Make N

AtCoder

IDarc139_b

Time2000ms

Memory256MB

Difficulty—

We have an integer $P=0$. Find the minimum total cost to make $P=N$ by doing the following three kinds of operations any number of times in any order. * Increase $P$ by $1$, at a cost of $X$. * Increase $P$ by $A$, at a cost of $Y$. * Increase $P$ by $B$, at a cost of $Z$. Solve each of the $T$ test cases given to you. ## Constraints * $1 \le T \le 100$ * $1 \le N,A,B,X,Y,Z \le 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $T$ $\mathrm{case}_1$ $\mathrm{case}_2$ $\vdots$ $\mathrm{case}_T$ Each test case is in the following format: $N\ A\ B\ X\ Y\ Z$ [samples]

Samples

Input #1

5
10 3 5 2 3 6
10 3 5 1 1000000000 1000000000
139 2 139 1 1 1
139 1 1 1 1 1
139 7 10 3845 26982 30923

Output #1

11
10
1
139
436604

In the first test case, below is one way to make $P=10$ at the cost of $11$, which is optimal.

*   Increase $P$ by $3$, making $P=3$, at a cost of $3$.
*   Increase $P$ by $1$, making $P=4$, at a cost of $2$.
*   Increase $P$ by $3$, making $P=7$, at a cost of $3$.
*   Increase $P$ by $3$, making $P=10$, at a cost of $3$.

API Response (JSON)

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      "statement_type": "Markdown",
      "content": "We have an integer $P=0$. Find the minimum total cost to make $P=N$ by doing the following three kinds of operations any number of times in any order.\n\n*   Increase $P$ by $1$, at a cost of $X$.\n*   I...",
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Full JSON Raw Segments