Bought Review

AtCoder

IDarc174_b

Time2000ms

Memory256MB

Difficulty—

Solve the following problem for $T$ test cases. On the gourmet review site EatCocoder, you can review restaurants with an integer number of stars from $1$ to $5$. Initially, the restaurant managed by Chef B has $A_i$ reviews with $i$ stars. $(1 \le i \le 5)$ The chef can pay a bribe of $P_i$ yen to the EatCocoder administration to have one additional $i$\-star review. $(1 \le i \le 5)$ After adding a total of $k$ reviews by bribery, there will be $A_1+A_2+A_3+A_4+A_5+k$ reviews in total. Chef B wants the average rating of these reviews to be at least $3$ stars. Determine the minimum total amount of bribery required to achieve this. ## Constraints * All input values are integers. * $1 \le T \le 10^4$ * $0 \le A_i \le 10^8$ * $1 \le A_1+A_2+A_3+A_4+A_5$ * $1 \le P_i \le 10^8$ ## Input The input is given from Standard Input in the following format: $T$ $\rm{Case}_1$ $\rm{Case}_2$ $\vdots$ $\rm{Case}$$_T$ Here, $\rm{Case}$$_i$ represents the $i$\-th test case. Each test case is given in the following format: $A_1$ $A_2$ $A_3$ $A_4$ $A_5$ $P_1$ $P_2$ $P_3$ $P_4$ $P_5$ [samples]

Samples

Input #1

6
1 0 1 0 0
1 2 3 4 5
0 2 2 0 0
1 1 1 1 5
0 1 2 0 0
1 1 1 5 3
1 1 1 0 0
1 1 1 1 1
0 0 0 0 1
1 1 1 1 1
100000000 100000000 100000000 0 0
100000000 100000000 100000000 100000000 100000000

Output #1

5
2
3
2
0
15000000000000000

This input contains six test cases.

*   For the first test case, you can, for example, do the following to have an average rating of at least $3$ stars with a bribe of $5$ yen, which is the minimum possible amount.
    *   Initially, there are $1,0,1,0,0$ reviews with $1,2,3,4,5$ stars, respectively.
    *   Pay a bribe of $P_5 = 5$ yen to add one $5$\-star review.
    *   As a result, there are $1,0,1,0,1$ reviews with $1,2,3,4,5$ stars, respectively, averaging $3$ stars.
*   For the second test case, you can, for example, do the following to have an average rating of at least $3$ stars with a bribe of $2$ yen, which is the minimum possible amount.
    *   Initially, there are $0,2,2,0,0$ reviews with $1,2,3,4,5$ stars, respectively.
    *   Pay a bribe of $P_4 \times 2 = 2$ yen to add two $4$\-star reviews.
    *   As a result, there are $0,2,2,2,0$ reviews of with $1,2,3,4,5$ stars, respectively, averaging $3$ stars.
*   For the third test case, you can, for example, do the following to have an average rating of at least $3$ stars with a bribe of $3$ yen, which is the minimum possible amount.
    *   Initially, there are $0,1,2,0,0$ reviews with $1,2,3,4,5$ stars, respectively.
    *   Pay a bribe of $P_5 = 3$ yen to add one $5$\-star review.
    *   As a result, there are $0,1,2,0,1$ reviews with $1,2,3,4,5$ stars, respectively, averaging $3.25$ stars.
*   For the fourth test case, you can, for example, do the following to have an average rating of at least $3$ stars with a bribe of $2$ yen, which is the minimum possible amount.
    *   Initially, there are $1,1,1,0,0$ reviews with $1,2,3,4,5$ stars, respectively.
    *   Pay a bribe of $P_4 = 1$ yen to add one $4$\-star review.
    *   Pay a bribe of $P_5 = 1$ yen to add one $5$\-star review.
    *   As a result, there are $1,1,1,1,1$ reviews with $1,2,3,4,5$ stars, respectively, averaging $3$ stars.
*   For the fifth test case, you can, for example, do the following to have an average rating of at least $3$ stars with a bribe of $0$ yen, which is the minimum possible amount.
    *   Initially, there are $0,0,0,0,1$ reviews with $1,2,3,4,5$ stars, respectively.
    *   Since the average is already $5$, which is not less than $3$, give no bribe.
*   For the sixth test case, note that the answer may not fit into a $32$\-bit signed integer.

API Response (JSON)

{
  "problem": {
    "name": "Bought Review",
    "description": {
      "content": "Solve the following problem for $T$ test cases. On the gourmet review site EatCocoder, you can review restaurants with an integer number of stars from $1$ to $5$.   Initially, the restaurant managed b",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc174_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Solve the following problem for $T$ test cases.\nOn the gourmet review site EatCocoder, you can review restaurants with an integer number of stars from $1$ to $5$.  \nInitially, the restaurant managed b...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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