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)

#![allow(unused_imports)]
#![allow(non_snake_case)]
use std::cmp::*;
use std::collections::*;
use std::io::Write;

#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}

fn solve(n: i128, a: i128, b: i128, c: i128, d: i128, mem: &mut HashMap<i128, i128>) -> i128 {
    if mem.contains_key(&n) {
        return mem[&n];
    }

    let mut res = n * d;
    res = min(
        res,
        solve((n + 4) / 5, a, b, c, d, mem) + c + (5 - (n % 5)) * d,
    );
    res = min(
        res,
        solve((n + 2) / 3, a, b, c, d, mem) + b + (3 - (n % 3)) * d,
    );
    res = min(
        res,
        solve((n + 1) / 2, a, b, c, d, mem) + a + (2 - (n % 2)) * d,
    );
    if n >= 5 {
        res = min(res, solve(n / 5, a, b, c, d, mem) + c + (n % 5) * d);
    }
    if n >= 3 {
        res = min(res, solve(n / 3, a, b, c, d, mem) + b + (n % 3) * d);
    }
    if n >= 2 {
        res = min(res, solve(n / 2, a, b, c, d, mem) + a + (n % 2) * d);
    }
    mem.insert(n, res);
    mem[&n]
}

fn main() {
    let t = read::<i128>();
    for _ in 0..t {
        let v = read_vec::<i128>();
        let (n, a, b, c, d) = (v[0], v[1], v[2], v[3], v[4]);
        let mut mem = HashMap::new();
        mem.insert(0, 0);
        mem.insert(1, d);
        let ans = solve(n, a, b, c, d, &mut mem);
        println!("{}", ans);
    }
}

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}