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: Accepted)

use std::collections::HashMap;
struct global {
    memo: std::collections::HashMap<u64, u64>,
}

impl global {
    fn solve(&mut self, n: u64, a: u64, b: u64, c: u64, d: u64) -> u64 {
        if let Some(&v) = self.memo.get(&n) {
            return v;
        }

        if n <= 1 {
            return d * n;
        }

        let &ans = [
            n.saturating_mul(d),
            self.solve(n / 2, a, b, c, d) + n % 2 * d + a,
            self.solve((n + 1) / 2, a, b, c, d) + (2 - n % 2) % 2 * d + a,
            self.solve(n / 3, a, b, c, d) + n % 3 * d + b,
            self.solve((n + 2) / 3, a, b, c, d) + (3 - n % 3) % 3 * d + b,
            self.solve(n / 5, a, b, c, d) + n % 5 * d + c,
            self.solve((n + 4) / 5, a, b, c, d) + (5 - n % 5) % 5 * d + c,
        ]
        .iter()
        .min()
        .unwrap();
        self.memo.insert(n, ans);
        return ans;
    }
}

fn main() {
    input! {
        t: usize,
        case: [(u64, u64, u64, u64, u64);t]
    }

    for (n, a, b, c, d) in case {
        println!(
            "{}",
            global {
                memo: HashMap::new()
            }
            .solve(n, a, b, c, d)
        );
    }
}

#[macro_export(local_inner_maccros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let mut s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

#[macro_export(lcal_inner_macros)]
macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

#[macro_export(lcal_inner_macros)]
macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}