Problem:
Score : 500 points

Problem Statement

Takahashi is at an all-you-can-eat restaurant.

The restaurant offers N kinds of dishes. It takes A_i minutes to eat the i-th dish, whose deliciousness is B_i.

The restaurant has the following rules:

You can only order one dish at a time. The dish ordered will be immediately served and ready to eat.

You cannot order the same kind of dish more than once.

Until you finish eating the dish already served, you cannot order a new dish.

After T-0.5 minutes from the first order, you can no longer place a new order, but you can continue eating the dish already served.

Let Takahashi's happiness be the sum of the deliciousness of the dishes he eats in this restaurant.

What is the maximum possible happiness achieved by making optimal choices?

Constraints

2 \leq N \leq 3000

1 \leq T \leq 3000

1 \leq A_i \leq 3000

1 \leq B_i \leq 3000

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N T
A_1 B_1
:
A_N B_N

Output

Print the maximum possible happiness Takahashi can achieve.

Sample Input 1

2 60
10 10
100 100

Sample Output 1

110

By ordering the first and second dishes in this order, Takahashi's happiness will be 110.

Note that, if we manage to order a dish in time, we can spend any amount of time to eat it.

Sample Input 2

3 60
10 10
10 20
10 30

Sample Output 2

60

Takahashi can eat all the dishes within 60 minutes.

Sample Input 3

3 60
30 10
30 20
30 30

Sample Output 3

50

By ordering the second and third dishes in this order, Takahashi's happiness will be 50.

We cannot order three dishes, in whatever order we place them.

Sample Input 4

10 100
15 23
20 18
13 17
24 12
18 29
19 27
23 21
18 20
27 15
22 25

Sample Output 4

145

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

//#pragma GCC optimize("O3")
//#pragma GCC target("avx")

#include <algorithm>
#include <cmath>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

// Types
using ll = long long int;
using str = string;
template <class T> using u_set = unordered_set<T>;
template <class K, class V> using u_map = unordered_map<K, V>;
template <class V> using graph = u_map<V, u_set<V>>;
template <class F,
          typename enable_if<is_function<F>::value, nullptr_t>::type = nullptr>
using fun = function<F>;

namespace io {
// Input
using IS = istream;
IS &in(IS &);
IS &in(IS &i) { return i; }
template <class T, class... Ts> IS &in(IS &i, T &a, Ts &... as) {
  return in(i >> a, as...);
}
template <class V> IS &operator>>(IS &i, vector<V> &a) {
  for_each(a.begin(), a.end(), [&i](auto &e) { i >> e; });
  return i;
}
template <class F, class S> IS &operator>>(IS &i, pair<F, S> &p) {
  return in(i, p.first, p.second);
}
template <class... Ts, size_t... I>
IS &tuple_in(IS &i, tuple<Ts...> &t, index_sequence<I...>) {
  return in(i, get<I>(t)...);
}
template <class... Ts> IS &operator>>(IS &i, tuple<Ts...> &t) {
  return tuple_in(i, t, make_index_sequence<sizeof...(Ts)>());
}
// Output
using OS = ostream;
OS &out(OS &o) { return o << endl; }
template <class T> OS &out(OS &o, T const &a) { return o << a << endl; }
template <class T, class... Ts> OS &out(OS &o, T const &a, Ts const &... as) {
  return out(o << a << " ", as...);
}
template <class F, class S> OS &operator<<(OS &o, pair<F, S> const &p) {
  return o << p.first << ":" << p.second;
}
template <class... Ts> OS &args_out(OS &o, Ts const &... ts);
OS &args_out(OS &o) { return o; }
template <class T> OS &args_out(OS &o, T const &t) { return o << t; }
template <class T0, class T1, class... Ts>
OS &args_out(OS &o, T0 const &t0, T1 const &t1, Ts const &... ts) {
  return args_out(o << t0 << ",", t1, ts...);
}
template <class... Ts, size_t... I>
OS &tuple_out(OS &o, tuple<Ts...> const &t, index_sequence<I...>) {
  return args_out(o, get<I>(t)...);
}
template <class... Ts> OS &operator<<(OS &o, tuple<Ts...> const &t) {
  return tuple_out(o << "(", t, make_index_sequence<sizeof...(Ts)>()) << ")";
}
template <
    class C,
    class T = typename iterator_traits<typename C::iterator>::value_type,
    typename enable_if<!is_same<C, str>::value, nullptr_t>::type = nullptr>
OS &operator<<(OS &o, C const &a) {
  return a.empty() ? (o << "[]") : ([&o, &a]() -> OS & {
    o << "[" << *a.begin();
    for_each(next(a.begin()), a.end(), [&o](auto const &e) { o << "," << e; });
    return o << "]";
  }());
}
} // namespace io
auto input = [](auto &... a) { io::in(cin, a...); };
auto print = [](auto const &... a) { io::out(cout, a...); };
#ifdef JUMPAKU_DEBUG
auto dump = [](auto const &... a) { io::out(cerr, a...); };
#else
auto dump = [](auto const &...) {};
#endif

