/*
URL https://
SCORE 0
AC false
WA false
TLE false
MLE false
TASK_TYPE
FAILURE_TYPE
NOTES
*/
#include <iostream>
#include <cstdint>
#include <utility>
#include <tuple>
#include <vector>
#include <stack>
#include <queue>
#include <unordered_map>
#include <unordered_set>
#include <map>
#include <set>
#include <algorithm>
#include <limits>
#include <numeric>
#include <iomanip>
#include <type_traits>
#include <functional>
#include <experimental/optional>

/* import STL */
// stream
using std::cout;
using std::cerr;
using std::cin;
using std::endl;
using std::flush;

// basic types
using std::nullptr_t;
using std::experimental::optional;
using std::pair;
using std::tuple;
using std::string;

// function for basic types
using std::experimental::make_optional;
using std::make_pair;
using std::make_tuple;
using std::get;

/* TODO remove them */
using std::vector;
using std::queue;
using std::stack;

// algorithms
using std::upper_bound;
using std::lower_bound;
using std::min_element;
using std::max_element;
using std::nth_element;
using std::accumulate;

/* macros */
// loops
#define REP(i, n) for (i64 i = 0; i < static_cast<decltype(i)>(n); ++i)
#define REPR(i, n) for (i64 i = (n) - 1; i >= static_cast<decltype(i)>(0); --i)
#define FOR(i, n, m) for (i64 i = (n); i < static_cast<decltype(i)>(m); ++i)
#define FORR(i, n, m) for (i64 i = (m) - 1; i >= static_cast<decltype(i)>(n); --i)
#define EACH(x, xs) for (auto &x: (xs))
#define EACH_V(x, xs) for (auto x: (xs))

// helpers
#define CTR(x) (x).begin(), (x).end()

/* utils for std::tuple */
namespace internal { namespace tuple_utils { // TODO rename to "internal::tuple"
    template<size_t...>
    struct seq {};

    template<size_t N, size_t... Is>
    struct gen_seq : gen_seq<N - 1, N - 1, Is...> {};

    template<size_t... Is>
    struct gen_seq<0, Is...> : seq<Is...> {};

    template<class Tuple, size_t... Is>
    void read(std::istream &stream, Tuple &t, seq<Is...>) {
        static_cast<void>((int[]) {0, (void(stream >> get<Is>(t)), 0)...});
    }

    template<class Tuple, size_t... Is>
    void print(std::ostream &stream, Tuple const &t, seq<Is...>) {
        static_cast<void>((int[]) {0, (void(stream << (Is == 0 ? "" : ", ") << get<Is>(t)), 0)...});
    }

    template<size_t I, class F, class A, class... Elems>
    struct ForEach {
        void operator()(A &arg, tuple<Elems...> const &t) const {
            F()(arg, get<I>(t));
            ForEach<I - 1, F, A, Elems...>()(arg, t);
        }

        void operator()(A &arg, tuple<Elems...> &t) const {
            F()(arg, get<I>(t));
            ForEach<I - 1, F, A, Elems...>()(arg, t);
        }
    };

    template<class F, class A, class... Elems>
    struct ForEach<0, F, A, Elems...> {
        void operator()(A &arg, tuple<Elems...> const &t) const {
            F()(arg, get<0>(t));
        }

        void operator()(A &arg, tuple<Elems...> &t) const {
            F()(arg, get<0>(t));
        }
    };

    template<class F, class A, class... Elems>
    void for_each(A &arg, tuple<Elems...> const &t) {
        ForEach<std::tuple_size<tuple<Elems...>>::value - 1, F, A, Elems...>()(arg, t);
    }

    template<class F, class A, class... Elems>
    void for_each(A &arg, tuple<Elems...> &t) {
        ForEach<std::tuple_size<tuple<Elems...>>::value - 1, F, A, Elems...>()(arg, t);
    }
}}

