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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;

namespace Contest
{
    class Program
    {
        static void Main(string[] args)
        {
            ABC145.E();
        }



        class ABC145
        {
            public static void A()
            {
                var R = Read.Int();
                Console.WriteLine(R * R);
            }
            public static void B()
            {
                var N = Read.Int();
                var S = Read.Str();
                Console.WriteLine(N % 2 == 0 && S.Substring(0, N / 2) == S.Substring(N / 2, N / 2) ? "Yes" : "No");
            }
            public static void C()
            {
                var N = Read.Int();
                var XY = Read.TupleInt(N);
                double sum = 0;
                for(int i = 0; i < N; ++i)
                {
                    var x1 = XY[i].Item1;
                    var y1 = XY[i].Item2;
                    for (int j = i + 1; j < N; ++j)
                    {
                        var x2 = XY[j].Item1;
                        var y2 = XY[j].Item2;
                        sum += Math.Sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
                    }
                }
                Console.WriteLine(sum / N * 2);
            }
            public static void D()
            {
                var X = Read.Int();
                var Y = Read.Int();
                if ((X + Y) % 3 != 0) { Console.WriteLine(0);return; }
                var a = X - (X + Y) / 3;
                var b = Y - (X + Y) / 3;
                Console.WriteLine(Util.Combin(a + b, 1000000007)(a + b, a));
            }
            public static void E()
            {
                var N = Read.Int();
                var T = Read.Int();
                var AB = Read.TupleInt(N);
                AB = AB.OrderBy(x => x.Item1).ToArray();
                var dp = new int[N + 1, T];
                for(int n = 0; n < N; ++n)
                {
                    var A = AB[n].Item1;
                    var B = AB[n].Item2;
                    for(int t = 0; t < T; ++t)
                    {
                        if (t >= A)
                        {
                            dp[n + 1, t] = Math.Max(dp[n, t], dp[n, t - A] + B);
                        }
                        else
                        {
                            dp[n + 1, t] = dp[n, t];
                        }
                    }
                }
                int max = 0;
                int maxB = 0;
                for(int n = N; n > 0; --n)
                {
                    max = Math.Max(max, dp[n, T - 1] + maxB);
                    maxB = Math.Max(maxB, AB[n - 1].Item2);
                }
                Console.WriteLine(max);
            }
            public static void F()
            {
                var N = Read.Int();
                var K = Read.Int();
                var H = Read.LongN();
                H = new long[] { 0 }.Concat(H).ToArray();
                var dp = new long[N + 1, N - K + 1];
                for (int len = 0; len <= N - K; ++len)
                {
                    dp[0, len] = len == 0 ? 0 : (long)1e18;
                }
                for (int n = 1; n <= N; ++n)
                {
                    dp[n, 0] = (long)1e18;
                    var h = H[n];
                    for(int len = 1; len <= N - K; ++len)
                    {
                        long min = (long)1e18;
                        for(int prev = 0; prev < n; ++prev)
                        {
                            min = Math.Min(min, dp[prev, len - 1] + Math.Max(0, h - H[prev]));
                        }
                        dp[n, len] = min;
                    }
                }
                Console.WriteLine(Enumerable.Range(1, N).Select(n => dp[n, N - K]).Min());
            }
        }


        class Util
        {
            public static long Inverse(long a, long p)
            {
                long b = p, c = 1, d = 0, e = 0, f = 0;
                while (b != 0)
                {
                    e = a / b;
                    f = b; b = a - e * b; a = f;
                    f = d; d = c - e * d; c = f;
                }
                c %= p;
                return c + (c < 0 ? p : 0);
            }

            public static long[] Facts(int n, long p)
            {
                var facts = new long[n + 1];
                facts[0] = 1;
                for (int i = 1; i <= n; ++i)
                {
                    facts[i] = (i * facts[i - 1]) % p;
                }
                return facts;
            }
            public static Func<int, int, long> Combin(int n, long P)
            {
                var fact = Facts(n, P);
                var inv = fact.Select(x => Inverse(x, P)).ToArray();
                return (N, M) =>
                {
                    if (N < 0 || N < M || M < 0) { return 0; }
                    return (((fact[N] * inv[M]) % P) * inv[N - M]) % P;
                };
            }
        }


        static class Read
        {
            static Queue<string> queue = new Queue<string>();
            static void Enqueue() { var ss = Console.ReadLine().Split(' '); foreach (var s in ss) { queue.Enqueue(s); } }
            public static int Int() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt32(queue.Dequeue()); }
            public static long Long() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt64(queue.Dequeue()); }
            public static string Str() { if (queue.Count == 0) { Enqueue(); } return queue.Dequeue(); }
            public static int[] IntN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray(); }
            public static long[] LongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray(); }
            public static string[] StrN() { return Console.ReadLine().Split(' '); }
            public static Tuple<int, int>[] TupleInt(int n) { List<Tuple<int, int>> list = new List<Tuple<int, int>>(); for (int i = 0; i < n; ++i) { var ab = Read.IntN(); list.Add(new Tuple<int, int>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<long, long>[] TupleLong(int n) { List<Tuple<long, long>> list = new List<Tuple<long, long>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<long, long>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<string, string>[] TupleStr(int n) { List<Tuple<string, string>> list = new List<Tuple<string, string>>(); for (int i = 0; i < n; ++i) { var ab = Read.StrN(); list.Add(new Tuple<string, string>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<double, double>[] TupleDouble(int n) { List<Tuple<double, double>> list = new List<Tuple<double, double>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<double, double>(ab[0], ab[1])); } return list.ToArray(); }
            public static long[,] LongMatrix(int r, int c)
            {
                var mat = new long[r, c];
                for (int i = 0; i < r; ++i)
                {
                    var x = Read.LongN();
                    for (int j = 0; j < c; ++j)
                    {
                        mat[i, j] = x[j];
                    }
                }
                return mat;
            }
            public static Dictionary<int, HashSet<int>> AdjacencyList(int N, int M, bool isDirectional = false)
            {
                Dictionary<int, HashSet<int>> dict = new Dictionary<int, HashSet<int>>();
                for (int i = 0; i <= N; ++i) { dict.Add(i, new HashSet<int>()); }
                for (int i = 0; i < M; ++i)
                {
                    var ab = Read.IntN(); dict[ab[0]].Add(ab[1]);
                    if (!isDirectional) { dict[ab[1]].Add(ab[0]); }
                }
                return dict;
            }
            public static Dictionary<int, Dictionary<int, long>> AdjacencyListWithWeight(int N, int M)
            {
                Dictionary<int, Dictionary<int, long>> dict = new Dictionary<int, Dictionary<int, long>>();
                for (int i = 0; i <= N; ++i)
                {
                    dict.Add(i, new Dictionary<int, long>());
                }
                for (int i = 0; i < M; ++i)
                {
                    var ab = Read.IntN();
                    dict[ab[0]].Add(ab[1], ab[2]);
                    dict[ab[1]].Add(ab[0], ab[2]);
                }
                return dict;
            }
        }
    }
}