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.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using static System.Math;
using static System.Array;
using static AtCoder.Tool;

namespace AtCoder
{
    class AC
    {
        const int MOD = 1000000007;
        const int INF = int.MaxValue / 2;
        const long SINF = long.MaxValue / 2;
        const double EPS = 1e-8;
        static readonly int[] dx = { 0, 1, 0, -1 };
        static readonly int[] dy = { 1, 0, -1, 0 };
        //static List<List<int>> G = new List<List<int>>();
        //static List<List<Edge>>G = new List<List<Edge>>();
        //static List<Edge> E = new List<Edge>();


        static void Main(string[] args)
        {
            //var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            //Console.SetOut(sw);
            var cin = new Scanner();

            var p = cin.SplitRead();
            int N = p[0];
            int T = p[1];

            var A = new long[N];
            var B = new long[N];

            for (var i = 0; i < N; i++)
            {
                var input = cin.SplitReadL();
                A[i] = input[0];
                B[i] = input[1];
            }

            var dp = new long[N + 1, T, 2];
            var ans = new List<long>();

            for (var i = 0; i <= N; i++)
            {
                for (var t = 0; t < T; t++)
                {
                    dp[i, t, 0] = 0;
                    dp[i, t, 1] = 0;
                }
            }

            for (var i = 0; i < N; i++)
            {
                for (var t = 0; t < T; t++)
                {
                    if (t + A[i] >= T)
                    {
                        dp[i + 1, t, 0] = Max(dp[i + 1, t, 0], dp[i, t, 0]);
                    }
                    else
                    {
                        dp[i + 1, t + A[i], 0] = Max(dp[i + 1, t + A[i], 0], Max(dp[i, t + A[i], 0], dp[i, t, 0] + B[i]));
                        dp[i + 1, t, 0] = Max(dp[i + 1, t, 0], dp[i, t, 0]);

                        dp[i + 1, t + A[i], 1] = Max(dp[i + 1, t + A[i], 1], dp[i, t, 1] + B[i]);
                       
                    }

                    dp[i + 1, t, 1] = Max(dp[i + 1, t, 1], Max(dp[i, t, 1], dp[i, t, 0] + B[i]));
                }
            }

            /*for(var i = 0; i < N + 1; i++)
            {
                for(var j = 0; j < T; j++)
                {
                    Console.Write($"{dp[i, j, 1]} ");
                }
                Console.WriteLine();
            }*/
            Console.WriteLine(Max(dp[N, T - 1, 0], dp[N, T - 1, 1]));


            //Console.Out.Flush();
        }

        struct Edge
        {
            public int from;

            public int to;
            public long dist;
            public Edge(int t, long c)
            {
                from = -1;
                to = t;
                dist = c;
            }
            public Edge(int f, int t, long c)
            {
                from = f;
                to = t;
                dist = c;
            }

        }
        struct Pair<T, U> : IComparable<Pair<T, U>>
        where T : IComparable<T>
        where U : IComparable<U>
        {
            public T first;
            public U second;
            private readonly bool CompWithFirst;

            public Pair(T f, U s, int comp)
            {
                first = f;
                second = s;
                CompWithFirst = comp == 1;
            }
            public Pair(T f, U s)
            {
                first = f;
                second = s;
                CompWithFirst = true;
            }