/* utils for Matrix (definition of Matrix) */
namespace internal { namespace matrix {
    template <typename V, int N>
    struct matrix_t {
        using type = std::vector<typename matrix_t<V, N-1>::type>;
    };
    template <typename V>
    struct matrix_t<V, 0> {
        using type = V;
    };

    template <typename V, int N>
    using Matrix = typename matrix_t<V, N>::type;

    template <typename V, typename It, int N>
    struct matrix_helper {
        static Matrix<V, N> create(const It &begin, const It &end, const V &default_value) {
            return Matrix<V, N>(*begin, matrix_helper<V, It, N - 1>::create(begin + 1, end, default_value));
        }
    };
    template <typename V, typename It>
    struct matrix_helper<V, It, 0> {
        static Matrix<V, 0> create(const It &begin __attribute__((unused)),
                                   const It &end __attribute__((unused)),
                                   const V &default_value) {
            return default_value;
        }
    };
}}

/* Primitive types */
using i8  =  int8_t; using  u8 =  uint8_t;
using i16 = int16_t; using u16 = uint16_t;
using i32 = int32_t; using u32 = uint32_t;
using i64 = int64_t; using u64 = uint64_t;
using usize = size_t;

/* Data structure type */
template <typename T> using Vector = std::vector<T>;
template <typename V> using OrderedSet = std::set<V>;
template <typename V> using HashSet = std::unordered_set<V>;
template <typename K, typename V> using OrderedMap = std::map<K, V>;
template <typename K, typename V> using HashMap = std::unordered_map<K, V>;
template <typename T, int N> using Matrix = internal::matrix::Matrix<T, N>;
template <typename T, typename Compare = std::less<T>, typename Container = std::vector<T>>
using PriorityQueue = std::priority_queue<T, Container, Compare>;

/* utils for Vector */
template <typename V>
Vector<V> make_pre_allocated_vector(size_t N) {
    Vector<V> retval;
    retval.reserve(N);
    return retval;
}

/* utils for Matrix */
template <class V, int N>
Matrix<V, N> make_matrix(const std::array<size_t, N> &shape, V default_value = V()) {
    return internal::matrix::matrix_helper<V, decltype(shape.begin()), N>::create(shape.begin(), shape.end(), default_value);
}

