// This is free and unencumbered software released into the public domain.

// Anyone is free to copy, modify, publish, use, compile, sell, or
// distribute this software, either in source code form or as a compiled
// binary, for any purpose, commercial or non-commercial, and by any
// means.

// In jurisdictions that recognize copyright laws, the author or authors
// of this software dedicate any and all copyright interest in the
// software to the public domain. We make this dedication for the benefit
// of the public at large and to the detriment of our heirs and
// successors. We intend this dedication to be an overt act of
// relinquishment in perpetuity of all present and future rights to this
// software under copyright law.

// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
// MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
// IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
// OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
// ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
// OTHER DEALINGS IN THE SOFTWARE.

// For more information, please refer to <http://unlicense.org>

/****************/
/* template.hpp */
/****************/

#include <algorithm>
#include <cassert>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits>

using std::cerr;
using std::cout;
using std::endl;
using std::max;
using std::min;
using std::swap;

struct BoolName : std::numpunct<char> {
  std::string t, f;
  BoolName(std::string t, std::string f) : t(t), f(f) {}
  std::string do_truename() const { return t; }
  std::string do_falsename() const { return f; }
};

void setBoolName(std::string t, std::string f) {
  cout.imbue(std::locale(cout.getloc(), new BoolName(t, f)));
}

struct Initializer {
  Initializer() {
    cout << std::fixed << std::setprecision(15) << std::boolalpha;
    setBoolName("Yes", "No");
  }
} initializer;

struct Input {
  bool eof;

  Input() : eof(false) {}

  operator char() {
    char v;
    this->eof = (std::scanf("%c", &v) != 1);
    return v;
  }

  operator int() {
    int v;
    this->eof = (std::scanf("%d", &v) != 1);
    return v;
  }

  operator long() {
    long v;
    this->eof = (std::scanf("%ld", &v) != 1);
    return v;
  }

  operator long long() {
    long long v;
    this->eof = (std::scanf("%lld", &v) != 1);
    return v;
  }

  operator unsigned int() {
    unsigned int v;
    this->eof = (std::scanf("%u", &v) != 1);
    return v;
  }

  operator unsigned long() {
    unsigned long v;
    this->eof = (std::scanf("%lu", &v) != 1);
    return v;
  }

  operator unsigned long long() {
    unsigned long long v;
    this->eof = (std::scanf("%llu", &v) != 1);
    return v;
  }

  operator double() {
    double v;
    this->eof = (std::scanf("%lf", &v) != 1);
    return v;
  }

  operator long double() {
    long double v;
    this->eof = (std::scanf("%Lf", &v) != 1);
    return v;
  }

  void ignore() const { getchar(); }
} in;

template <typename T> T abs(T a) { return a >= 0 ? a : -a; }

template <typename T, typename S> bool chmin(T &a, const S &b) {
  return a > b ? a = b, true : false;
}

template <typename T, typename S> bool chmax(T &a, const S &b) {
  return a < b ? a = b, true : false;
}

template <typename T, typename S> std::function<S(T)> cast() {
  return [](const T &t) { return static_cast<S>(t); };
}

template <typename T> T copy(const T &a) { return T(a); }

class ZeroPadding {
public:
  ZeroPadding(int n) : n(n) {}

  int n;
};

std::ostream &operator<<(std::ostream &os, const ZeroPadding &z) {
  os << std::setw(z.n) << std::setfill('0');
  return os;
}

template <typename T> constexpr T inf() {
  return std::numeric_limits<T>::max() / 2 - 1;
}

/******************/
/* arithmetic.hpp */
/******************/

template <typename T> class Addition {
public:
  template <typename V> T operator+(const V &v) const {
    return T(static_cast<const T &>(*this)) += v;
  }

  T operator++() { return static_cast<T &>(*this) += 1; }
};

template <typename T> class Subtraction {
public:
  template <typename V> T operator-(const V &v) const {
    return T(static_cast<const T &>(*this)) -= v;
  }
};

template <typename T> class Multiplication {
public:
  template <typename V> T operator*(const V &v) const {
    return T(static_cast<const T &>(*this)) *= v;
  }
};

template <typename T> class Division {
public:
  template <typename V> T operator/(const V &v) const {
    return T(static_cast<const T &>(*this)) /= v;
  }
};

template <typename T> class Modulus {
public:
  template <typename V> T operator%(const V &v) const {
    return T(static_cast<const T &>(*this)) %= v;
  }
};

template <typename T>
class IndivisibleArithmetic : public Addition<T>,
                              public Subtraction<T>,
                              public Multiplication<T> {};

template <typename T>
class Arithmetic : public IndivisibleArithmetic<T>, public Division<T> {};
/*************/
/* tuple.hpp */
/*************/

#include <tuple>

template <typename... T> class Tuple : public std::tuple<T...> {
public:
  Tuple(Input &in) : std::tuple<T...>() { (void)in; }
};

template <typename T, typename... S>
class Tuple<T, S...> : public std::tuple<T, S...> {
public:
  Tuple() : std::tuple<T, S...>() {}

