head_len + 1, res[v].loop_v, res[v].loop_len };
                    return 0;
                } else {
                    dep[v] = dep[u] + 1;
                    int c = dfs(dfs, v);
                    if (c > 0) { // in cycle
                        res[u] = { u, 0, u, res[v].loop_len };
                        return c - 1;
                    } else { // out of cycle
                        res[u] = { u, res[v].head_len + 1, res[v].loop_v, res[v].loop_len };
                        return 0;
                    }
                }
            };
            for (int i = 0; i < _n; ++i, ++time) if (vis[i] == _n) dfs(dfs, i);
            return res;
        }

        /**
         * Calculates k'th iterate: f(f(f(...f(i)))) for all 0 <= i < N in O(N) time.
         * Reference: https://noshi91.hatenablog.com/entry/2019/09/22/114149
         */
        std::vector<int> kth_iterate(const long long k) const {
            assert(k >= 0);
            std::vector<int> res(_n);
            std::vector<int> forest_roots;
            std::vector<std::vector<int>> forest(_n);
            std::vector<std::vector<std::pair<long long, int>>> qs(_n);
            for (const auto& path : infinite_paths()) {
                const int v = path.head_v;
                (path.head_len == 0 ? forest_roots : forest[_nxt[v]]).push_back(v);
                if (path.head_len >= k) continue;
                qs[path.loop_v].emplace_back(k - path.head_len, v);
            }
            std::vector<int> dfs_path(_n);
            auto dfs = [&](auto dfs, int u, int d) -> void {
                dfs_path[d] = u;
                if (d >= k) res[u] = dfs_path[d - k];
                for (int v : forest[u]) dfs(dfs, v, d + 1);
            };
            for (int root : forest_roots) dfs(dfs, root, 0);
            std::vector<int8_t> seen(_n, false);
            for (int root : forest_roots) {
                if (seen[root]) continue;
                std::vector<int> cycle{ root };
                for (int v = _nxt[root]; v != root; v = _nxt[v]) cycle.push_back(v);
                const int len = cycle.size();
                for (int i = 0; i < len; ++i) {
                    const int s = cycle[i];
                    seen[s] = true;
                    for (const auto& [rem, res_index] : qs[s]) {
                        res[res_index] = cycle[(i + rem) % len];
                    }
                }
            }
            return res;
        }

    private:
        int _n;
        std::vector<int> _nxt;

        static int floor_log2(long long v) {
            int l = 0;
            while (1LL << (l + 1) <= v) ++l;
            return l;
        }
    };
} // namespace suisen

namespace suisen {
class HeavyLightDecomposition {
    public:
        template <typename Q>
        using is_point_update_query = std::is_invocable<Q, int>;
        template <typename Q>
        using is_range_update_query = std::is_invocable<Q, int, int>;
        template <typename Q, typename T>
        using is_point_get_query  = std::is_same<std::invoke_result_t<Q, int>, T>;
        template <typename Q, typename T>
        using is_range_fold_query = std::is_same<std::invoke_result_t<Q, int, int>, T>;

        using Graph = std::vector<std::vector<int>>;