/* utils for STL iterators */
namespace internal {
    template <typename Iterator, typename F>
    struct MappedIterator {
        MappedIterator(const Iterator &it, const F &function) : it(it), function(function) {}
        auto operator *() const {
            return this->function(this->it);
        }
        void operator++() { ++this->it; }
        void operator+=(size_t n) { this->it += n; }
        auto operator+(size_t n) const {
            return MappedIterator<Iterator, F>(this->it + n, this->function);
        }
        bool operator==(const MappedIterator<Iterator, F> &rhs) const {
            return this->it == rhs.it;
        }
        bool operator!=(const MappedIterator<Iterator, F> &rhs) const {
            return !(*this == rhs);
        }
    private:
        Iterator it;
        F function;
    };
    template <typename Iterator, typename P>
    struct FilteredIterator {
        FilteredIterator(const Iterator &it, const Iterator &end, const P &predicate)
                : it(it), end(end), predicate(predicate) {
            if (this->it != end) {
                if (!predicate(this->it)) {
                    this->increment();
                }
            }
        }
        decltype(auto) operator *() const {
            return *this->it;
        }
        auto operator ->() const {
            return this->it;
        }
        void operator++() {
            this->increment();
        }
        void operator+=(size_t n) {
            REP (i, n) {
                this->increment();
            }
        }
        auto operator+(size_t n) const {
            auto retval = *this;
            retval += n;
            return retval;
        }
        bool operator==(const FilteredIterator<Iterator, P> &rhs) const {
            return this->it == rhs.it;
        }
        bool operator!=(const FilteredIterator<Iterator, P> &rhs) const {
            return !(*this == rhs);
        }
    private:
        void increment() {
            if (this->it == this->end) {
                return ;
            }
            ++this->it;
            while (this->it != this->end && !this->predicate(this->it)) {
                ++this->it;
            }
        }
        Iterator it;
        Iterator end;
        P predicate;
    };
    template <typename Iterator, typename ElementIterator>
    struct FlattenedIterator {
        FlattenedIterator(const Iterator &it, const Iterator &end) : it(make_pair(it, ElementIterator())), end(end) {
            if (this->it.first != this->end) {
                this->it.second = it->begin();
            }
            this->find_valid();
        }
        decltype(auto) operator *() const {
            return this->it;
        }
        const pair<Iterator, ElementIterator> *operator ->() const {
            return &this->it;
        }
        void operator++() {
            this->increment();
        }
        void operator+=(size_t n) {
            REP (i, n) {
                this->increment();
            }
        }
        auto operator+(size_t n) const {
            auto retval = *this;
            retval += n;
            return retval;
        }
        bool operator==(const FlattenedIterator<Iterator, ElementIterator> &rhs) const {
            if (this->it.first != rhs.it.first) {
                return false;
            }
            if (this->it.first == this->end || rhs.it.first == rhs.end) {
                if (this->end == rhs.end) {
                    return true;
                } else {
                    return false;
                }
            } else {
                return this->it.second == rhs.it.second;
            }
        }
        bool operator!=(const FlattenedIterator<Iterator, ElementIterator> &rhs) const {
            return !(*this == rhs);
        }
    private:
        bool is_end() const {
            return this->it.first == this->end;
        }
        bool is_valid() const {
            if (this->is_end()) return false;
            if (this->it.second == this->it.first->end()) return false;
            return true;
        }
        void _increment() {
            if (this->it.second == this->it.first->end()) {
                ++this->it.first;
                if (this->it.first != this->end) {
                    this->it.second = this->it.first->begin();
                }
            } else {
                ++this->it.second;
            }
        }
        void find_valid() {
            while (!this->is_end() && !this->is_valid()) {
                this->_increment();
            }
        }
        void increment() {
            this->_increment();
            while (!this->is_end() && !this->is_valid()) {
                this->_increment();
            }

        }
        pair<Iterator, ElementIterator> it;
        Iterator end;
    };
}

template <class Iterator>
struct Container {
    Container(const Iterator &begin, const Iterator &end) : m_begin(begin), m_end(end) {}
    const Iterator& begin() const {
        return this->m_begin;
    }
    const Iterator& end() const {
        return this->m_end;
    }
    Iterator m_begin;
    Iterator m_end;
};

template <typename C, typename F>
auto iterator_map(const C &c, F function) {
    using Iterator = std::remove_const_t<std::remove_reference_t<decltype(c.begin())>>;
    return Container<internal::MappedIterator<Iterator, F>>(
            internal::MappedIterator<Iterator, F>(c.begin(), function),
            internal::MappedIterator<Iterator, F>(c.end(), function));
}

template <typename C, typename P>
auto iterator_filter(const C &c, P predicate) {
    using Iterator = std::remove_const_t<std::remove_reference_t<decltype(c.begin())>>;
    return Container<internal::FilteredIterator<Iterator, P>>(
            internal::FilteredIterator<Iterator, P>(c.begin(), c.end(), predicate),
            internal::FilteredIterator<Iterator, P>(c.end(), c.end(), predicate));
}

template <typename C>
auto iterator_flatten(const C &c) {
    using Iterator = std::remove_const_t<std::remove_reference_t<decltype(c.begin())>>;
    using ElementIterator = std::remove_const_t<std::remove_reference_t<decltype(c.begin()->begin())>>;
    return Container<internal::FlattenedIterator<Iterator, ElementIterator>>(
            internal::FlattenedIterator<Iterator, ElementIterator>(c.begin(), c.end()),
            internal::FlattenedIterator<Iterator, ElementIterator>(c.end(), c.end()));
}