  Tuple(T t, S... s) : std::tuple<T, S...>(t, s...) {}

  Tuple(const std::tuple<T, S...> &t) : std::tuple<T, S...>(t) {}

  Tuple(Input &in) {
    auto a = std::tuple<T>(in);
    std::tuple<S...> b = Tuple<S...>(in);
    std::tuple<T, S...> c = std::tuple_cat(a, b);
    *this = c;
  }

  template <int n> auto &get() { return std::get<n>(*this); }

  template <int n> const auto &get() const { return std::get<n>(*this); }
};

template <typename... T> Tuple<T...> makeTuple(const T &... args) {
  return Tuple<T...>(args...);
}

namespace std {
template <typename... T>
class tuple_size<Tuple<T...>>
    : public std::integral_constant<size_t, sizeof...(T)> {};
template <std::size_t I, typename... T> class tuple_element<I, Tuple<T...>> {
public:
  using type = tuple_element_t<I, std::tuple<T...>>;
};
} // namespace std

/*****************/
/* container.hpp */
/*****************/

#include <vector>

template <typename T> class Container : public T {
private:
  using S = typename T::value_type;
  using Itr = typename T::iterator;

public:
  Container() : T() {}

  Container(int n) : T(n) {}

  Container(int n, S s) : T(n, s) {}

  template <typename Itr> Container(Itr first, Itr last) : T(first, last) {}

  Container(const std::initializer_list<S> &v) : T(v) {}

  Container(int n, Input &in) {
    std::vector<S> v(n);
    for (auto &i : v) {
      i = in;
    }
    *this = Container<T>(v.begin(), v.end());
  }

  S max() const { return *std::max_element(this->begin(), this->end()); }

  template <typename Function> auto max(Function func) const {
    std::vector<std::pair<decltype(func(S())), S>> res;
    for (const auto &i : *this) {
      res.emplace_back(func(i), i);
    }
    return std::max_element(res.begin(), res.end())->second;
  }

  S min() const { return *std::min_element(this->begin(), this->end()); }

  Tuple<S, S> minmax() const {
    auto itrs = std::minmax_element(this->begin(), this->end());
    return Tuple<S, S>(*itrs.first, *itrs.second);
  }

  template <typename Function> auto min(Function func) const {
    std::vector<std::pair<decltype(func(S())), S>> res;
    for (const auto &i : *this) {
      res.emplace_back(func(i), i);
    }
    return std::min_element(res.begin(), res.end())->second;
  }

  int argmax() const {
    return std::distance(std::max_element(this->begin(), this->end()),
                         this->begin());
  }

  int argmin() const {
    return std::distance(std::min_element(this->begin(), this->end()),
                         this->begin());
  }

  int find(const S &a) const {
    return std::distance(std::find(this->begin(), this->end(), a),
                         this->begin());
  }

  bool contains(const S &a) const {
    return std::find(this->begin(), this->end(), a) != this->end();
  }

  int size() const { return T::size(); }

  std::pair<Itr, Itr> equal_range(const S &a) {
    return std::equal_range(this->begin(), this->end(), a);
  }

  template <typename Function> bool all_of(Function func) const {
    return std::all_of(this->begin(), this->end(), func);
  }

  template <typename Function> bool any_of(Function func) const {
    return std::any_of(this->begin(), this->end(), func);
  }

  template <typename Function> bool none_of(Function func) const {
    return std::none_of(this->begin(), this->end(), func);
  }

  int count(const S &s) const {
    return std::count(this->begin(), this->end(), s);
  }

  bool is_sorted() const { return std::is_sorted(this->begin(), this->end()); }

  void output(std::string sep = "\n", std::string end = "\n") const {
    bool first = true;
    for (const auto &i : *this) {
      if (!first) {
        cout << sep;
      }
      first = false;
      cout << i;
    }
    cout << end;
  }
};

/***********/
/* map.hpp */
/***********/

#include <map>

template <typename T, typename S> class Map : public Container<std::map<T, S>> {
public:
  Map() : Container<std::map<T, S>>() {}

  bool contains(const T &a) const { return this->count(a) != 0; }

  int count(const T &t) const { return this->count(t); }
};
/***************/
/* ordered.hpp */
/***************/

template <typename T> class Ordered {
public:
  template <typename V> bool operator==(const V &v) const {
    return !(static_cast<T>(v) < static_cast<const T &>(*this) ||
             static_cast<const T &>(*this) < static_cast<T>(v));
  }

  template <typename V> bool operator!=(const V &v) const {
    return static_cast<T>(v) < static_cast<const T &>(*this) ||
           static_cast<const T &>(*this) < static_cast<T>(v);
  }

  template <typename V> bool operator>(const V &v) const {
    return static_cast<T>(v) < static_cast<const T &>(*this);
  }

  template <typename V> bool operator<=(const V &v) const {
    return !(static_cast<T>(v) < static_cast<const T &>(*this));
  }

  template <typename V> bool operator>=(const V &v) const {
    return !(static_cast<const T &>(*this) < static_cast<T>(v));
  }
};

/**************/
/* vector.hpp */
/**************/

#include <numeric>

template <typename T>
class Vector : public Container<std::vector<T>>, public Ordered<Vector<T>> {
public:
  Vector() = default;

  Vector(const Vector<T> &v) = default;

  Vector(int n) : Container<std::vector<T>>(n) {}

  Vector(int n, T t) : Container<std::vector<T>>(n, t) {}

  template <typename Itr>
  Vector(Itr first, Itr last) : Container<std::vector<T>>(first, last) {}

  Vector(const std::initializer_list<T> &v) : Container<std::vector<T>>(v) {}

  Vector(int n, Input &in) : Container<std::vector<T>>(n, in) {}

  Vector &operator+=(const Vector &v) {
    if (this->size() < v.size()) {
      this->resize(v.size());
    }
    for (int i = 0; i < v.size(); ++i) {
      (*this)[i] += v[i];
    }
    return *this;
  }