        HeavyLightDecomposition() = default;
        HeavyLightDecomposition(Graph &g) : n(g.size()), visit(n), leave(n), head(n), ord(n), siz(n), par(n, -1), dep(n, 0) {
            for (int i = 0; i < n; ++i) if (par[i] < 0) dfs(g, i, -1);
            int time = 0;
            for (int i = 0; i < n; ++i) if (par[i] < 0) hld(g, i, -1, time);
        }
        HeavyLightDecomposition(Graph &g, const std::vector<int> &roots) : n(g.size()), visit(n), leave(n), head(n), ord(n), siz(n), par(n, -1), dep(n, 0) {
            for (int i : roots) dfs(g, i, -1);
            int time = 0;
            for (int i : roots) hld(g, i, -1, time);
        }
        int size() const {
            return n;
        }
        int lca(int u, int v) const {
            for (;; v = par[head[v]]) {
                if (visit[u] > visit[v]) std::swap(u, v);
                if (head[u] == head[v]) return u;
            }
        }
        int la(int u, int k, int default_value = -1) const {
            if (k < 0) return default_value;
            while (u >= 0) {
                int h = head[u];
                if (visit[u] - k >= visit[h]) return ord[visit[u] - k];
                k -= visit[u] - visit[h] + 1;
                u = par[h];
            }
            return default_value;
        }
        int jump(int u, int v, int d, int default_value = -1) const {
            if (d < 0) return default_value;
            const int w = lca(u, v);
            int uw = dep[u] - dep[w];
            if (d <= uw) return la(u, d);
            int vw = dep[v] - dep[w];
            return d <= uw + vw ? la(v, (uw + vw) - d) : default_value;
        }
        int dist(int u, int v) const {
            return dep[u] + dep[v] - 2 * dep[lca(u, v)];
        }
        template <typename T, typename Q, typename F, constraints_t<is_range_fold_query<Q, T>, std::is_invocable_r<T, F, T, T>> = nullptr>
        T fold_path(int u, int v, T identity, F bin_op, Q fold_query, bool is_edge_query = false) const {
            T res = identity;
            for (;; v = par[head[v]]) {
                if (visit[u] > visit[v]) std::swap(u, v);
                if (head[u] == head[v]) break;
                res = bin_op(fold_query(visit[head[v]], visit[v] + 1), res);
            }
            return bin_op(fold_query(visit[u] + is_edge_query, visit[v] + 1), res);
        }
        template <
            typename T, typename Q1, typename Q2, typename F,
            constraints_t<is_range_fold_query<Q1, T>, is_range_fold_query<Q2, T>, std::is_invocable_r<T, F, T, T>> = nullptr
        >
        T fold_path_noncommutative(int u, int v, T identity, F bin_op, Q1 fold_query, Q2 fold_query_rev, bool is_edge_query = false) const {
            T res_u = identity, res_v = identity;
            // a := lca(u, v)
            // res = fold(u -> a) + fold(a -> v)
            while (head[u] != head[v]) {
                if (visit[u] < visit[v]) { // a -> v
                    res_v = bin_op(fold_query(visit[head[v]], visit[v] + 1), res_v);
                    v = par[head[v]];
                } else { // u -> a
                    res_u = bin_op(res_u, fold_query_rev(visit[head[u]], visit[u] + 1));
                    u = par[head[u]];
                }
            }
            if (visit[u] < visit[v]) { // a = u
                res_v = bin_op(fold_query(visit[u] + is_edge_query, visit[v] + 1), res_v);
            } else { // a = v
                res_u = bin_op(res_u, fold_query_rev(visit[v] + is_edge_query, visit[u] + 1));
            }
            return bin_op(res_u, res_v);
        }
        template <typename Q, constraints_t<is_range_update_query<Q>> = nullptr>
        void update_path(int u, int v, Q update_query, bool is_edge_query = false) const {
            for (;; v = par[head[v]]) {
                if (visit[u] > visit[v]) std::swap(u, v);
                if (head[u] == head[v]) break;
                update_query(visit[head[v]], visit[v] + 1);
            }
            update_query(visit[u] + is_edge_query, visit[v] + 1);
        }
        template <typename T, typename Q, constraints_t<is_range_fold_query<Q, T>> = nullptr>
        T fold_subtree(int u, Q fold_query, bool is_edge_query = false) const {
            return fold_query(visit[u] + is_edge_query, leave[u]);
        }
        template <typename Q, constraints_t<is_range_update_query<Q>> = nullptr>
        void update_subtree(int u, Q update_query, bool is_edge_query = false) const {
            update_query(visit[u] + is_edge_query, leave[u]);
        }
        template <typename T, typename Q, constraints_t<is_point_get_query<Q, T>> = nullptr>
        T get_point(int u, Q get_query) const {
            return get_query(visit[u]);
        }
        template <typename Q, constraints_t<is_point_update_query<Q>> = nullptr>
        void update_point(int u, Q update_query) const {
            update_query(visit[u]);
        }
        std::vector<int> inv_ids() const {
            std::vector<int> inv(n);
            for (int i = 0; i < n; ++i) inv[visit[i]] = i;
            return inv;
        }
        int get_visit_time(int u) const {
            return visit[u];
        }
        int get_leave_time(int u) const {
            return leave[u];
        }
        int get_head(int u) const {
            return head[u];
        }
        int get_kth_visited(int k) const {
            return ord[k];
        }
        int get_subtree_size(int u) const {
            return siz[u];
        }
        int get_parent(int u) const {
            return par[u];
        }
        int get_depth(int u) const {
            return dep[u];
        }
        std::vector<int> get_roots() const {
            std::vector<int> res;
            for (int i = 0; i < n; ++i) if (par[i] < 0) res.push_back(i);
            return res;
        }
    private:
        int n;
        std::vector<int> visit, leave, head, ord, siz, par, dep;
        int dfs(Graph &g, int u, int p) {
            par[u] = p;
            siz[u] = 1;
            int max_size = 0;
            for (int &v : g[u]) {
                if (v == p) continue;
                dep[v] = dep[u] + 1;
                siz[u] += dfs(g, v, u);
                if (max_size < siz[v]) {
                    max_size = siz[v];
                    std::swap(g[u].front(), v);
                }
            }
            return siz[u];
        }
        void hld(Graph &g, int u, int p, int &time) {
            visit[u] = time, ord[time] = u, ++time;
            head[u] = p >= 0 and g[p].front() == u ? head[p] : u;
            for (int v : g[u]) {
                if (v != p) hld(g, v, u, time);
            }
            leave[u] = time;
        }
};
} // namespace suisen