/* input */
template <class F, class S>
std::istream &operator>>(std::istream &stream, pair<F, S> &pair) {
    stream >> pair.first;
    stream >> pair.second;
    return stream;
}
template <class ...Args>
std::istream &operator>>(std::istream &stream, tuple<Args...> &tuple) {
    internal::tuple_utils::read(stream, tuple, internal::tuple_utils::gen_seq<sizeof...(Args)>());
    return stream;
}

template <class T>
T read() {
    T t;
    cin >> t;
    return t;
}
template <class F, class S>
pair<F, S> read() {
    pair<F, S> p;
    cin >> p;
    return p;
}
template <class T1, class T2, class T3, class ...Args>
tuple<T1, T2, T3, Args...> read() {
    tuple<T1, T2, T3, Args...> t;
    cin >> t;
    return t;
}
template <typename T, typename F = std::function<T()>>
Vector<T> read(const usize length, F r) {
    auto retval = make_pre_allocated_vector<T>(length);
    REP (i, length) {
        retval.emplace_back(r());
    }
    return retval;
}

template <class T>
Vector<T> read(const usize length) {
    return read<T>(length, [] { return read<T>(); });
}
template <class F, class S>
Vector<pair<F, S>> read(const usize length) {
    return read<pair<F, S>>(length);
}
template <class T1, class T2, class T3, class ...Args>
Vector<tuple<T1, T2, T3, Args...>> read(const usize length) {
    return read<tuple<T1, T2, T3, Args...>>(length);
}

namespace internal {
    template <typename T>
    struct oneline {
        std::string operator()(const T &t) const {
            std::ostringstream oss;
            oss << t;
            return oss.str();
        }
    };
    template <typename F, typename S>
    struct oneline<pair<F, S>> {
        std::string operator()(const pair<F, S> &p) const {
            std::ostringstream oss;
            oss << "{" << oneline<F>()(p.first) << ", " << oneline<S>()(p.second) << "}";
            return oss.str();
        }
    };
    template <typename ...Args>
    struct oneline<tuple<Args...>> {
        struct oneline_tuple {
            template<class V>
            void operator()(Vector<std::string> &strs, const V &v) const {
                strs.emplace_back(oneline<V>()(v));
            }
        };
        std::string operator()(const tuple<Args...> &t) const {
            std::ostringstream oss;
            Vector<std::string> strs;
            internal::tuple_utils::for_each<oneline_tuple, Vector<std::string>, Args...>(strs, t);
            oss << "{";
            REPR (i, strs.size()) {
                oss << strs[i];
                if (i != 0) {
                    oss << ", ";
                }
            }
            oss << "}";
            return oss.str();
        }
    };
    template <>
    struct oneline<bool> {
        std::string operator()(const bool b) const {
            return b ? "true" : "false";
        }
    };
    template <typename X>
    struct oneline<Vector<X>> {
        std::string operator()(const Vector<X> &vec) const {
            std::string retval = "[";
            auto f = oneline<X>();
            REP (i, vec.size()) {
                retval += f(vec[i]);
                if (i != static_cast<i64>(vec.size() - 1)) {
                    retval += ", ";
                }
            }
            retval += "]";
            return retval;
        }
    };
    template <typename X>
    struct oneline<OrderedSet<X>> {
        std::string operator()(const OrderedSet<X> &s) const {
            std::string retval = "{";
            auto f = oneline<X>();
            size_t ctr = 0;
            EACH (x, s) {
                retval += f(x);
                ctr += 1;
                if (ctr != s.size()) {
                    retval += ", ";
                }
            }
            retval += "}";
            return retval;
        }
    };
    template <typename X>
    struct oneline<HashSet<X>> {
        std::string operator()(const HashSet<X> &s) const {
            std::string retval = "{";
            auto f = oneline<X>();
            size_t ctr = 0;
            EACH (x, s) {
                retval += f(x);
                ctr += 1;
                if (ctr != s.size()) {
                    retval += ", ";
                }
            }
            retval += "}";
            return retval;
        }
    };
    template <typename K, typename V>
    struct oneline<OrderedMap<K, V>> {
        std::string operator()(const OrderedMap<K, V> &s) const {
            std::string retval = "{";
            auto f1 = oneline<K>();
            auto f2 = oneline<V>();
            size_t ctr = 0;
            EACH (x, s) {
                retval += f1(x.first);
                retval += ": ";
                retval += f2(x.second);
                ctr += 1;
                if (ctr != s.size()) {
                    retval += ", ";
                }
            }
            retval += "}";
            return retval;
        }
    };
    template <typename K, typename V>
    struct oneline<HashMap<K, V>> {
        std::string operator()(const HashMap<K,V> &s) const {
            std::string retval = "{";
            auto f1 = oneline<K>();
            auto f2 = oneline<V>();
            size_t ctr = 0;
            EACH (x, s) {
                retval += f1(x.first);
                retval += ": ";
                retval += f2(x.second);
                ctr += 1;
                if (ctr != s.size()) {
                    retval += ", ";
                }
            }
            retval += "}";
            return retval;
        }
    };

