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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#undef _GLIBCXX_DEBUG

#include "bits/stdc++.h"
#include "ext/pb_ds/assoc_container.hpp"
#include "ext/pb_ds/tree_policy.hpp"
#include "ext/rope"

using namespace std;
using namespace __gnu_pbds;
using namespace __gnu_cxx;

void trace(int x)                         { cerr << x; }
void trace(long x)                        { cerr << x; }
void trace(long long x)                   { cerr << x; }
void trace(unsigned x)                    { cerr << x; }
void trace(unsigned long x)               { cerr << x; }
void trace(unsigned long long x)          { cerr << x; }
void trace(float x)                       { cerr << x; }
void trace(double x)                      { cerr << x; }
void trace(long double x)                 { cerr << x; }
void trace(char x)                        { cerr << '\'' << x << '\''; }
void trace(const char *x)                 { cerr << '\"' << x << '\"'; }
void trace(const string &x)               { cerr << '\"' << x << '\"'; }
void trace(bool x)                        { cerr << (x ? "true" : "false"); }

template <typename A, typename B>                         void trace(const pair <A, B> &x)         { cerr << '{'; trace(x.first); cerr << ','; trace(x.second); cerr << '}'; }
template <typename A, typename B, typename C>             void trace(const tuple <A, B, C> &x)     { cerr << '{'; trace(get <0> (x)); cerr << ','; trace(get <1> (x)); cerr << ','; trace(get <2> (x)); cerr << '}'; }
template <typename A, typename B, typename C, typename D> void trace(const tuple <A, B, C, D> &x)  { cerr << '{'; trace(get <0> (x)); cerr << ','; trace(get <1> (x)); cerr << ','; trace(get <2> (x)); cerr << ','; trace(get <3> (x)); cerr << '}'; }
template <typename T>                                     void trace(const T &x)                   { int f = 0; cerr << '{'; for (auto &i: x) cerr << (f++ ? "," : ""), trace(i); cerr << "}"; }
template <size_t N>                                       void trace(bitset <N> v)                 { cerr << '{'; for (size_t i = 0; i < N; i++) cerr << static_cast <char> ('0' + v[i]); cerr << '}'; }
void _print()                                                                                      { cerr << "]\n"; }
template <typename T, typename... V>                      void _print(T t, V... v)                 { trace(t); if (sizeof...(v)) cerr << ", "; _print(v...); }

#ifndef ONLINE_JUDGE
      #define debug(x...) cerr << "[" << #x << "] = ["; _print(x)
#else
      #define debug(x...)
#endif // ONLINE_JUDGE

template <typename T> using ordered_set                = tree <T, null_type, less <T>, rb_tree_tag, tree_order_statistics_node_update>;
template <typename T1, typename T2> using ordered_map  = tree <T1, T2, less <T1>, rb_tree_tag, tree_order_statistics_node_update>;

template <class T> T binaryExpo(T a, T p)              { if (p == 0) { return 1LL; } if (p == 1) { return a; } if (p & 1) { return a * binaryExpo(a, p - 1); } T ret = binaryExpo(a, p / 2); return ret * ret; }
template <class T> T bigMod(T a, T p, T m)             { if (p == 0) { return 1LL % m; } if (p == 1) { return a % m; } if (p & 1) { return (a % m * bigMod(a, p - 1, m)) % m; } T ret = bigMod(a, p / 2, m) % m; return (ret * ret) % m; }
template <class T> T modInv(T a, T m)                  { return bigMod(a, m - 2, m); }

template <class T> bool MIN(T &a, T b)                 { return a > b ? (a = b, true) : false; }
template <class T> bool MAX(T &a, T b)                 { return a < b ? (a = b, true) : false; }

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

inline long long ON(long long mask, int pos)           { return mask |= (1LL << pos); }
inline long long OFF(long long mask, int pos)          { return mask &= ~(1LL << pos); }
inline long long TOGGLE(long long mask, int pos)       { return mask ^= (1LL << pos); }
inline bool CHECK(long long mask, int pos)             { return (bool)(mask >> pos & 1LL); }

inline int ONE(long long mask)                         { return __builtin_popcountll(mask); }
inline int LZERO(long long mask)                       { return 31 - __builtin_clzll(mask); }
inline int TZERO(long long mask)                       { return __builtin_ctzll(mask); }

#define ll              long long int
#define ull             unsigned long long int
#define ld              long double
#define endl            '\n'
#define pii             pair <int, int>
#define pll             pair <ll, ll>
#define mk              make_pair
#define ff              first
#define ss              second
#define all(a)          (a).begin(), (a).end()
#define rall(a)         (a).rbegin(), (a).rend()
#define eb              emplace_back
#define pb              push_back
#define pf              push_front
#define sz(a)           (int)(a.size())
#define ook             order_of_key             // The number of items in a set that are strictly smaller than k
#define fbo             find_by_order            // It returns an iterator to the i'th largest element
#define ATCODER         if (fopen("in.txt", "r")) { freopen("in.txt", "r", stdin); }

#define int             long long int

const int maxn = 3000 + 5;
const int logn = 19;
const long long MOD = 1e9 + 7;
const long long INF = 1e18;

int n;
int maxTime;
int eatingTime[maxn];
int deliciousness[maxn];

int dp[maxn][maxn];

int solve(int pos, int tym) {
      if (pos > n or tym >= maxTime) {
            return 0;
      }
      int &ret = dp[pos][tym];
      if (~ret) {
            return ret;
      }
      ret = solve(pos + 1, tym);
      int go = deliciousness[pos] + solve(pos + 1, tym + eatingTime[pos]);
      MAX(ret, go);
      return ret;
}

signed main()
{
      ios_base::sync_with_stdio(false);
      cin.tie(nullptr); cout.tie(nullptr);
      cout.precision(12);

      bool FILEIO = 0;
      if (FILEIO and fopen("in.txt", "r")) {
            freopen("in.txt", "r", stdin);
      }

      cin >> n >> maxTime;
      for (int i = 1; i <= n; i++) {
            cin >> eatingTime[i] >> deliciousness[i];
      }
      memset(dp, -1, sizeof dp);
      cout << solve(1, 0) << endl;

      #ifndef ONLINE_JUDGE
            cerr << endl << "Time : " << 1.0 * clock() / CLOCKS_PER_SEC << " s." << endl;
      #endif // ONLINE_JUDGE
}