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, Ordering};
use std::collections::{BinaryHeap, HashSet};

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_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

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

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")
    };
}

#[derive(Debug, PartialEq, Eq)]
struct Query {
    cost: u64,
    num: u64,
}

impl Ord for Query {
    fn cmp(&self, other: &Self) -> Ordering {
        self.cost.cmp(&other.cost).reverse()
    }
}

impl PartialOrd for Query {
    fn partial_cmp(&self, other: &Query) -> Option<Ordering> {
        Some(self.cmp(other))
    }
}

fn solve(v: Vec<u64>) {
    let (n, a, b, c, d) = (v[0], v[1], v[2], v[3], v[4]);
    let threshold = (1e+20 as u64) / d;

    let mut queue = BinaryHeap::new();
    let mut seens = HashSet::new();

    queue.push(Query { cost: 0, num: n });

    while !queue.is_empty() {
        let q: Query = queue.pop().unwrap();

        if q.num == 0 {
            println!("{}", q.cost);
            return;
        }

        if seens.contains(&q.num) {
            continue;
        }

        seens.insert(q.num);

        if q.num < threshold {
            queue.push(Query {
                num: 0,
                cost: q.cost + q.num * d,
            });
        }

        for [k, v] in [[2, a], [3, b], [5, c]].iter() {
            if q.num < *k {
                break;
            }

            let m = q.num % *k;
            let n = q.num / *k;

            if m == 0 {
                queue.push(Query {
                    num: n,
                    cost: q.cost + *v,
                });
            } else {
                queue.push(Query {
                    num: n,
                    cost: q.cost + *v + (d * m),
                });
                queue.push(Query {
                    num: n + 1,
                    cost: q.cost + *v + (d * (*k - m)),
                });
            }
        }
    }

    panic!("aaa");
}

fn main() {
    input! { n: u64, vs: [[u64; 5]; n] }

    for v in vs {
        solve(v);
    }
}