  Vector &operator+=(const T &v) {
    for (auto &i : *this) {
      i += v;
    }
    return *this;
  }

  Vector &operator-=(const Vector &v) {
    if (this->size() < v.size()) {
      this->resize(v.size());
    }
    for (int i = 0; i < v.size(); ++i) {
      (*this)[i] -= v[i];
    }
    return *this;
  }

  Vector &operator-=(const T &v) {
    for (auto &i : *this) {
      i -= v;
    }
    return *this;
  }

  Vector &operator*=(const Vector &v) {
    for (int i = 0; i < this->size(); ++i) {
      (*this)[i] *= v[i];
    }
    return *this;
  }

  Vector &operator*=(const T &v) {
    for (auto &i : *this) {
      i *= v;
    }
    return *this;
  }

  Vector &operator/=(const Vector &v) {
    for (int i = 0; i < this->size(); ++i) {
      (*this)[i] /= v[i];
    }
    return *this;
  }

  Vector &operator/=(const T &v) {
    for (auto &i : *this) {
      i /= v;
    }
    return *this;
  }

  Vector &operator%=(const Vector &v) {
    for (int i = 0; i < this->size(); ++i) {
      (*this)[i] %= v[i];
    }
    return *this;
  }

  Vector &operator%=(const T &v) {
    for (auto &i : *this) {
      i %= v;
    }
    return *this;
  }

  Vector operator+(const Vector &v) const { return Vector(*this) += v; }

  Vector operator+(const T &v) const { return Vector(*this) += v; }

  Vector operator-(const Vector &v) const { return Vector(*this) -= v; }

  Vector operator-(const T &v) const { return Vector(*this) -= v; }

  Vector operator*(const Vector &v) const { return Vector(*this) *= v; }

  Vector operator*(const T &v) const { return Vector(*this) *= v; }

  Vector operator/(const Vector &v) const { return Vector(*this) /= v; }

  Vector operator/(const T &v) const { return Vector(*this) /= v; }

  Vector operator%(const Vector &v) const { return Vector(*this) %= v; }

  Vector operator%(const T &v) const { return Vector(*this) %= v; }

  bool operator<(const Vector &v) const {
    if (this->size() != v.size()) {
      return this->size() < v.size();
    }
    for (int i = 0; i < this->size(); ++i) {
      if ((*this)[i] != v[i]) {
        return (*this)[i] < v[i];
      }
    }
    return false;
  }

  Vector operator-() const { return *this * -1; }

  T inner_product(const Vector<T> &v) const {
    return std::inner_product(this->begin(), this->end(), v.begin(), T(0));
  }

  Vector<T> &partial_sort(int k, bool reverse = false) {
    if (!reverse) {
      std::partial_sort(this->begin(), this->begin() + k, this->end());
    } else {
      std::partial_sort(this->begin(), this->begin() + k, this->end(),
                        std::greater<T>());
    }
    return *this;
  }

  Vector<T> &sort() {
    std::sort(this->begin(), this->end());
    return *this;
  }

  template <typename Function> Vector<T> &sort(Function func) {
    std::sort(this->begin(), this->end(), func);
    return *this;
  }

  Vector<T> &rsort() {
    std::sort(this->rbegin(), this->rend());
    return *this;
  }

  Vector<int> argsort() const {
    Vector<Tuple<T, int>> v;
    for (int i = 0; i < this->size(); ++i) {
      v.emplace_back((*this)[i], i);
    }
    v.sort();
    auto f = [](const Tuple<T, int> &t) { return t.template get<1>(); };
    return v.transform(f);
  }

  Vector<T> &nth_element(int n, bool reverse = false) {
    if (!reverse) {
      std::nth_element(this->begin(), this->begin() + n, this->end());
    } else {
      std::nth_element(this->begin(), this->begin() + n, this->end(),
                       std::greater<T>());
    }
    return *this;
  }

  Vector<T> subvector(int a) const {
    return Vector<T>(this->begin(), this->begin() + a);
  }

  Vector<T> subvector(int a, int b) const {
    return Vector<T>(this->begin() + a, this->begin() + b);
  }

  template <typename Function> auto transform(Function func) const {
    Vector<decltype(func(T()))> res;
    std::transform(this->begin(), this->end(), std::back_inserter(res), func);
    return res;
  }

  Vector<T> partial_sum() const {
    Vector<T> res;
    std::partial_sum(this->begin(), this->end(), std::back_inserter(res));
    return res;
  }

  template <typename Function> Vector<T> partial_sum(Function func) const {
    Vector<T> res;
    std::partial_sum(this->begin(), this->end(), std::back_inserter(res), func);
    return res;
  }

  Vector<T> &reverse() {
    std::reverse(this->begin(), this->end());
    return *this;
  }

  template <typename Function> int count_if(Function func) const {
    return std::count_if(this->begin(), this->end(), func);
  }

  Vector<T> adjacent_difference() const {
    Vector<T> res;
    std::adjacent_difference(this->begin(), this->end(),
                             std::back_inserter(res));
    return res;
  }

  T lower_bound(T t) const {
    return std::lower_bound(this->begin(), this->end(), t) - this->begin();
  }

  T upper_bound(T t) const {
    return std::upper_bound(this->begin(), this->end(), t) - this->begin();
  }

