Problem: 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.

Examples

Input

2 60
10 10
100 100


Output

110


Input

3 60
10 10
10 20
10 30


Output

60


Input

3 60
30 10
30 20
30 30


Output

50


Input

10 100
15 23
20 18
13 17
24 12
18 29
19 27
23 21
18 20
27 15
22 25


Output

145

Solution (in JAVA):

Solution:
// template for atcoder
import java.util.*;
import java.io.*;
import static java.lang.Math.*;

public class Main {

    private static final int MOD = (int)1e9 + 7; //998244353;
    private static final long INF = (long)1e15;


    public Main(FastScanner in, PrintWriter out) {
        int N = in.nextInt();
        int T = in.nextInt();
        int[][] D = new int[N][];
        for (int i = 0; i < N; i++) {
            D[i] = new int[]{in.nextInt(), in.nextInt()};
        }
        Arrays.sort(D, Comparator.comparingInt(a -> a[0]));
        int[][] dp = new int[T][N + 1];
        for (int t = 1; t < T; t++) {
            for (int i = 1; i <= N; i++) {
                int c = D[i - 1][0], d = D[i - 1][1];
                dp[t][i] = dp[t][i - 1];
                if (t >= c)
                    dp[t][i] = Math.max(dp[t][i], dp[t - c][i - 1] + d);
            }
        }
        int res = 0, maxD = 0;
        for (int i = N; i >= 0; i--) {
            res = Math.max(res, dp[T - 1][i] + maxD);
            if (i > 0)
                maxD = Math.max(maxD, D[i - 1][1]);
        }
        out.println(res);
    }

    public void Main0(FastScanner in, PrintWriter out) {
        int N = in.nextInt();
        int T = in.nextInt();
        int[] A = new int[N];
        int[] B = new int[N];
        for (int i = 0; i < N; i++) {
            A[i] = in.nextInt();
            B[i] = in.nextInt();
        }
        int[][] dp = new int[T + 1][N + 1];
        // for (int t = 0; t <= T; t++) {
        for (int t = 1; t <= T; t++) {
            for (int i = 1; i <= N; i++) {
                // dp[t][i] = Math.max(dp[t][i], dp[t][i - 1]);
                // if (t < T) {
                    // int nt = Math.min(T, t + A[i - 1]);
                    // int d = B[i - 1];
                    // dp[nt][i] = Math.max(dp[nt][i], dp[t][i - 1] + d);
                // }
                int c = A[i - 1], d = B[i - 1];
                dp[t][i] = dp[t][i - 1];
                if (t >= c)
                    dp[t][i] = Math.max(dp[t][i], dp[t - c][i - 1] + d);
            }
        }
        int res = dp[T][N];
        for (int t = T - 1; t > 0; t--) {
            int max = 0, i = N, j = t;
            while (i > 0) {
                if (dp[j][i] == dp[j][i - 1]) {
                    max = Math.max(max, B[i - 1]);
                } else {
                    j -= A[i - 1];
                }
                i--;
            }
            res = Math.max(res, dp[t][N] + max);
        }
        out.println(res);
    }

    private int gcd(int a, int b) {
        while (true) {
            if (b == 0) return a;
            int tmp = a;
            a = b;
            b = tmp % b;
        }
    }

    private long gcd(long a, long b) {
        while (true) {
            if (b == 0) return a;
            long tmp = a;
            a = b;
            b = tmp % b;
        }
    }

    private long powm(long x, long p) {
        long res = 1;
        while (p > 0) {
            if (p % 2 == 1)
                res = res * x % MOD;
            x = x * x % MOD;
            p /= 2;
        }
        return res;
    }

    public static void main(String[] args) {
        PrintWriter out = new PrintWriter(System.out);
        // Scanner in = new Scanner(
                // new BufferedReader(new InputStreamReader(System.in)));
        FastScanner in = new FastScanner(System.in);

        Main sol = new Main(in, out);
        out.close();
    }
}

// Pair
class Pair<T extends Comparable<? super T>, U extends Comparable<? super U>> implements Comparable<Pair<T, U>> {
    T a;
    U b;
    Pair() { }
    Pair(T a, U b) {
        this.a = a;
        this.b = b;
    }

    @Override
    public String toString() { return "("+a.toString()+", "+b.toString()+")"; }

    @Override
    public int hashCode() { return Objects.hash(a, b); }

    @Override
    public boolean equals(Object obj) {
        if(this == obj) return true;
        if(obj == null) return false;
        if(this.getClass() != obj.getClass()) return false;
        Pair that = (Pair) obj;
        if(this.a.getClass() != that.a.getClass()) return false;
        if(this.b.getClass() != that.b.getClass()) return false;
        if(!this.a.equals(that.a)) return false;
        if(!this.b.equals(that.b)) return false;
        return true;
    }

    @Override
    public int compareTo(Pair<T, U> that) {
        int c = (this.a).compareTo(that.a);
        if(c == 0) c = (this.b).compareTo(that.b);
        return c;
    }
}


class FastScanner{
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;

    public FastScanner(InputStream stream)
    {
        this.stream = stream;
    }

    int read()
    {
        if (numChars == -1)
            throw new InputMismatchException();
        if (curChar >= numChars){
            curChar = 0;
            try{
                numChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }

    boolean isSpaceChar(int c)
    {
        return c==' '||c=='\n'||c=='\r'||c=='\t'||c==-1;
    }

    boolean isEndline(int c)
    {
        return c=='\n'||c=='\r'||c==-1;
    }

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

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

    double nextDouble()
    {
        return Double.parseDouble(next());
    }

    String next(){
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do{
            res.appendCodePoint(c);
            c = read();
        }while(!isSpaceChar(c));
        return res.toString();
    }

    String nextLine(){
        int c = read();
        while (isEndline(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do{
            res.appendCodePoint(c);
            c = read();
        }while(!isEndline(c));
        return res.toString();
    }
}