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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.util.Arrays;
import java.util.Comparator;
import java.util.StringJoiner;
import java.util.StringTokenizer;

public class Main {

    static int N, T;
    static Dish[] D;

    public static void main(String[] args) {
        FastScanner sc = new FastScanner(System.in);
        N = sc.nextInt();
        T = sc.nextInt();
        D = new Dish[N];
        for (int i = 0; i < N; i++) {
            D[i] = new Dish(sc.nextInt(), sc.nextInt());
        }

        System.out.println(solve());
    }

    static class Dish {
        int cost, value;

        public Dish(int cost, int value) {
            this.cost = cost;
            this.value = value;
        }
    }

    static int solve() {
        // 最もおいしいのは最後に注文すればよい
        // => T-1分でナップサック + 最も美味しいの
        Arrays.sort(D, Comparator.comparingInt(d -> d.value));
        int[] dp = new int[T];
        Arrays.fill(dp, -1);
        dp[0] = 0;
        for (int i = 0; i < N-1; i++) {
            Dish d = D[i];
            for (int j = T-1; j >= 0; j--) {
                if( dp[j] != -1 && d.cost + j <= T-1 ) {
                    dp[d.cost + j] = Math.max(dp[j] + d.value, dp[d.cost + j]);
                }
            }
        }
        Dish most = D[N-1];
        return max(dp) + most.value;
    }

    @SuppressWarnings("unused")
    static class FastScanner {
        private BufferedReader reader;
        private StringTokenizer tokenizer;

        FastScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }

        String next() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        String nextLine() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    return reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken("\n");
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

        int[] nextIntArray(int n, int delta) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt() + delta;
            return a;
        }

        long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) a[i] = nextLong();
            return a;
        }
    }

    static void writeLines(int[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (int a : as) pw.println(a);
        pw.flush();
    }

    static void writeLines(long[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (long a : as) pw.println(a);
        pw.flush();
    }

    static void writeSingleLine(int[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (int i = 0; i < as.length; i++) {
            if (i != 0) pw.print(" ");
            pw.print(as[i]);
        }
        pw.println();
        pw.flush();
    }

    static int max(int... as) {
        int max = Integer.MIN_VALUE;
        for (int a : as) max = Math.max(a, max);
        return max;
    }

    static int min(int... as) {
        int min = Integer.MAX_VALUE;
        for (int a : as) min = Math.min(a, min);
        return min;
    }

    static void debug(Object... args) {
        StringJoiner j = new StringJoiner(" ");
        for (Object arg : args) {
            if (arg == null) j.add("null");
            else if (arg instanceof int[]) j.add(Arrays.toString((int[]) arg));
            else if (arg instanceof long[]) j.add(Arrays.toString((long[]) arg));
            else if (arg instanceof double[]) j.add(Arrays.toString((double[]) arg));
            else if (arg instanceof Object[]) j.add(Arrays.toString((Object[]) arg));
            else j.add(arg.toString());
        }
        System.err.println(j.toString());
    }

    static void printSingleLine(int[] array) {
        PrintWriter pw = new PrintWriter(System.out);
        for (int i = 0; i < array.length; i++) {
            if (i != 0) pw.print(" ");
            pw.print(array[i]);
        }
        pw.println();
        pw.flush();
    }

    static int lowerBound(int[] array, int value) {
        int lo = 0, hi = array.length, mid;
        while (lo < hi) {
            mid = (hi + lo) / 2;
            if (array[mid] < value) lo = mid + 1;
            else hi = mid;
        }
        return lo;
    }

    static int upperBound(int[] array, int value) {
        int lo = 0, hi = array.length, mid;
        while (lo < hi) {
            mid = (hi + lo) / 2;
            if (array[mid] <= value) lo = mid + 1;
            else hi = mid;
        }
        return lo;
    }
}