  T accumulate() const {
    return std::accumulate(this->begin(), this->end(), T());
  }

  template <typename S, typename Function>
  S accumulate(S n, Function func) const {
    return std::accumulate(this->begin(), this->end(), n, func);
  }

  template <typename Int> static Vector<T> makeVector(Int n) {
    return Vector<T>(n);
  }

  template <typename Int> static Vector<T> makeVector(Input &in, Int n) {
    return Vector<T>(n, in);
  }

  template <typename Int, typename... Ints>
  static auto makeVector(Input &in, Int n, Ints... ints) {
    Vector<decltype(makeVector(in, ints...))> res;
    for (int i = 0; i < n; ++i) {
      res.emplace_back(makeVector(in, ints...));
    }
    return res;
  }

  template <typename Int, typename... Ints>
  static auto makeVector(Int n, Ints... ints) {
    Vector<decltype(makeVector(ints...))> res;
    for (int i = 0; i < n; ++i) {
      res.emplace_back(makeVector(ints...));
    }
    return res;
  }

  Vector<T> &unique() {
    this->erase(std::unique(this->begin(), this->end()), this->end());
    return *this;
  }

  bool next_permutation() {
    return std::next_permutation(this->begin(), this->end());
  }

  Vector<T> &rotate(int n) {
    std::rotate(this->begin(), this->begin() + n, this->end());
    return *this;
  }

  Map<T, int> countAll() const {
    Map<T, int> res;
    for (const auto &i : *this) {
      ++res[i];
    }
    return res;
  }

  T matmul(const T &a) const {
    return this->transform([&](const T &i) { return i.inner_product(a); });
  }
};

template <typename T> Vector<T> iota(int n, T m = 0) {
  Vector<T> v(n);
  std::iota(v.begin(), v.end(), m);
  return v;
}

template <typename T, typename S> void read(Vector<T> &t, Vector<S> &s) {
  for (int i = 0; i < t.size(); ++i) {
    t[i] = T(in);
    s[i] = S(in);
  }
}

template <typename T, typename S, typename U>
void read(Vector<T> &t, Vector<S> &s, Vector<U> &u) {
  for (int i = 0; i < t.size(); ++i) {
    t[i] = T(in);
    s[i] = S(in);
    u[i] = U(in);
  }
}

template <typename T> Vector<T> operator+(const T &a, const Vector<T> &b) {
  return b + a;
}

template <typename T> Vector<T> operator-(const T &a, const Vector<T> &b) {
  return -b + a;
}

template <typename T> Vector<T> operator*(const T &a, const Vector<T> &b) {
  return b * a;
}

/**************/
/* string.hpp */
/**************/

#include <string>

class String : public std::string {
public:
  constexpr static auto npos = std::string::npos;

  String() : std::string() {}

  String(char c) : std::string(1, c) {}

  String(int n) : std::string(std::to_string(n)) {}

  String(long n) : std::string(std::to_string(n)) {}

  String(long long n) : std::string(std::to_string(n)) {}

  String(const char *s) : std::string(s) {}

  String(const std::string &s) : std::string(s) {}

  String(int n, char c) : std::string(n, c) {}

  String(Input &in) {
    std::cin >> *this;
    in.eof = std::cin.eof();
  }

  String &operator+=(const String &s) { return *this = *this + s; }

  String operator+(const String &s) const { return std::operator+(*this, s); }

  String &operator+=(const char *s) { return *this = *this + s; }

  String operator+(const char *s) const { return std::operator+(*this, s); }

  String &operator+=(char s) { return *this = *this + s; }

  String operator+(char s) const { return std::operator+(*this, s); }

  static String getline() {
    String v;
    std::getline(std::cin, v);
    in.eof = std::cin.eof();
    return v;
  }

  String substr(size_t pos, size_t n_pos = std::string::npos) {
    return std::string::substr(pos, n_pos);
  }

  String &reverse() {
    std::reverse(this->begin(), this->end());
    return *this;
  }

  Vector<String> split(char delim = ' ') const {
    std::stringstream ss(*this);
    Vector<String> res;
    for (std::string tmp; std::getline(ss, tmp, delim);) {
      if (tmp != "") {
        res.emplace_back(tmp);
      }
    }
    return res;
  }

  String &toupper() {
    for (auto &c : *this) {
      c = std::toupper(c);
    }
    return *this;
  }

  String &tolower() {
    for (auto &c : *this) {
      c = std::tolower(c);
    }
    return *this;
  }

  template <typename Function> String transform(Function func) const {
    String res;
    std::transform(this->begin(), this->end(), std::back_inserter(res), func);
    return res;
  }

  bool contains(const String &s) const {
    return this->find(s) != std::string::npos;
  }

  String &erase(char c) {
    String res;
    for (char i : *this) {
      if (i != c) {
        res += i;
      }
    }
    return *this = res;
  }

  int count(char c) const { return std::count(this->begin(), this->end(), c); }

  template <bool Repeat = false>
  String &replaceAll(const String &from, const String &to) {
    for (size_t pos = 0; (pos = this->find(from, pos)) != std::string::npos;) {
      this->replace(pos, from.size(), to);
      if (!Repeat) {
        pos += to.size();
      }
    }
    return *this;
  }

  String &sort() {
    std::sort(this->begin(), this->end());
    return *this;
  }

  String &rsort() {
    std::sort(this->rbegin(), this->rend());
    return *this;
  }

  String &unique() {
    std::string::erase(std::unique(this->begin(), this->end()), this->end());
    return *this;
  }

