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문제

Farmer John's cows love their video games! FJ noticed that after playing these games that his cows produced much more milk than usual, surely because contented cows make more milk.

The cows disagree, though, on which is the best game console. One cow wanted to buy the Xbox 360 to play Halo 3; another wanted to buy the Nintendo Wii to play Super Smash Brothers Brawl; a third wanted to play Metal Gear Solid 4 on the PlayStation 3. FJ wants to purchase the set of game consoles (no more than one each) and games (no more than one each -- and within the constraints of a given budget) that helps his cows produce the most milk and thus nourish the most children.

FJ researched N (1 <= N <= 50) consoles, each with a console price P_i (1 <= P_i <= 1000) and a number of console-specific games G_i (1 <= G_i <= 10). A cow must, of course, own a console before she can buy any game that is specific to that console. Each individual game has a game price GP_j (1 <= GP_j price <= 100) and a production value (1 <= PV_j <= 1,000,000), which indicates how much milk a cow will produce after playing the game. Lastly, Farmer John has a budget V (1 <= V <= 100,000) which is the maximum amount of money he can spend. Help him maximize the sum of the production values of the games he buys.

Consider one dataset with N=3 consoles and a V=$800 budget. The first console costs $300 and has 2 games with cost $30 and $25 and production values as shown:

    Game #    Cost    Production Value
      1       $30          50
      2       $25          80

The second console costs $600 and has only 1 game:

    Game #    Cost    Production Value
      1       $50          130

The third console costs $400 and has 3 games:

    Game #    Cost    Production Value
      1       $40         70
      2       $30         40
      3       $35         60

Farmer John should buy consoles 1 and 3, game 2 for console 1, and games 1 and 3 for console 3 to maximize his expected production at 210:

                                Production Value
        Budget:     $800      
        Console 1  -$300
           Game 2   -$25              80
        Console 3  -$400
           Game 1   -$40              70
           Game 3   -$35              60
      -------------------------------------------
        Total:         0 (>= 0)      210

입력

  • Line 1: Two space-separated integers: N and V
  • Lines 2..N+1: Line i+1 describes the price of and the games available for console i; it contains: P_i, G_i, and G_i pairs of space-separated integers GP_j, PV_j

 

출력

  • Line 1: The maximum production value that Farmer John can get with his budget.

 

예제 입력

3 800
300 2 30 50 25 80
600 1 50 130
400 3 40 70 30 40 35 60

예제 출력

210

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