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.Text;
using System.Threading.Tasks;
using System.Text.RegularExpressions;

public class ABC
{
    //          long[] sp = Console.ReadLine().Split().Select(long .Parse).ToArray();
    //          int[] sp = Console.ReadLine().Split().Select(int.Parse).ToArray();
    //          int N =  int.Parse(Console.ReadLine());
    //CompLib.Collections.PriorityQueue<?>

    public static void Main()
    {
        int N, T;
        new readint(out N, out T);
        int[] A = new int[N];
        int[] B = new int[N];
        Tuple<int, int>[] AB = new Tuple<int, int>[N];
        for (int i = 0; i < N; i++)
        {
            new readint(out A[i], out B[i]);
            AB[i] = new Tuple<int, int>(A[i], B[i]);
        }

        Array.Sort(AB, comparer);

        int[,] DP = new int[N + 1, T + 1];

        for (int consideredMeals = 1; consideredMeals <= N; consideredMeals++)
        {
            for (int minutes = 0; minutes < T; minutes++)
            {
                // consideredMeals-1番目の食べ物を食べたかどうか
                int tabemonoindex = consideredMeals - 1;
                int ATE = 0;
                int notATE = DP[consideredMeals - 1, minutes];

                if (minutes - AB[tabemonoindex].Item1>=0)
                {
                    ATE = DP[consideredMeals - 1, minutes - AB[tabemonoindex].Item1] + AB[tabemonoindex].Item2;

                }
                DP[consideredMeals, minutes] = Math.Max(ATE, notATE);


            }
        }

        for (int consideredMeals = 1; consideredMeals <= N; consideredMeals++)
        {
           
            int ATE = 0;
            int notATE = DP[consideredMeals - 1, T];

            {
                ATE = DP[consideredMeals - 1, T - 1] + AB[consideredMeals - 1].Item2;
            }
            DP[consideredMeals, T] = Math.Max(ATE, notATE);
        }

        Console.WriteLine(DP[N, T]);
    }

    public static int comparer(Tuple<int, int> a, Tuple<int, int> b)
    {
        if (a.Item1 > b.Item1) return 1;
        else if (a.Item1 < b.Item1) return -1;
        else if (a.Item2 > b.Item2) return -1;
        else if (a.Item2 < b.Item2) return 1;
        else return 0;
    }
}



class readint
{



    public readint(out int i)
    {
        i = int.Parse(Console.ReadLine());

    }
    public readint(out int a, out int b)
    {
        int[] sp = Console.ReadLine().Split().Select(int.Parse).ToArray();
        a = sp[0];
        b = sp[1];

    }
    public readint(out int a, out int b, out int c)
    {
        int[] sp = Console.ReadLine().Split().Select(int.Parse).ToArray();
        a = sp[0];
        b = sp[1];
        c = sp[2];
    }
    public readint(out int a, out int b, out int c, out int d)
    {
        int[] sp = Console.ReadLine().Split().Select(int.Parse).ToArray();
        a = sp[0];
        b = sp[1];
        c = sp[2];
        d = sp[3];

    }

}

class readlong
{


    public readlong(out long i)
    {
        i = long.Parse(Console.ReadLine());

    }
    public readlong(out long a, out long b)
    {
        long[] sp = Console.ReadLine().Split().Select(long.Parse).ToArray();
        a = sp[0];
        b = sp[1];

    }
    public readlong(out long a, out long b, out long c)
    {
        long[] sp = Console.ReadLine().Split().Select(long.Parse).ToArray();
        a = sp[0];
        b = sp[1];
        c = sp[2];
    }
    public readlong(out long a, out long b, out long c, out long d)
    {
        long[] sp = Console.ReadLine().Split().Select(long.Parse).ToArray();
        a = sp[0];
        b = sp[1];
        c = sp[2];
        d = sp[3];

    }

}







class Util
{





    public static long GCD(long a, long b)
    {
        if (a < b)
            swap(ref a, ref b);
        if (a % b == 0) return b;
        return GCD(b, a % b);

    }
    public static int GCD(int a, int b)
    {
        if (a < b)
            swap(ref a, ref b);
        if (a % b == 0) return b;
        return GCD(b, a % b);
    }

    public static void swap<T>(ref T a, ref T b)
    {
        T temp = b;
        b = a;
        a = temp;