// Hash
namespace hashcode {
template <class... Ts> uint64_t hash_args(uint64_t h, Ts const &... ts);
uint64_t hash_args(uint64_t h) { return h; }
template <class T, class... Ts>
uint64_t hash_args(uint64_t h, T const &t, Ts const &... ts) {
  constexpr hash<T> hasher;
  return hash_args(((h << 19) - h) ^ hasher(t), ts...);
}
template <class... Ts, size_t... I>
uint64_t hash_tuple(tuple<Ts...> const &t, index_sequence<I...>) {
  return hash_args(59, get<I>(t)...);
}
} // namespace hashcode
namespace std {
template <class... Ts> struct hash<tuple<Ts...>> {
  size_t operator()(tuple<Ts...> const &t) const {
    uint64_t h = hashcode::hash_tuple(t, index_sequence_for<Ts...>());
    return h ^ (h >> 32);
  }
};
} // namespace std

// Range
namespace ranges {
template <class T> struct iterator_base {
  using difference_type = ll;
  using value_type = T;
  using pointer = T *;
  using reference = T &;
  using iterator_category = random_access_iterator_tag;
  ll i;
  iterator_base(ll const &i = 0) : i(i) {}
  bool operator==(iterator_base const &itr) const { return i == itr.i; }
  bool operator!=(iterator_base const &itr) const { return i != itr.i; }
  ll operator-(iterator_base const &itr) const { return i - itr.i; }
};
template <class T> struct seq_base {
  ll const b;
  ll const e;
  seq_base(ll b, ll e) : b(b), e(e) {}
  ll size() const { return e - b; }
  bool empty() const { return size() == 0; }
};
template <class T> struct seq : seq_base<T> {
  struct iterator : iterator_base<T> {
    seq *s;
    iterator(seq *s, ll const &i) : iterator_base<T>(i), s(s) {}
    iterator operator++(int) { return iterator(s, this->i++); }
    iterator operator--(int) { return iterator(s, this->i--); }
    iterator operator+(ll const &n) { return iterator(s, this->i + n); }
    iterator operator-(ll const &n) { return iterator(s, this->i - n); }
    iterator &operator+=(ll const &n) {
      this->i += n;
      return *this;
    }
    iterator &operator-=(ll const &n) { return *this += (-n); }
    iterator &operator++() { return *this += 1; }
    iterator &operator--() { return *this -= 1; }
    T operator*() const { return (*s)[this->i]; }
  };
  function<T(ll)> const f;
  seq(ll n, function<T(ll)> const &f) : seq(0, n, f) {}
  seq(ll b, ll e, function<T(ll)> const &f) : seq_base<T>(b, e), f(f) {}
  iterator begin() { return iterator(this, this->b); }
  iterator end() { return iterator(this, this->e); }
  ll operator[](ll i) const { return f(i); }
};
struct range : seq_base<ll> {
  struct iterator : iterator_base<ll> {
    iterator(ll const &i) : iterator_base<ll>(i) {}
    iterator operator++(int) { return iterator(i++); }
    iterator operator--(int) { return iterator(i--); }
    iterator operator+(ll const &n) const { return iterator(i + n); }
    iterator operator-(ll const &n) const { return iterator(i - n); }
    iterator &operator+=(ll const &n) {
      i += n;
      return *this;
    }
    iterator &operator-=(ll const &n) { return *this += (-n); }
    iterator &operator++() { return *this += 1; }
    iterator &operator--() { return *this -= 1; }
    ll operator*() const { return i; }
  };
  range(ll n) : range(0LL, n) {}
  range(ll b, ll e) : seq_base<ll>(b, e) {}
  iterator begin() const { return iterator(b); }
  iterator end() const { return iterator(e); }
  ll operator[](ll i) const { return i + b; }
};
} // namespace ranges
using range = ranges::range;
range::iterator range_end(ll i) { return ranges::range::iterator(i); }
range::iterator range_begin(ll i) { return range_end(i); }
template <class F> auto seq(ll b, ll e, F const &f) {
  using T = decltype(f(declval<ll>()));
  return ranges::seq<T>(b, e, f);
}
template <class F> auto seq(ll n, F const &f) { return seq(0, n, f); }
template <class T = ll> vector<T> vec(size_t n, T &&init = T()) {
  return vector<T>(n, init);
}