    template <typename V>
    struct keys { /* no implementation */ };
    template <typename X>
    struct keys<std::vector<X>> {
        Vector<size_t> operator()(const Vector<X> &v) const {
            Vector<size_t> keys;
            REP (i, v.size()) {
                keys.emplace_back(i);
            }
            return keys;
        }
    };
    template <typename K, typename V>
    struct keys<OrderedMap<K, V>> {
        Vector<K> operator()(const OrderedMap<K, V> &c) const {
            Vector<K> keys;
            EACH (elem, c) {
                keys.emplace_back(elem.first);
            }
            return keys;
        }
    };
    template <typename K, typename V>
    struct keys<HashMap<K, V>> {
        Vector<K> operator()(const HashMap<K, V> &c) const {
            Vector<K> keys;
            EACH (elem, c) {
                keys.emplace_back(elem.first);
            }
            return keys;
        }
    };
}

template <typename T>
void dump(const T& t) {
    using namespace internal;
    std::cerr << oneline<T>()(t) << std::endl;
}
template <typename V1, typename V2, typename ...Args>
void dump(const V1 &v1, const V2 &v2, const Args&... args) {
    using namespace internal;
    using F = typename oneline<tuple<V1, V2, Args...>>::oneline_tuple;
    auto x = std::make_tuple(v1, v2, args...);
    Vector<std::string> strs;
    internal::tuple_utils::for_each<F, Vector<std::string>, V1, V2, Args...>(strs, x);
    REPR (i, strs.size()) {
        std::cerr << strs[i];
        if (i != 0) {
            std::cerr << ", ";
        }
    }
    std::cerr << std::endl;
}

template <typename C>
std::string as_set(const C& ctr) {
    Vector<std::string> values;

    using namespace internal;
    EACH (x, ctr) {
        values.emplace_back(oneline<decltype(x)>()(x));
    }
    std::string retval = "---\n";
    REP (i, values.size()) {
        retval += values[i];
        retval += "\n";
    }
    retval += "---";

    return retval;
}

template <typename C>
std::string as_map(const C& ctr) {
    using namespace internal;

    auto ks = keys<C>()(ctr);
    Vector<std::string> keys;
    Vector<std::string> values;

    EACH (key, ks) {
        keys.emplace_back(oneline<decltype(key)>()(key));
        values.emplace_back(oneline<decltype(ctr.at(key))>()(ctr.at(key)));
    }
    size_t l = 0;
    EACH (key, keys) {
        l = std::max(l, key.size());
    }
    std::string retval = "---\n";
    REP (i, values.size()) {
        retval += keys[i];
        REP (j, l - keys[i].size()) {
            retval += " ";
        }
        retval += ": ";
        retval += values[i];
        retval += "\n";
    }
    retval += "---";

    return retval;
}

template <typename C>
std::string as_table(const C &ctr) {
    using namespace internal;
    auto rkeys = keys<C>()(ctr);
    auto ckeys = OrderedSet<std::string>();

    auto values = Vector<pair<std::string, OrderedMap<std::string, std::string>>>();