    }
    public static long LCM(long a, long b)
    {
        return a * b / GCD(a, b);
    }
    public static long LCM(int a, int b)
    {
        return Math.BigMul(a, b) / GCD(a, b);
    }


    public static int M = (int)(Math.Pow(10, 9)) + 7;
    private static int[] factorial_modM;
    public static int Multiple_modM(int a, int b)
    {
        return (int)(Math.BigMul(a, b) % M);
    }
    public static void factorial_modM_Prepare(int n)
    {
        factorial_modM = new int[n + 1];
        factorial_modM[0] = 1;
        for (int i = 1; i <= n; ++i)
        {
            factorial_modM[i] = Multiple_modM(factorial_modM[i - 1], i);
        }
    }
    public static int Factorial(int n)
    {
        return factorial_modM[n];
    }
    public static int Pow(int a, int m)
    {
        switch (m)
        {
            case 0:
                return 1;
            case 1:
                return a;
            default:
                int p1 = Pow(a, m / 2);
                int p2 = Multiple_modM(p1, p1);
                return ((m % 2) == 0) ? p2 : Multiple_modM(p2, a);
        }
    }
    public static int Div(int a, int b)
    {
        return Multiple_modM(a, Pow(b, M - 2));
    }
    public static int nCr_modM(int n, int r)
    {
        if (r < 0) return 0;

        if (n < r) { return 0; }
        if (n == r) { return 1; }
        int res = Factorial(n);
        res = Div(res, Factorial(r));
        res = Div(res, Factorial(n - r));
        return res;
    }

}

class UnionFind<T>
{
    public int tree_height;
    public UnionFind<T> parent;
    public T item
    {
        get;
        private set;
    }

    public UnionFind(T item)
    {
        tree_height = 0;
        parent = this;
    }

    public UnionFind<T> FindAdam()
    {
        if (parent == this) return this;
        else
        {
            UnionFind<T> ParentOfParent = parent.FindAdam();
            parent = ParentOfParent;//縦長な構成をつなぎ直している
            return ParentOfParent;
        }
    }
    public static void Unite(UnionFind<T> a, UnionFind<T> b)
    {
        UnionFind<T> ParentOfA = a.FindAdam();
        UnionFind<T> ParentOfB = b.FindAdam();
        if (ParentOfA.tree_height < ParentOfB.tree_height)
        {
            ParentOfA.parent = ParentOfB;
            ParentOfB.tree_height = Math.Max(ParentOfA.tree_height + 1, ParentOfB.tree_height);
        }
        else
        {
            ParentOfB.parent = ParentOfA;
            ParentOfA.tree_height = Math.Max(ParentOfB.tree_height + 1, ParentOfA.tree_height);
        }

    }

}

//Treap 平衡二分木
class Treap<T> where T : IComparable
{
    private class Node
    {
        private static Random g_rand = new Random();
        private readonly int m_rank = g_rand.Next();
        private readonly T m_value;
        private Node m_lch;
        private Node m_rch;
        private int m_count;

        public Node(T value)
        {
            m_value = value;
            m_count = 1;
        }

        private static int Count(Node node)
        {
            return (node != null) ? node.m_count : 0;
        }

        private Node Update()
        {
            m_count = Count(m_lch) + Count(m_rch) + 1;
            return this;
        }

        public static Node Merge(Node a, Node b)
        {
            if (a == null) { return b; }
            if (b == null) { return a; }

            if (a.m_rank < b.m_rank)
            {
                a.m_rch = Merge(a.m_rch, b);
                return a.Update();
            }
            else
            {
                b.m_lch = Merge(a, b.m_lch);
                return b.Update();
            }
        }

        public static Tuple<Node, Node> Split(Node t, int k)
        {
            if (t == null) { return new Tuple<Node, Node>(null, null); }

            if (k <= Count(t.m_lch))
            {
                var pair = Split(t.m_lch, k);
                t.m_lch = pair.Item2;
                return new Tuple<Node, Node>(pair.Item1, t.Update());
            }
            else
            {
                var pair = Split(t.m_rch, k - Count(t.m_lch) - 1);
                t.m_rch = pair.Item1;
                return new Tuple<Node, Node>(t.Update(), pair.Item2);
            }
        }

