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 proconio::{fastout, input};
use std::cmp::Ordering;
use std::collections::{BinaryHeap, HashSet};

#[derive(Debug, Eq, PartialEq)]
struct Query {
    num: u64,
    cost: 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() {
    input! {n:u64, a:u64, b:u64, c:u64, d:u64};
    let mut queue = BinaryHeap::new();
    let mut seens = HashSet::new();
    let threshold = 1e+20 as u64 / d;

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

    while !queue.is_empty() {
        let query = queue.pop().unwrap();

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

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

        seens.insert(query.num);

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

        for [k, p] in [[2, a], [3, b], [5, c]].iter() {
            if query.num < *k {
                continue;
            }

            let dval = query.num / *k;
            let mval = query.num % *k;

            if mval == 0 {
                queue.push(Query {
                    num: dval,
                    cost: query.cost + p,
                });
            } else {
                queue.push(Query {
                    num: dval,
                    cost: query.cost + p + d * mval,
                });
                queue.push(Query {
                    num: dval + 1,
                    cost: query.cost + p + d * (*k - mval),
                });
            }
        }
    }

    panic!("not finished");
}

#[fastout]
fn main() {
    input! {t: usize};

    for _ in 0..t {
        solve();
    }
}