  String &rotate(int n) {
    std::rotate(this->begin(), this->begin() + n, this->end());
    return *this;
  }

  bool next_permutation() {
    return std::next_permutation(this->begin(), this->end());
  }

  template <typename T, typename Function1, typename Function2>
  T inner_product(const String &v, T init, Function1 func1,
                  Function2 func2) const {
    return std::inner_product(this->begin(), this->end(), v.begin(), init,
                              func1, func2);
  }

  template <typename Function> int find_if(Function func) const {
    return std::find_if(this->begin(), this->end(), func) - this->begin();
  }

  template <typename Function> bool all_of(Function func) const {
    return std::all_of(this->begin(), this->end(), func);
  }

  template <typename Function> bool any_of(Function func) const {
    return std::any_of(this->begin(), this->end(), func);
  }

  template <typename Function> bool none_of(Function func) const {
    return std::none_of(this->begin(), this->end(), func);
  }

  int size() const { return std::string::size(); }

  operator int() const { return std::stoi(*this); }

  operator long() const { return std::stol(*this); }

  operator long long() const { return std::stoll(*this); }

  operator float() const { return std::stof(*this); }

  operator double() const { return std::stod(*this); }

  operator long double() const { return std::stold(*this); }
};

/*******************/
/* big_decimal.hpp */
/*******************/

#include <array>
#include <cmath>

template <int IntegerSize = 6, int DecimalSize = 9>
class BigDecimal : public Arithmetic<BigDecimal<IntegerSize, DecimalSize>>,
                   public Ordered<BigDecimal<IntegerSize, DecimalSize>> {
private:
  constexpr static int BitSize = 31;
  constexpr static bool PLUS = false;
  constexpr static bool MINUS = true;

  const static long double EPSILON;

  bool sign;
  std::array<int64_t, IntegerSize + DecimalSize> d;

public:
  BigDecimal() { *this = BigDecimal(0); }

  BigDecimal(int n) {
    sign = PLUS;
    for (auto &i : d) {
      i = 0;
    }
    d[DecimalSize] = n;
    normal();
  }

  BigDecimal(int64_t n) {
    sign = PLUS;
    for (auto &i : d) {
      i = 0;
    }
    d[DecimalSize] = n;
    normal();
  }

  BigDecimal(String str) {
    *this = BigDecimal(0);
    bool minus = false;
    if (str[0] == '-') {
      minus = true;
      str = str.substr(1);
    }
    BigDecimal t = 1;
    bool decimal = false;
    for (int i = 0; i < str.size(); ++i) {
      if (str[i] == '.') {
        decimal = true;
      } else {
        if (decimal) {
          *this += (t /= 10) * (str[i] - '0');
        } else {
          *this = *this * 10 + (str[i] - '0');
        }
      }
    }
    if (minus) {
      sign = MINUS;
    } else {
      sign = PLUS;
    }
  }

  BigDecimal(double r) {
    *this = BigDecimal(0);
    int n;
    BigDecimal b = (r >= 0 ? BigDecimal(1) : BigDecimal(-1));
    r = 2 * abs(std::frexp(abs(r), &n));
    b <<= n - 1;
    while (r) {
      if (r >= 1) {
        *this += b;
        r -= 1;
      }
      r *= 2;
      b >>= 1;
    }
  }

  BigDecimal(long double r) {
    *this = BigDecimal(0);
    int n;
    BigDecimal b = (r >= 0 ? BigDecimal(1) : BigDecimal(-1));
    r = 2 * abs(std::frexp(abs(r), &n));
    b <<= n - 1;
    while (r) {
      if (r >= 1) {
        *this += b;
        r -= 1;
      }
      r *= 2;
      b >>= 1;
    }
  }

  BigDecimal(Input &in) { *this = BigDecimal(String(in)); }

  BigDecimal &normal() {
    for (int i = 0; i < IntegerSize + DecimalSize - 1; ++i) {
      d[i + 1] += d[i] >> BitSize;
      d[i] &= (1ll << BitSize) - 1;
    }
    if (d.back() < 0) {
      sign = !sign;
      for (auto &i : d) {
        i = -i;
      }
      normal();
    }
    if (d.back() >= (1ll << BitSize)) {
      throw "overflow";
    }
    if (std::all_of(d.begin(), d.end(), [](int64_t i) { return i == 0; })) {
      sign = PLUS;
    }
    return *this;
  }

  BigDecimal operator-() const {
    BigDecimal bd(*this);
    bd.sign = !bd.sign;
    return bd;
  }

  BigDecimal operator<<(int a) const { return BigDecimal(*this) <<= a; }
  BigDecimal operator>>(int a) const { return BigDecimal(*this) >>= a; }
  BigDecimal operator%(const BigDecimal &a) const {
    return BigDecimal(*this) %= a;
  }

  BigDecimal &operator<<=(int a) {
    if (a < 0) {
      return *this >>= -a;
    }
    while (a >= BitSize) {
      if (d.back()) {
        throw "overflow";
      }
      for (int i = IntegerSize + DecimalSize; --i > 0;) {
        d[i] = d[i - 1];
      }
      d[0] = 0;
      a -= BitSize;
    }
    if (d.back() >= (1ll << (BitSize - a))) {
      throw "overflow";
    }
    for (auto &i : d) {
      i <<= a;
    }
    return normal();
  }