        public int FindIndex(T value)
        {
            int L = Count(m_lch);
            if (value.CompareTo(m_value) < 0)
            {
                return (m_lch != null) ? m_lch.FindIndex(value) : 0;
            }
            else if (value.CompareTo(m_value) > 0)
            {
                return (m_rch != null) ? m_rch.FindIndex(value) + L + 1 : L + 1;
            }
            else
            {
                return L;
            }
        }

        public T this[int i]
        {
            get
            {
                int L = Count(m_lch);
                if (i < L)
                {
                    return m_lch[i];
                }
                else if (i > L)
                {
                    return m_rch[i - L - 1];
                }
                else
                {
                    return m_value;
                }
            }
        }
    }

    private Node node;

    public void Insert(T value)
    {
        if (node != null)
        {
            int k = node.FindIndex(value);
            var pair = Node.Split(node, k);
            node = Node.Merge(Node.Merge(pair.Item1, new Node(value)), pair.Item2);
        }
        else
        {
            node = new Node(value);
        }
    }

    public int FindIndex(T value)
    {
        return node.FindIndex(value);
    }

    public T this[int i]
    {
        get
        {
            return node[i];
        }
    }
}

static class Permutation<T>
{
    private static void Search(List<T[]> perms, Stack<T> stack, T[] a)
    {
        int N = a.Length;
        if (N == 0)
        {
            perms.Add(stack.Reverse().ToArray());
        }
        else
        {
            var b = new T[N - 1];
            Array.Copy(a, 1, b, 0, N - 1);
            for (int i = 0; i < a.Length; ++i)
            {
                stack.Push(a[i]);
                Search(perms, stack, b);
                if (i < b.Length) { b[i] = a[i]; }
                stack.Pop();
            }
        }
    }
    public static IEnumerable<T[]> All(IEnumerable<T> src)
    {
        var perms = new List<T[]>();
        Search(perms, new Stack<T>(), src.ToArray());
        return perms;
    }
}

namespace CompLib.Collections
{
    #region PriorityQueue
    /// <summary>
    /// 指定した型のインスタンスを最も価値が低い順に取り出すことが可能な可変サイズのコレクションを表します．
    /// </summary>
    /// <typeparam name="T">優先度付きキュー内の要素の型を指定します．</typeparam>
    /// <remarks>内部的にはバイナリヒープによって実装されています．</remarks>
    public class PriorityQueue<T>
    {
        readonly List<T> heap = new List<T>();
        readonly Comparison<T> cmp;

        /// <summary>
        /// デフォルトの比較子を使用してインスタンスを初期化します．
        /// </summary>
        /// <remarks>この操作は O(1) で実行されます．</remarks>
        public PriorityQueue() { cmp = Comparer<T>.Default.Compare; }

        /// <summary>
        /// デリゲートで表されるような比較関数を使用してインスタンスを初期化します．
        /// </summary>
        /// <param name="comparison"></param>
        /// <remarks>この操作は O(1) で実行されます．</remarks>
        public PriorityQueue(Comparison<T> comparison) { cmp = comparison; }

        /// <summary>
        /// 指定された比較子を使用してインスタンスを初期化します．
        /// </summary>
        /// <param name="comparer"></param>
        /// <remarks>この操作は O(1) で実行されます．</remarks>
        public PriorityQueue(IComparer<T> comparer) { cmp = comparer.Compare; }

        /// <summary>
        /// 優先度付きキューに要素を追加します．
        /// </summary>
        /// <param name="item">優先度付きキューに追加される要素</param>
        /// <remarks>最悪計算量 O(log N) で実行されます．</remarks>
        public void Enqueue(T item)
        {
            var pos = heap.Count;
            heap.Add(item);
            while (pos > 0)
            {
                var par = (pos - 1) / 2;
                if (cmp(heap[par], item) <= 0)
                    break;
                heap[pos] = heap[par];
                pos = par;
            }
            heap[pos] = item;