    /* Stringify all data */
    EACH (rkey, rkeys) {
        auto rkey_str = oneline<decltype(rkey)>()(rkey);
        values.emplace_back(rkey_str, OrderedMap<std::string, std::string>());

        auto row = ctr.at(rkey);
        auto ks = keys<decltype(row)>()(row);
        EACH (ckey, ks) {
            auto ckey_str = oneline<decltype(ckey)>()(ckey);
            ckeys.emplace(ckey_str);
            values.back().second.emplace(ckey_str, oneline<decltype(row.at(ckey))>()(row.at(ckey)));
        }
    }

    /* Calculate string length */
    size_t max_row_key_length = 0;
    EACH (value, values) {
        max_row_key_length = std::max(max_row_key_length, value.first.size());
    }

    OrderedMap<std::string, size_t> max_col_length;
    EACH (ckey, ckeys) {
        max_col_length.emplace(ckey, ckey.size());
    }

    EACH (value, values) {
        EACH (elem, value.second) {
            auto ckey = elem.first;
            auto value = elem.second;
            max_col_length[ckey] = std::max(max_col_length[ckey], value.size());
        }
    }

    std::string retval = "---\n";
    /* Header */
    REP(i, max_row_key_length) {
        retval += " ";
    }
    retval += "  ";
    size_t cnt = 0;
    EACH (ckey, ckeys) {
        retval += ckey;
        REP (j, max_col_length[ckey] - ckey.size()) {
            retval += " ";
        }

        cnt += 1;
        if (cnt != ckeys.size()) {
            retval += ", ";
        }
    }
    retval += "\n------\n";

    /* Values */
    EACH (value, values) {
        retval += value.first;
        REP(i, max_row_key_length - value.first.size()) {
            retval += " ";
        }
        retval += "| ";

        size_t cnt = 0;
        EACH (ckey, ckeys) {
            auto v = std::string("");
            if (value.second.find(ckey) != value.second.end()) {
                v = value.second.at(ckey);
            }
            retval += v;
            REP (j, max_col_length[ckey] - v.size()) {
                retval += " ";
            }

            cnt += 1;
            if (cnt != ckeys.size()) {
                retval += ", ";
            }

        }

        retval += "\n";
    }
    retval += "---";
    return retval;
}


// Hash
namespace std {
    template <class F, class S>
    struct hash<pair<F, S>> {
        size_t operator ()(const pair<F, S> &p) const {
            return hash<F>()(p.first) ^ hash<S>()(p.second);
        }
    };

    template <class ...Args>
    struct hash<tuple<Args...>> {
        struct hash_for_element {
            template<class V>
            void operator()(size_t &size, const V &v) const {
                size ^= std::hash<V>()(v);
            }
        };

        size_t operator ()(const tuple<Args...> &t) const {
            size_t retval = 0;

            internal::tuple_utils::for_each<hash_for_element, size_t, Args...>(retval, t);

            return retval;
        }
    };
}
#define MAIN
void body();

