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



Sample input:
2 60
10 10
100 100


Sample output:
110

Submission status: Accepted

Solution code:
import sys
from io import StringIO
import unittest
import os

# 再帰処理上限(dfs作成時に設定するのが面倒なので限度近い値を組み込む)
sys.setrecursionlimit(999999999)


# youk_library(debug)
def list_to_tsv_string(target: [], limit_row: int = 0, limit_column: int = 0):
    import csv

    # 行列を制限内に縮める
    if limit_row is not 0:
        target = target[:limit_row]
    if limit_column is not 0:
        target = [i[:limit_column] for i in target]

    # 行番号、列番号を追加
    # 行番号
    target = [[cnt] + i for cnt, i in enumerate(target)]
    # 列番号
    work = [i for i in range(len(target[0]))]
    target.insert(0, work)
    # tsv出力
    with open("temp.txt", "w", newline="") as f:
        writer = csv.writer(f, delimiter="\t")
        writer.writerows(target)


# 実装を行う関数
def resolve(test=""):
    try:
        # 入力の取得
        n, t = map(int, input().split())
        ab_s = [list(map(int, input().split())) for i in range(n)]

        # ------------
        # DP準備
        # ------------
        # DPの鉄則1? 「カスタム添え字として使用する」要素でソート。
        #   ->本問題の場合、カスタム添え字は「使用する時間」。この昇順でソート。
        ab_s.sort(key=lambda xx: [xx[0]])

        # DPの鉄則2?「DP対象のリスト[0]に添字調整用のダミーを追加。
        #   ->先頭から1つ選ぶ=ab_s[1]という風に、直観的に扱えるようになる。
        ab_s = [[0, 0]] + ab_s

        # DP配列の作成。
        # dp[0][使用する時間(累計):0~6000] = おいしさの最大値(-1=存在しないパターン)
        dp = [[-1 for j in range(6000 + 1)]]

        # DP配列の初期化。(何も選ばない場合の値をセット) ※ここは問題により固有※
        # 今回は・・料理を何も食べない=おいしさ0
        dp[0][0] = 0

        # ------------
        # DP
        # ------------
        # 先頭からi個選ぶループ
        for i in range(1, 999999999):

            # 次の行を追加(前の行を複写して追加) ※適時append()すると見やすい。
            dp.append(dp[i - 1].copy())

            # 最後の要素まで検証したならDP終了
            if len(ab_s) <= i:
                break

            # 検証対象の情報を取り出し ※ここは問題により固有※
            time, delicious = ab_s[i]

            # カスタム添え字ループ
            for j in range(999999999):

                # 制限時間を超えたら要素の検証を終える。次の要素へ。 ※ここは問題ごとに設定※
                if j > t - 1:
                    break

                # 値が0未満は「存在しないパターン」なので検証しない。
                if dp[i][j] < 0:
                    continue

                # 最適解を取得 ※ここは問題ごとに設定※
                val = max(dp[i][j + time], dp[i - 1][j] + delicious)

                # 最適解を反映 ※ここは問題ごとに設定※
                dp[i][j + time] = val

        # ------------
        # 結果を出力
        # ------------
        print(max(dp[i]))

    except IndexError as err:
        print("インデックスエラー:", err.args[0])


# テストクラス
class TestClass(unittest.TestCase):
    def assertIO(self, assert_input, output):
        stdout, sat_in = sys.stdout, sys.stdin
        sys.stdout, sys.stdin = StringIO(), StringIO(assert_input)
        resolve(sys._getframe().f_back.f_code.co_name)
        sys.stdout.seek(0)
        out = sys.stdout.read()[:-1]
        sys.stdout, sys.stdin = stdout, sat_in
        self.assertEqual(out, output)

    # 自作テストパターン
    def test_original1(self):
        test_input = """3 10
1 10
3000 20
1 20"""
        output = """50"""
        self.assertIO(test_input, output)

    def test_original2(self):
        test_input = """2 10
9 1
3000 3000"""
        output = """3001"""
        self.assertIO(test_input, output)

    def test_original3(self):
        test_input = """3000 3000
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1 1
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1 1
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1 1
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1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1"""
        output = """5999"""
        self.assertIO(test_input, output)

    def test_input_1(self):
        test_input = """2 60
10 10
100 100"""
        output = """110"""
        self.assertIO(test_input, output)

    def test_input_2(self):
        test_input = """3 60
10 10
10 20
10 30"""
        output = """60"""
        self.assertIO(test_input, output)

    def test_input_3(self):
        test_input = """3 60
30 10
30 20
30 30"""
        output = """50"""
        self.assertIO(test_input, output)

    def test_input_4(self):
        test_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"""
        self.assertIO(test_input, output)


# 実装orテストの呼び出し
if __name__ == "__main__":
    if os.environ.get("USERNAME") is None:
        # AtCoder提出時の場合
        resolve()

    else:
        # 自PCの場合
        unittest.main(verbosity=2)