#include <atcoder/dsu>
#include <atcoder/math>

void solve() {
    int n, L, R;
    read(n, L, R);
    vector<int> a(n);
    read(a);
    for (auto &e : a) --e;
    FunctionalGraph g(a);
    auto paths = g.infinite_paths();

    atcoder::dsu uf(n);
    vector<int> ss;
    REP(i, n) {
        int j = a[i];
        if (uf.same(i, j)) {
            ss.push_back(j);
        } else {
            uf.merge(i, j);
        }
    }

    vector<int> pos(n, -1);

    atcoder::dsu uf_cycle(n);

    set<pair<int, int>> ce;
    vector<int> cv;
    for (int s : ss) {
        int id = 0;
        for (int v = s;;) {
            pos[v] = id++;

            cv.push_back(v);
            ce.emplace(v, a[v]);
            uf_cycle.merge(v, a[v]);
            v = a[v];
            if (v == s) break;
        }
    }

    vector<vector<int>> t(n);
    REP(i, n) {
        int j = a[i];
        if (ce.count({ i, j })) {
            continue;
        }
        t[j].push_back(i);
    }
    vector<int> d(n);
    HeavyLightDecomposition hld(t, cv);
    for (int r : cv) {
        auto dfs = [&](auto dfs, int u) -> void {
            for (int v : t[u]) {
                d[v] = d[u] + 1;
                dfs(dfs, v);
            }
        };
        dfs(dfs, r);
    }
    
    auto f = [&](int u, int v) -> pair<int, int> {
        if (paths[u].loop_v != paths[v].loop_v) {
            if (paths[v].loop_v != v) return { -1, -1 };
            int x = paths[u].loop_v;
            if (not uf_cycle.same(x, v)) return { -1, -1 };
            // u -> x
            // x -> v
            int a = d[u];
            int px = pos[x];
            int pv = pos[v];
            int l = paths[x].loop_len;
            if (px <= pv) {
                a += pv - px;
            } else {
                a += pv - px + l;
            }
            return { a, l };
        }
        int tu = hld.get_visit_time(u);
        int tvl = hld.get_visit_time(v);
        int tvr = hld.get_leave_time(v);
        if (tvl <= tu and tu < tvr) {
            return { d[u] - d[v], paths[v].loop_v != v ? iinf : paths[v].loop_len };
        }
        return { -1, -1 };
    };

    int q;
    read(q);
    LOOP(q) {
        int s, t;
        read(s, t);
        --s, --t;

        auto [a, b] = f(s, t);
        if (a == -1) {
            print(-1);
            continue;
        }
        assert(a > 0 and b > 0);
        if (b == iinf) {
            // kL <= a <= kR
            int kl = fld(a, L), kr = cld(a, R);
            print(kr <= kl ? kr : -1);
            continue;
        }
        // xL <= A+yB <= xR
        constexpr long long INF = 10000000;
        long long xmin = cld(a, R);

        long long offset_sumR = atcoder::floor_sum(xmin, b, R, -a);
        long long offset_sumL = atcoder::floor_sum(xmin, b, L, -(a + 1));
        long long ng = cld(a, R) - 1, ok = INF;
        while (ok - ng > 1) {
            long long x = (ok + ng) / 2;
            long long sumR = atcoder::floor_sum(x + 1, b, R, -a) - offset_sumR;
            long long sumL = atcoder::floor_sum(x + 1, b, L, -(a + 1)) - offset_sumL;
            (sumL < sumR ? ok : ng) = x;
        }
        print(ok == INF ? -1 : ok);
    }
}

int main() {
    int test_case_num = 1;
    // read(test_case_num);
    LOOP(test_case_num) solve();
    return 0;
}