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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.PriorityQueue;
import java.util.StringTokenizer;



public class Main{
	
	static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    }
	
	static class Pair
	{
		int x;
		int y;
		Pair(int x,int y)
		{
			this.x = x;
			this.y = y;
		}
		
	    @Override
	    public int hashCode() {
	        return (this.x ^ this.y);
	    }

	    @Override
	    public boolean equals(Object obj) {
	        if (this == obj)
	            return true;
	        if (obj == null)
	            return false;
	        if (getClass() != obj.getClass())
	            return false;
	        Pair other = (Pair) obj;
	        if (x != other.x)
	            return false;
	        if (y != other.y)
	            return false;
	        return true;
	    }
	}
	
	static class Edge
	{
		int x;
		int y;
		Edge(int x,int y)
		{
			this.x = x;
			this.y = y;
		}
	}
	
	static class Compare { 
		  
	    static void compare(Pair arr[]) 
	    { 
	        // Comparator to sort the pair according to second element 
	        Arrays.sort(arr, new Comparator<Pair>() { 
	            @Override public int compare(Pair p1, Pair p2) 
	            { 	
	            	if(p1.y != p2.y)
	                return p1.y - p2.y; 
	            	
	            	else
	            	return p2.x-p1.x;
	            } 
	        }); 
	  
	       
	    } 
	} 
	
	public static int topDown(int ind,int rem)
	{
		if(ind == n || rem < 0)
		{
			return 0;
		}
		//System.out.println(ind+" "+rem);
		if(dp[ind][rem] > 0) return dp[ind][rem];
		
		int ans= 0;
		
		ans = Math.max(ans,pr[ind].y+topDown(ind+1,rem-pr[ind].x));
		
		ans = Math.max(ans,topDown(ind+1,rem));
		
		dp[ind][rem] = ans;
		return ans;
	}
	
	static Pair pr[];
	static int n,t;
	static int dp[][];
	public static void main(String[] args) 
	{
		OutputStream outputStream = System.out;
        FastReader sc = new FastReader();
        PrintWriter out = new PrintWriter(outputStream);
        
        n = sc.nextInt();
        t = sc.nextInt();
        
        pr = new Pair[n];
        
        for(int i = 0; i < n; i++)
        {
        	pr[i] = new Pair(0,0);
        	pr[i].x = sc.nextInt();
        	pr[i].y = sc.nextInt();
        }
        
        dp = new int[n][t+1];
        
        int ans = topDown(0,t);
        out.println(ans);
        
        out.close();
	}

}