ll gcd(ll p, ll q) { return (q == 0) ? p : gcd(q, p % q); }
ll lcm(ll p, ll q) { return p / gcd(q, p) * q; }

// MOD
ll pow(ll a, ll n, ll m) {
  if (n == 0)
    return 1;
  if (n & 1)
    return ((a % m) * pow(a, n - 1, m)) % m;
  auto b = pow(a, n / 2, m);
  return (b * b) % m;
}
ll inv(ll a, ll p) { return pow(a, p - 2, p); }

template <ll N, ll M> struct Factrial {
  Factrial() {
    fact[0] = 1;
    for (int i = 1; i <= N; ++i)
      fact[i] = (fact[i - 1] * i) % M;
    finv[N] = inv(fact[N], M);
    for (int i = N; i > 0; --i)
      finv[i - 1] = (finv[i] * i) % M;
  }
  array<ll, N + 1> fact;
  array<ll, N + 1> finv;
  ll comb(ll n, ll m) const {
    if (m < 0 || n < m)
      return 0LL;
    return (fact[n] * ((finv[m] * finv[n - m]) % M)) % M;
  }
};

constexpr ll MOD = 1e9 + 7;

using Key = tuple<ll, ll>;
ll f(Key const &key, vector<tuple<ll, ll>> const &AB, u_map<Key, ll> &dp) {
  ll t = get<0>(key);
  ll i = get<1>(key);
  if (t <= 0)
    return 0;
  auto Ai = get<0>(AB[i]);
  auto Bi = get<1>(AB[i]);
  if (i == 0)
    return Bi;
  // if (dp.contains(key))
  if (dp.find(key) != dp.end())
    return dp[key];
  return dp[key] =
             max(f(Key{t - Ai, i - 1}, AB, dp) + Bi, f(Key{t, i - 1}, AB, dp));
}
int main() {
  ll N, T;
  input(N, T);
  auto AB = vec<tuple<ll, ll>>(N);
  input(AB);
  sort(AB.begin(), AB.end(),
       [](auto const &x0, auto const &x1) { return get<0>(x0) > get<0>(x1); });
  // dump(N, T, AB);
  auto dp = u_map<Key, ll>(24);
  dp.reserve(1e7);
  ll ans = f(Key{T, N - 1}, AB, dp);
  print(ans);
}