#include <stdexcept>
#include <cmath>

#ifndef MAIN
#include "common.cc"
#endif

/**
 * セグメント木
 *
 * @tparam V1 もとのコンテナの要素の型
 * @tparam V2 Segment木が扱う型
 * @tparam Accumulate V1からV2への変換関数。(V2, V2) -> V2と(V1) -> V2をオーバーロードしている必要がある。
 */
template <typename V1, typename V2, typename Accumulate>
struct SegmentTree {
    template <typename Iterator>
    SegmentTree(const Iterator &begin, const Iterator &end) : m_acc(Accumulate()), m_size(end - begin) {
        size_t n = 1;
        while (n < this->size()) {
            n *= 2;
        }
        this->m_tree.resize(2 * n - 1);

        this->initialize(begin, 0, 0, n);
    }
    template <typename Iterator>
    SegmentTree(const Iterator &begin, const Iterator &end, const Accumulate &acc) : m_acc(acc), m_size(end - begin) {
        size_t n = 1;
        while (n < this->size()) {
            n *= 2;
        }
        this->m_tree.resize(2 * n - 1);

        this->initialize(begin, 0, 0, n);
    }
    SegmentTree(const Vector<V1> &elems) : m_acc(Accumulate()), m_size(elems.size()) {
        size_t n = 1;
        while (n < this->size()) {
            n *= 2;
        }
        this->m_tree.resize(2 * n - 1);

        this->initialize(elems.begin(), 0, 0, n);
    }
    SegmentTree(const Vector<V1> &elems, const Accumulate &acc) : m_acc(acc), m_size(elems.size()) {
        size_t n = 1;
        while (n < this->size()) {
            n *= 2;
        }
        this->m_tree.resize(2 * n - 1);

        this->initialize(elems.begin(), 0, 0, n);
    }

    /**
     * [begin, end)に対応する値をreturnする。
     *
     * @param begin queryをかける先頭の要素
     * @param end queryをかける最後の要素+1
     * @return Accumulate(xs[begin], xs[begin+1], ... xs[end-1])
     * @throw out_of_range [begin, end)が領域外の場合、out_of_rangeをthrowする
     */
    V2 query(size_t begin, size_t end) const {
        auto v = this->query(begin, end, 0, 0, (this->m_tree.size() + 1) / 2);
        if (v) {
            return v.value();
        } else {
            throw std::out_of_range("");
        }
    }

    /**
     * indexの値をvalueに変更する
     *
     * @param index 変更する要素のindex
     * @param value 変更後の値
     */
    void update(size_t index, const V1 &value) {
        // 葉を表す要素へ
        auto k = index + (this->m_tree.size() + 1) / 2 - 1;
        this->m_tree[k] = this->m_acc(value);
        while (k > 0) {
            k = (k - 1) / 2;
            this->m_tree[k] = this->m_acc(value);

            size_t chl = k * 2 + 1;
            size_t chr = k * 2 + 2;
            if (this->m_tree[chl] && this->m_tree[chr]) {
                // 子ノードが両方valid
                this->m_tree[k] = this->m_acc(this->m_tree[chl].value(), this->m_tree[chr].value());
            } else if (this->m_tree[chl]) {
                // 右側は範囲外
                this->m_tree[k] = this->m_tree[chl];
            } else {
                // 両方範囲外
                this->m_tree[k] = {};
            }
        }
    }

    size_t size() const {
        return this->m_size;
    }
private:
    /**
     * m_tree[index]をbegin,...で初期化する。
     * l, rは計算簡略化のために引数にしている。
     *
     * @tparam Iterator Iteratorの型
     * @param begin 保存する要素の先頭
     * @param k 更新するindex
     * @param l 補助変数 (indexに対応するrangeの先頭)
     * @param r 補助変数 (indexに対応するrangeの末尾+1)
     */
    template <typename Iterator>
    void initialize(const Iterator &begin, size_t k, size_t l, size_t r) {
        if (r - l == 1) {
            // leafの場合
            if (l < this->size()) {
                this->m_tree[k] = make_optional(this->m_acc(*(begin + l)));
            } else {
                this->m_tree[k] = {};
            }
        } else {
            // nodeの場合
            size_t chl = k * 2 + 1;
            size_t chr = k * 2 + 2;
            this->initialize(begin, chl, l, (l + r) / 2);
            this->initialize(begin, chr, (l + r) / 2, r);
            if (this->m_tree[chl] && this->m_tree[chr]) {
                // 子ノードが両方valid
                this->m_tree[k] = this->m_acc(this->m_tree[chl].value(), this->m_tree[chr].value());
            } else if (this->m_tree[chl]) {
                // 右側は範囲外
                this->m_tree[k] = this->m_tree[chl];
            } else {
                // 両方範囲外
                this->m_tree[k] = {};
            }
        }
    }
    /**
     * [begin, end)に対応する値をreturnする。
     * index, l, rは計算簡略化のための補助変数
     *
     * @param begin queryの先頭
     * @param end queryの末尾+1
     * @param k 着目しているセグメント木の要素
     * @param l indexが扱うrangeの先頭
     * @param r　indexが扱うrangeの末尾+1
     * @return Accumulate(xs[begin], xs[begin+1], ... xs[end-1])
     */
    std::experimental::optional<V2> query(size_t begin, size_t end, size_t k, size_t l, size_t r) const {
        if (r <= begin || end <= l) {
            // query対象と扱うrangeが交差しない
            return {};
        }