        }

        /// <summary>
        /// 優先度付きキューから最も価値が低い要素を削除し，返します．
        /// </summary>
        /// <returns>優先度付きキューから削除された要素．</returns>
        /// <remarks>最悪計算量 O(log N) で実行されます．</remarks>
        public T Dequeue()
        {
            var ret = heap[0];
            var pos = 0;
            var x = heap[heap.Count - 1];

            while (pos * 2 + 1 < heap.Count - 1)
            {
                var lch = pos * 2 + 1;
                var rch = pos * 2 + 2;
                if (rch < heap.Count - 1 && cmp(heap[rch], heap[lch]) < 0) lch = rch;
                if (cmp(heap[lch], x) >= 0)
                    break;
                heap[pos] = heap[lch];
                pos = lch;
            }
            heap[pos] = x;
            heap.RemoveAt(heap.Count - 1);
            return ret;

        }
        /// <summary>
        ///  優先度付きキューに含まれる最も価値が低い要素を削除せずに返します．
        /// </summary>
        /// <returns>優先度付きキューに含まれる最も価値が低い要素．</returns>
        /// <remarks>この操作は O(1) で実行されます．</remarks>
        public T Peek() { return heap[0]; }

        /// <summary>
        /// 優先度付きキュー内の要素の数を取得します．
        /// </summary>
        /// <returns>優先度付キュー内にある要素の数</returns>
        /// <remarks>最悪計算量 O(1) で実行されます．</remarks>
        public int Count { get { return heap.Count; } }
        /// <summary>
        /// 優先度付きキュー内に要素が存在するかどうかを O(1) で判定します．
        /// </summary>
        /// <returns>優先度付キュー内にある要素が存在するならば true，そうでなければ　false．</returns>
        /// <remarks>この操作は O(1) で実行されます．</remarks>
        public bool Any() { return heap.Count > 0; }

        /// <summary>
        /// 優先度付きキューに含まれる要素を昇順に並べて返します．
        /// </summary>
        /// <remarks>この操作は計算量 O(N log N)で実行されます．</remarks>
        public T[] Items
        {
            get
            {
                var ret = heap.ToArray();
                Array.Sort(ret, cmp);
                return ret;
            }
        }
    }
    #endregion
}

/// <summary>
/// SEGTREEは1-BASE運用でございます
/// よろしくおねがいします
/// </summary>
/// <typeparam name="T"></typeparam>

class Segtree<T>
{
    int n;//高さ
    T[] tree;//本体
    Func<T, T, T> f;//更新関数。a -> b -> ab使ったなにか
    T exnum;//初期値
    int count;
    public Segtree(int m, Func<T, T, T> f, T ex)
    {
        this.count = 0;
        this.f = f;
        this.exnum = ex;
        n = 1;
        while (n < m) n <<= 1;

        tree = new T[(n << 1) - 1];
        for (int i = 0; i < tree.Length; i++) tree[i] = ex;
    }
    public Segtree(int m, T ini, Func<T, T, T> f, T ex) : this(m, f, ex)
    {
        this.count = 0;
        for (int i = 0; i < m; ++i) tree[i + n - 1] = ini;
        all_update();
    }
    public void assign_without_update(int j, T x)
    {
        tree[j + n - 1] = x;
    }
    public void update(int j, T x)//j番目をxにする
    {
        int i = j + n - 1;
        tree[i] = x;
        while (i > 0)
        {
            i = (i - 1) >> 1;
            tree[i] = f(tree[(i << 1) + 1], tree[(i << 1) + 2]);
        }
        this.count++;
    }


    public void all_update()
    {
        for (int i = n - 2; i >= 0; i--)
            tree[i] = f(tree[(i << 1) + 1], tree[(i << 1) + 2]);
    }
    public T look(int i) { return tree[i + n - 1]; }

    public void delete(int j)
    {
        int i = j + n - 1;
        tree[i] = exnum;
        int moved = 0;

        while (true)
        {
            tree[i + 1] = tree[i];
            T check = tree[i];
            moved++;
            if (moved + j + 2 > count)
            {
                break;
            }

        }
        all_update();
    }


    // [s, t)
    public T run(int s, int t) { return query(s, t, 0, 0, n); }
    T query(int s, int t, int k, int l, int r)
    {
        if (r <= s || t <= l) return exnum;
        if (s <= l && r <= t) return tree[k];

        return f(query(s, t, (k << 1) + 1, l, (l + r) >> 1), query(s, t, (k + 1) << 1, (l + r) >> 1, r));
    }
}