  BigDecimal &operator>>=(int a) {
    if (a < 0) {
      return *this <<= -a;
    }
    while (a >= BitSize) {
      for (int i = 0; i < IntegerSize + DecimalSize - 1; ++i) {
        d[i] = d[i + 1];
      }
      d.back() >>= BitSize;
      a -= BitSize;
    }
    for (int i = 0; i < IntegerSize + DecimalSize - 1; ++i) {
      d[i] |= d[i + 1] << BitSize;
      d[i + 1] = 0;
    }
    for (auto &i : d) {
      i >>= a;
    }
    return normal();
  }

  BigDecimal &operator+=(const BigDecimal &a) {
    if (sign == a.sign) {
      for (int i = 0; i < IntegerSize + DecimalSize; ++i) {
        d[i] += a.d[i];
      }
    } else {
      for (int i = 0; i < IntegerSize + DecimalSize; ++i) {
        d[i] -= a.d[i];
      }
    }
    return normal();
  }

  BigDecimal &operator-=(const BigDecimal &a) { return *this += -a; }

  BigDecimal &operator*=(const BigDecimal &a) {
    BigDecimal res = 0;
    for (int i = 0; i < IntegerSize + DecimalSize; ++i) {
      if (i < DecimalSize) {
        res = (res + *this * a.d[i]) >> BitSize;
      } else {
        res += *this * a.d[i] << (i - DecimalSize) * BitSize;
      }
    }
    res.sign = (sign == a.sign ? PLUS : MINUS);
    return *this = res.normal();
  }

  BigDecimal &operator*=(const unsigned int &a) {
    for (auto &i : d) {
      i *= a;
    }
    return normal();
  }

  BigDecimal &operator/=(const BigDecimal &a) {
    if (a == 0) {
      throw "divide by zero";
    }
    BigDecimal rev = 1. / a.toDouble();
    for (int i = 0; i < 7; ++i) {
      rev = (rev << 1) - a * rev * rev;
    }
    rev.sign = a.sign;
    return *this *= rev;
  }

  BigDecimal &operator%=(const BigDecimal &a) {
    if (a == 0) {
      throw "modulo by zero";
    }
    return *this -= floor(*this / a) * a;
  }

  BigDecimal operator-(const BigDecimal &v) const {
    return BigDecimal(*this) -= v;
  }

  BigDecimal &operator++() { return *this += 1; }

  BigDecimal &operator++(int) {
    BigDecimal bd = *this;
    *this += 1;
    return bd;
  }

  BigDecimal &operator--() { return *this -= 1; }

  BigDecimal &operator--(int) {
    BigDecimal bd = *this;
    *this -= 1;
    return bd;
  }

  bool operator<(const BigDecimal &a) const {
    BigDecimal aa = a - EPSILON;
    if (sign == MINUS) {
      if (aa.sign == MINUS) {
        if (a.sign == MINUS) {
          return -a < -*this;
        } else {
          return *this + EPSILON < a + EPSILON;
        }
      } else {
        return true;
      }
    }
    if (aa.sign == MINUS) {
      return false;
    }
    for (int i = IntegerSize + DecimalSize; i-- > 0;) {
      if (d[i] != aa.d[i]) {
        return d[i] < aa.d[i];
      }
    }
    return false;
  }

  bool equals(const BigDecimal &a) const { return sign == a.sign && d == a.d; }

  int toInt() const {
    int res = 0;
    for (int i = 0; i < IntegerSize; ++i) {
      res += d[DecimalSize + i] << BitSize * i;
    }
    if (sign == MINUS) {
      return -res;
    }
    return res;
  }

  int64_t toLongLong() const {
    int64_t res = 0;
    for (int i = 0; i < IntegerSize; ++i) {
      res += d[DecimalSize + i] << BitSize * i;
    }
    if (sign == MINUS) {
      return -res;
    }
    return res;
  }

  String toString(int digit = 100, String mode = "near") const {
    String str;
    BigDecimal a = *this, bd = 1;
    if (a.sign == MINUS) {
      str += "-";
      a.sign = PLUS;
    }
    if (mode == "near") {
      BigDecimal round = BigDecimal(0.5);
      for (int i = 0; i < digit; ++i) {
        round /= 10;
      }
      a += round + EPSILON;
    }
    if (mode == "ceil") {
      BigDecimal round = 1;
      for (int i = 0; i < digit; ++i) {
        round /= 10;
      }
      a += round - EPSILON;
    }
    for (; bd <= a; bd *= 10) {
      ++digit;
    }
    if (bd > 1) {
      bd /= 10;
      --digit;
    }
    for (int i = 0; i < digit + 1; ++i) {
      if (bd == 0) {
        str += "0";
        continue;
      }
      if (bd * 10 == 1) {
        str += ".";
      }
      int d = 0;
      while (bd < a) {
        a -= bd;
        ++d;
      }
      if (d > 9) {
        d -= 10;
        auto itr = str.end();
        while (true) {
          if (itr == str.begin()) {
            str = "1" + str;
            break;
          }
          --itr;
          if (*itr == '.') {
            continue;
          }
          ++*itr;
          if (*itr > '9') {
            *itr = '0';
          } else {
            break;
          }
        }
      }
      str += '0' + d;
      bd /= 10;
    }
    return str;
  }

  double toDouble() const {
    double res = 0;
    for (int i = 0; i < IntegerSize + DecimalSize; ++i) {
      res += d[i] * pow(2, (i - DecimalSize) * BitSize);
    }
    if (sign == MINUS) {
      return -res;
    }
    return res;
  }

