Problem:
Score : 400 points

Problem Statement

You start with the number 0 and you want to reach the number N.

You can change the number, paying a certain amount of coins, with the following operations:

Multiply the number by 2, paying A coins.

Multiply the number by 3, paying B coins.

Multiply the number by 5, paying C coins.

Increase or decrease the number by 1, paying D coins.

You can perform these operations in arbitrary order and an arbitrary number of times.

What is the minimum number of coins you need to reach N?

You have to solve T testcases.

Constraints

1 \le T \le 10

1 \le N \le 10^{18}

1 \le A, B, C, D \le 10^9

All numbers N, A, B, C, D are integers.

Input

The input is given from Standard Input. The first line of the input is

T

Then, T lines follow describing the T testcases.
Each of the T lines has the format

N A B C D

Output

For each testcase, print the answer on Standard Output followed by a newline.

Sample Input 1

5
11 1 2 4 8
11 1 2 2 8
32 10 8 5 4
29384293847243 454353412 332423423 934923490 1
900000000000000000 332423423 454353412 934923490 987654321

Sample Output 1

20
19
26
3821859835
23441258666

For the first testcase, a sequence of moves that achieves the minimum cost of 20 is:

Initially x = 0.

Pay 8 to increase by 1 (x = 1).

Pay 1 to multiply by 2 (x = 2).

Pay 1 to multiply by 2 (x = 4).

Pay 2 to multiply by 3 (x = 12).

Pay 8 to decrease by 1 (x = 11).

For the second testcase, a sequence of moves that achieves the minimum cost of 19 is:

Initially x = 0.

Pay 8 to increase by 1 (x = 1).

Pay 1 to multiply by 2 (x = 2).

Pay 2 to multiply by 5 (x = 10).

Pay 8 to increase by 1 (x = 11).

Solution in OCaml (4.10.0) (judge verdict: Wrong Answer)

Scanf.scanf "%d" (fun t ->
    let module M = Map.Make (struct type t = int let compare = compare end) in
    for i = 1 to t do
        Scanf.scanf " %d %d %d %d %d" (fun n a b c d ->
            let rec calc =
                let map = ref (M.add 0 0 (M.singleton 1 d)) in
                fun k ->
                if M.mem k !map then M.find k !map else (
                    let ans = if k < max_int / d then k * d else max_int in
                    let ans = List.fold_left (fun acc i ->
                        if (k + i) mod 2 <> 0 then acc else
                            min acc (calc ((k + i) / 2) + a + d * abs i)
                            ) ans [ -1; 0 ]
                    in
                    let ans = List.fold_left (fun acc i ->
                        if (k + i) mod 3 <> 0 then acc else
                            min acc (calc ((k + i) / 3) + b + d * abs i)
                            ) ans [ -1; 0; 1 ]
                    in
                    let ans = List.fold_left (fun acc i ->
                        if (k + i) mod 5 <> 0 then acc else
                            min acc (calc ((k + i) / 5) + c + d * abs i)
                            ) ans [ -2; -1; 0; 1; 2 ]
                    in
                    map := M.add k ans !map;
                    ans
                  )
            in
            Printf.printf "%d\n" @@ calc n
        )
    done
)