        if (begin <= l && r <= end) {
            // query対象に完全に含まれる
            return this->m_tree[k];
        } else {
            auto vl = this->query(begin, end, k * 2 + 1, l, (l + r) / 2);
            auto vr = this->query(begin, end, k * 2 + 2, (l + r) / 2, r);
            if (vl && vr) {
                // 子ノードが両方valid
                return this->m_acc(vl.value(), vr.value());
            } else if (vl) {
                // 右側は範囲外
                return vl.value();
            } else if (vr) {
                // 左側は範囲外
                return vr.value();
            } else {
                // 両方範囲外
                return {};
            }
        }
    }

    Accumulate m_acc;
    Vector<std::experimental::optional<V2>> m_tree;
    size_t m_size;
};

namespace internal {
    template <typename V>
    struct Minimum {
        V operator()(const V &v) const { return v; }
        V operator()(const V &l, const V &r) const { return std::min(l, r); }
    };
}

template <typename V>
using RangeMinimumQuery = SegmentTree<V, V, internal::Minimum<V>>;


// main function (DO NOT EDIT)
int main (int argc, char **argv) {
    cin.tie(0);
    std::ios_base::sync_with_stdio(false);

    cout << std::fixed;
    body();

    return 0;
}

struct Accumulator {
    std::pair<size_t, i64> operator()(const std::pair<size_t, i64> &elem) const {
        return elem;
    }
    std::pair<size_t, i64> operator()(const std::pair<size_t, i64> &lhs, const std::pair<size_t, i64> &rhs) const {
        if (lhs.second > rhs.second) {
            return lhs;
        } else {
            return rhs;
        }
    }
};

void body() {
    auto N = read<i64>();
    auto M = read<i64>();
    auto ABs = read<i64, i64>(N);

    sort(CTR(ABs), [](auto lhs, auto rhs) { return lhs.first < rhs.first; });

    auto As = Vector<i64>(N);
    auto Bs_with_indexes = Vector<std::pair<size_t, i64>>(N);
    REP (i, N) {
        As[i] = ABs[i].first;
        Bs_with_indexes[i] = make_pair(i, ABs[i].second);
    }
    SegmentTree<std::pair<size_t, i64>, std::pair<size_t, i64>, Accumulator> q(Bs_with_indexes);

    i64 ans = 0;
    REPR(i, M + 1) {
        // i日目の仕事を決める
        // 間にあう仕事のを見つける
        // i + Ax <= M より Ax <= M - iを見つければ良い
        auto it = std::upper_bound(CTR(As), M - i);
        // ABs[:r]であれば間に合う
        auto r = it - As.begin();

        if (r == 0) continue ;
        auto w = q.query(0, r);
        ans += w.second;

        // もうこの仕事はできないので報酬を0にする
        q.update(w.first, make_pair(w.first, 0));
    }

    cout << ans << endl;
}


Measured memory_bytes: 10368