  bool isPlus() const { return sign == PLUS; }

  bool isMinus() const { return sign == MINUS; }

  template <int I, int D>
  friend BigDecimal<I, D> pow(const BigDecimal<I, D> &x,
                              const BigDecimal<I, D> &y);
  template <int I, int D> friend BigDecimal<I, D> floor(BigDecimal<I, D> x);
};

template <int IntegerSize, int DecimalSize>
const long double BigDecimal<IntegerSize, DecimalSize>::EPSILON =
    std::pow<long double>(2, -(BitSize - 4) * DecimalSize);

template <int IntegerSize, int DecimalSize>
BigDecimal<IntegerSize, DecimalSize> pi() {
  const static BigDecimal<IntegerSize, DecimalSize> PI =
      (atan(BigDecimal<IntegerSize, DecimalSize>(1) / 5) << 4) -
      (atan(BigDecimal<IntegerSize, DecimalSize>(1) / 239) << 2);
  return PI;
}

template <int IntegerSize, int DecimalSize>
BigDecimal<IntegerSize, DecimalSize>
operator+(const int &a, BigDecimal<IntegerSize, DecimalSize> b) {
  return BigDecimal<IntegerSize, DecimalSize>(a) + b;
}

template <int IntegerSize, int DecimalSize>
BigDecimal<IntegerSize, DecimalSize>
operator-(const int &a, BigDecimal<IntegerSize, DecimalSize> b) {
  return BigDecimal<IntegerSize, DecimalSize>(a) - b;
}

template <int IntegerSize, int DecimalSize>
BigDecimal<IntegerSize, DecimalSize>
operator*(const int &a, BigDecimal<IntegerSize, DecimalSize> b) {
  return BigDecimal<IntegerSize, DecimalSize>(a) * b;
}

template <int IntegerSize, int DecimalSize>
BigDecimal<IntegerSize, DecimalSize>
operator/(const int &a, BigDecimal<IntegerSize, DecimalSize> b) {
  return BigDecimal<IntegerSize, DecimalSize>(a) / b;
}

template <int IntegerSize, int DecimalSize>
std::ostream &operator<<(std::ostream &os,
                         BigDecimal<IntegerSize, DecimalSize> a) {
  os << a.toString(os.precision());
  return os;
}

template <int IntegerSize, int DecimalSize>
BigDecimal<IntegerSize, DecimalSize>
sin(BigDecimal<IntegerSize, DecimalSize> x) {
  BigDecimal<IntegerSize, DecimalSize> res = 0, xx = -x * x;
  for (int i = 1;; i += 2) {
    x /= max(i * (i - 1), 1);
    if (x.equals(0)) {
      break;
    }
    res += x;
    x *= xx;
  }
  return res;
}

template <int IntegerSize, int DecimalSize>
BigDecimal<IntegerSize, DecimalSize>
cos(BigDecimal<IntegerSize, DecimalSize> x) {
  BigDecimal<IntegerSize, DecimalSize> res = 0, xx = -x * x;
  x = 1;
  for (int i = 0;; i += 2) {
    x /= max(i * (i - 1), 1);
    if (x.equals(0)) {
      break;
    }
    res += x;
    x *= xx;
  }
  return res;
}

template <int IntegerSize, int DecimalSize>
BigDecimal<IntegerSize, DecimalSize>
tan(const BigDecimal<IntegerSize, DecimalSize> &x) {
  return sin(x) / cos(x);
}

template <int IntegerSize, int DecimalSize>
BigDecimal<IntegerSize, DecimalSize>
asin(BigDecimal<IntegerSize, DecimalSize> x) {
  if (abs(x) > 1) {
    throw "out of domain";
  }
  if (x > 1 / sqrt(BigDecimal<IntegerSize, DecimalSize>(2))) {
    return (pi<IntegerSize, DecimalSize>() >> 1) - asin(sqrt(1 - x * x));
  }
  if (x < -1 / sqrt(BigDecimal<IntegerSize, DecimalSize>(2))) {
    return -(pi<IntegerSize, DecimalSize>() >> 1) + asin(sqrt(1 - x * x));
  }
  BigDecimal<IntegerSize, DecimalSize> res = 0, xx = x * x >> 2;
  for (int i = 0;; ++i) {
    x *= max(i * 2 * (i * 2 - 1), 1);
    x /= max(i * i, 1);
    auto add = x / (i * 2 + 1);
    if (add.equals(0)) {
      break;
    }
    res += add;
    x *= xx;
  }
  return res;
}

template <int IntegerSize, int DecimalSize>
BigDecimal<IntegerSize, DecimalSize>
acos(const BigDecimal<IntegerSize, DecimalSize> &x) {
  return (pi<IntegerSize, DecimalSize>() >> 1) - asin(x);
}

template <int IntegerSize, int DecimalSize>
BigDecimal<IntegerSize, DecimalSize>
atan(BigDecimal<IntegerSize, DecimalSize> x) {
  if (x.isMinus()) {
    return -atan(-x);
  }
  if (abs(x) > sqrt(2) + 1) {
    return (pi<IntegerSize, DecimalSize>() >> 1) - atan(1 / x);
  }
  if (abs(x) > sqrt(2) - 1) {
    return (pi<IntegerSize, DecimalSize>() >> 2) + atan((x - 1) / (x + 1));
  }
  BigDecimal<IntegerSize, DecimalSize> res = 0, xx = -x * x;
  for (int i = 1;; i += 2) {
    auto add = x / i;
    if (add.equals(0)) {
      break;
    }
    res += add;
    x *= xx;
  }
  return res;
}

