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::cmp::min;
use std::io::{stdin, Read};

#[allow(unused_macros)]
macro_rules! parse {
    ($it: ident ) => {};
    ($it: ident, ) => {};
    ($it: ident, $var:ident : $t:tt $($r:tt)*) => {
        let $var = parse_val!($it, $t);
        parse!($it $($r)*);
    };
    ($it: ident, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = parse_val!($it, $t);
        parse!($it $($r)*);
    };
}

#[allow(unused_macros)]
macro_rules! parse_val {
    ($it: ident, [$t:tt; $len:expr]) => {
        (0..$len).map(|_| parse_val!($it, $t)).collect::<Vec<_>>();
    };
    ($it: ident, ($($t: ty),*)) => {
        ($(parse_val!($it, $t)),*)
    };
    ($it: ident, $t: ty) => {
        $it.next().unwrap().parse::<$t>().unwrap()
    };
}

fn solve(s: &str) {
    let mut it = s.split_whitespace();
    parse!(it, t: usize);
    for _ in 0..t {
        parse!(it, n: usize, a: usize, b: usize, c: usize, d: usize);
        let mut q = std::collections::VecDeque::new();
        q.push_back((n, 0));
        let mut ret = std::usize::MAX;
        let mut seen = std::collections::HashMap::new();
        seen.insert(n, 0);
        if n == 1 {
            ret = d;
        }
        while let Some((x, s)) = q.pop_front() {
            let (p, flag0) = d.overflowing_mul(x);
            let (p, flag1) = p.overflowing_add(s);
            if !(flag0 || flag1) {
                ret = min(ret, p);
            };
            if x == 1 || x == 0 {
                if x == 0 {
                    ret = min(ret, s);
                }
                continue;
            }

            let y = match x % 2 {
                0 => (x / 2, s + a),
                1 => ((x - 1) / 2, s + a + d),
                _ => unreachable!(),
            };
            if let Some(v) = seen.get(&y.0) {
                if *v > y.1 {
                    seen.insert(y.0, y.1);
                    q.push_back(y);
                }
            } else {
                seen.insert(y.0, y.1);
                q.push_back(y);
            }

            if x % 2 == 1 {
                let y = ((x + 1) / 2, s + a + d);
                if let Some(v) = seen.get(&y.0) {
                    if *v > y.1 {
                        seen.insert(y.0, y.1);
                        q.push_back(y);
                    }
                } else {
                    seen.insert(y.0, y.1);
                    q.push_back(y);
                }
            }

            let y = match x % 3 {
                0 => (x / 3, s + b),
                1 => ((x - 1) / 3, s + b + d),
                2 => ((x + 1) / 3, s + b + d),
                _ => unreachable!(),
            };
            if let Some(v) = seen.get(&y.0) {
                if *v > y.1 {
                    seen.insert(y.0, y.1);
                    q.push_back(y);
                }
            } else {
                seen.insert(y.0, y.1);
                q.push_back(y);
            }
            let y = match x % 5 {
                0 => (x / 5, s + c),
                1 => ((x - 1) / 5, s + c + d),
                2 => ((x - 2) / 5, s + c + 2 * d),
                3 => ((x + 2) / 5, s + c + 2 * d),
                4 => ((x + 1) / 5, s + c + d),
                _ => unreachable!(),
            };
            if let Some(v) = seen.get(&y.0) {
                if *v > y.1 {
                    seen.insert(y.0, y.1);
                    q.push_back(y);
                }
            } else {
                seen.insert(y.0, y.1);
                q.push_back(y);
            }
        }
        println!("{}", ret);
    }
}

fn main() {
    let mut s = String::new();
    stdin().read_to_string(&mut s).unwrap();
    solve(&s);
}

#[cfg(test)]
mod tests {
    use super::*;
    #[test]
    fn test_input() {
        let s = "
        ";
        solve(s);
    }
}