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 Rust (1.42.0) (judge verdict: Wrong Answer)

use proconio::input;

fn main() {
    input! {
        t: usize,
        nabcd: [(i128, i128, i128, i128, i128); t],
    }

    for (n, a, b, c, d) in nabcd {
        let mut kouho = vec![n * d];
        for i in 0..=64 {
            for j in 0..=64 {
                for k in 0..=64 {
                    let pow_a = match 2i128.checked_pow(i) {
                        Some(x) => x,
                        None => break,
                    };

                    let pow_b = match 3i128.checked_pow(j) {
                        Some(x) => x,
                        None => break,
                    };

                    let pow_c = match 5i128.checked_pow(k) {
                        Some(x) => x,
                        None => break,
                    };

                    let sum = match pow_a
                        .checked_mul(pow_b)
                        .map(|x| x.checked_mul(pow_c))
                        .flatten()
                    {
                        Some(x) => x,
                        None => break,
                    };

                    if n <= sum && sum <= n * 5 {
                        let coins = a * i as i128 + b * j as i128 + c * k as i128 + d;
                        kouho.push(coins + (sum - n).abs() * d);
                        if sum % 2 == 0 {
                            kouho.push(coins - 1 + (n - (sum / 2)).abs() * d);
                        }
                        if sum % 3 == 0 {
                            kouho.push(coins - 1 + (n - (sum / 3)).abs() * d);
                        }
                        if sum % 4 == 0 {
                            kouho.push(coins - 1 + (n - (sum / 4)).abs() * d);
                        }
                        if sum % 5 == 0 {
                            kouho.push(coins - 1 + (n - (sum / 5)).abs() * d);
                        }
                    }
                }
            }
        }

        println!("{}", kouho.iter().min().unwrap());
    }
}