template <int IntegerSize, int DecimalSize>
BigDecimal<IntegerSize, DecimalSize>
atan2(const BigDecimal<IntegerSize, DecimalSize> &y,
      const BigDecimal<IntegerSize, DecimalSize> &x) {
  if (x == 0) {
    if (y > 0) {
      return pi<IntegerSize, DecimalSize>() / 2;
    }
    if (y < 0) {
      return -pi<IntegerSize, DecimalSize>() / 2;
    }
    throw "origin can't define argument";
  }
  if (x.isPlus()) {
    return atan(y / x);
  }
  if (y.isPlus()) {
    return atan(y / x) + pi<IntegerSize, DecimalSize>();
  }
  return atan(y / x) - pi<IntegerSize, DecimalSize>();
}

template <int IntegerSize, int DecimalSize>
BigDecimal<IntegerSize, DecimalSize>
sinh(BigDecimal<IntegerSize, DecimalSize> x) {
  BigDecimal<IntegerSize, DecimalSize> res = 0, xx = x * x;
  for (int i = 1;; i += 2) {
    x /= max(i * (i - 1), 1);
    if (x.equals(0)) {
      break;
    }
    res += x;
    x *= xx;
  }
  return res;
}

template <int IntegerSize, int DecimalSize>
BigDecimal<IntegerSize, DecimalSize>
cosh(BigDecimal<IntegerSize, DecimalSize> x) {
  BigDecimal<IntegerSize, DecimalSize> res = 0, xx = x * x;
  x = 1;
  for (int i = 0;; i += 2) {
    x /= max(i * (i - 1), 1);
    if (x.equals(0)) {
      break;
    }
    res += x;
    x *= xx;
  }
  return res;
}

template <int IntegerSize, int DecimalSize>
BigDecimal<IntegerSize, DecimalSize>
tanh(const BigDecimal<IntegerSize, DecimalSize> &x) {
  return sinh(x) / cosh(x);
}

template <int IntegerSize, int DecimalSize>
BigDecimal<IntegerSize, DecimalSize>
exp(const BigDecimal<IntegerSize, DecimalSize> &x) {
  BigDecimal<IntegerSize, DecimalSize> res = 0, xx = 1;
  for (int i = 0;; ++i) {
    xx /= max(i, 1);
    if (xx.equals(0)) {
      break;
    }
    res += xx;
    xx *= x;
  }
  return res;
}

template <int IntegerSize, int DecimalSize>
BigDecimal<IntegerSize, DecimalSize>
log(const BigDecimal<IntegerSize, DecimalSize> &x) {
  BigDecimal<IntegerSize, DecimalSize> y = log(x.toDouble());
  BigDecimal<IntegerSize, DecimalSize> z = x / exp(y);
  BigDecimal<IntegerSize, DecimalSize> a = (z - 1) / (z + 1);
  BigDecimal<IntegerSize, DecimalSize> res = 0, b = a, aa = a * a;
  for (int i = 1;; i += 2) {
    if (b.equals(0)) {
      break;
    }
    res += b / i;
    b *= aa;
  }
  return y + res * 2;
}

template <int IntegerSize, int DecimalSize>
BigDecimal<IntegerSize, DecimalSize>
log10(const BigDecimal<IntegerSize, DecimalSize> &x) {
  return log(x) / log(BigDecimal<IntegerSize, DecimalSize>(10));
}

template <int IntegerSize, int DecimalSize>
BigDecimal<IntegerSize, DecimalSize>
pow(const BigDecimal<IntegerSize, DecimalSize> &x,
    const BigDecimal<IntegerSize, DecimalSize> &y) {
  if (x.isMinus()) {
    if (floor(y) == y) {
      return floor(y).d[DecimalSize] % 2 ? -pow(-x, floor(y))
                                         : pow(-x, floor(y));
    }
    throw "power of negative number";
  }
  return exp(y * log(x));
}

template <int IntegerSize, int DecimalSize>
BigDecimal<IntegerSize, DecimalSize>
sqrt(const BigDecimal<IntegerSize, DecimalSize> &x) {
  BigDecimal<IntegerSize, DecimalSize> r = 1 / sqrt(x.toDouble());
  for (int i = 0; i < 7; ++i) {
    r *= (3 - x * r * r) >> 1;
  }
  return BigDecimal<IntegerSize, DecimalSize>(1) / r;
}

template <int IntegerSize, int DecimalSize>
BigDecimal<IntegerSize, DecimalSize>
abs(const BigDecimal<IntegerSize, DecimalSize> &x) {
  return x.isPlus() ? x : -x;
}

template <int IntegerSize, int DecimalSize>
BigDecimal<IntegerSize, DecimalSize>
ceil(const BigDecimal<IntegerSize, DecimalSize> &x) {
  if (x.isMinus()) {
    return -floor(-x);
  }
  auto f = floor(x);
  return f == x ? f : x + 1;
}

template <int IntegerSize, int DecimalSize>
BigDecimal<IntegerSize, DecimalSize>
floor(BigDecimal<IntegerSize, DecimalSize> x) {
  if (x.isMinus()) {
    return -ceil(-x);
  }
  x += BigDecimal<IntegerSize, DecimalSize>::EPSILON;
  for (int i = 0; i < DecimalSize; ++i) {
    x.d[i] = 0;
  }
  return x;
}

/************/
/* main.cpp */
/************/

int main() {
  BigDecimal<> v(in), t(in);
  cout << int((v * t).toDouble()) << endl;
}