            public int CompareTo(Pair<T, U> other)
            {
                return CompWithFirst ? first.CompareTo(other.first) : second.CompareTo(other.second);
            }
        }
    }
    class Modulo
    {
        private const int M = 1000000007;
        private readonly int[] m_facs;
        public int Mul(int a, int b) //掛け算
        {
            return (int)(Math.BigMul(a, b) % M);
        }
        public Modulo(int n)
        {
            m_facs = new int[n + 1];
            m_facs[0] = 1;
            for (int i = 1; i <= n; ++i)
            {
                m_facs[i] = Mul(m_facs[i - 1], i);
            }
        }
        public int Fac(int n)
        {
            return m_facs[n];
        }
        public int Pow(int a, int m) //累乗
        {
            switch (m)
            {
                case 0:
                    return 1;
                case 1:
                    return a;
                default:
                    int p1 = Pow(a, m / 2);
                    int p2 = Mul(p1, p1);
                    return ((m % 2) == 0) ? p2 : Mul(p2, a);
            }
        }
        public int Div(int a, int b) //除算
        {
            return Mul(a, Pow(b, M - 2));
        }
        public int Ncr(int n, int r) //二項係数
        {
            if (n < r) { return 0; }
            if (n == r) { return 1; }
            int res = Fac(n);
            res = Div(res, Fac(r));
            res = Div(res, Fac(n - r));
            return res;
        }
        public Modulo() { }
    }
    public class PriorityQueue<T> where T : IComparable<T>
    {

        private List<T> Q;
        private readonly int r;

        public PriorityQueue(bool ascending)
        {
            if (ascending)
            {
                r = 1;
            }
            else
            {
                r = -1;
            }
            Q = new List<T>();
        }


        private void PushHeap(List<T> list, T item)
        {
            int n = list.Count();
            list.Add(item);

            while (n != 0)
            {
                int pIndex = (n - 1) / 2;

                if (list[n].CompareTo(list[pIndex]) * r > 0)
                {
                    Swap(Q, n, pIndex);
                }
                else { break; }

                n = pIndex;
            }
        }

        private void PopHeap(List<T> list)
        {
            int n = list.Count() - 1;
            list[0] = list[n];
            list.RemoveAt(n);

            int cur = 0;
            int comp;

            while (2 * cur + 1 <= n - 1)
            {
                int c1 = 2 * cur + 1;
                int c2 = 2 * (cur + 1);
                if (c1 == n - 1)
                {
                    comp = c1;
                }
                else
                {

                    comp = list[c1].CompareTo(list[c2]) * r > 0 ? c1 : c2;
                }

                if (list[cur].CompareTo(list[comp]) * r < 0)
                {
                    Swap(Q, cur, comp);
                }
                else { break; }

                cur = comp;
            }
        }

        private void Swap(List<T> list, int a, int b)
        {
            T keep = list[a];
            list[a] = list[b];
            list[b] = keep;
        }



        public void Enqueue(T value)
        {
            PushHeap(Q, value);
        }

        public T Dequeue()
        {
            T ret = Q[0];
            PopHeap(Q);
            return ret;
        }

        public T Peek()
        {
            return Q[0];
        }

        public int Count()
        {
            return Q.Count();
        }

        public bool Contains(T search)
        {
            return Q.Contains(search);
        }
    }
    public class Scanner
    {
        public int[] SplitRead()
        {
            int[] array = Console.ReadLine().Split().Select(int.Parse).ToArray();
            return array;
        }
        public long[] SplitReadL()
        {
            long[] array = Console.ReadLine().Split().Select(long.Parse).ToArray();
            return array;
        }
    }
    public static class Tool
    {
        static public void Initialize<T>(ref T[] array, T initialvalue)
        {
            for (var i = 0; i < array.Length; i++)
            {
                array[i] = initialvalue;
            }
        }

        static public T MaxLot<T>(params T[] val) where T : IComparable<T>
        {
            T ret = val[0];
            for (var i = 1; i < val.Count(); i++)
            {
                if (ret.CompareTo(val[i]) < 0) { ret = val[i]; }
            }
            return ret;
        }
        static public T MinLot<T>(params T[] val) where T : IComparable<T>
        {
            T ret = val[0];
            for (var i = 1; i < val.Count(); i++)
            {
                if (ret.CompareTo(val[i]) > 0) { ret = val[i]; }
            }
            return ret;
        }

        static public void Swap<T>(T[] a, int i, int j)
        {
            T k = a[i];
            a[i] = a[j];
            a[j] = k;
        }

    }

}