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::Reverse;
use std::collections::{BTreeMap, BinaryHeap};
const INF: i64 = 1 << 62;
fn main() {
    let (r, w) = (std::io::stdin(), std::io::stdout());
    let mut sc = IO::new(r.lock(), w.lock());
    let t: usize = sc.read();
    for _ in 0..t {
        let n: i64 = sc.read();
        let a: i64 = sc.read();
        let b: i64 = sc.read();
        let c: i64 = sc.read();
        let d: i64 = sc.read();
        println!("{}", solve(n, a, b, c, d));
    }
}

fn solve(n: i64, a: i64, b: i64, c: i64, d: i64) -> i64 {
    let mut dist = BTreeMap::new();
    dist.insert(n, 0);
    let mut heap = BinaryHeap::new();
    heap.push((Reverse(0), n));

    while let Some((Reverse(cost), x)) = heap.pop() {
        let mut candidates = vec![];

        let x1 = (x + 1) / 2 * 2;
        let next_cost = (x - x1).abs() * d + a;
        let next_x = (x + 1) / 2;
        candidates.push((next_x, next_cost));

        let x2 = x / 2 * 2;
        let next_cost = (x - x2).abs() * d + a;
        let next_x = x / 2;
        candidates.push((next_x, next_cost));

        let x1 = (x + 2) / 3 * 3;
        let next_cost = (x - x1).abs() * d + b;
        let next_x = x1 / 3;
        candidates.push((next_x, next_cost));

        let x1 = x / 3 * 3;
        let next_cost = (x - x1).abs() * d + b;
        let next_x = x1 / 3;
        candidates.push((next_x, next_cost));

        let x1 = (x + 4) / 5 * 5;
        let next_cost = (x - x1).abs() * d + c;
        let next_x = x1 / 5;
        candidates.push((next_x, next_cost));

        let x1 = x / 5 * 5;
        let next_cost = (x - x1).abs() * d + c;
        let next_x = x1 / 5;
        candidates.push((next_x, next_cost));
        for (next_x, next_cost) in candidates.into_iter() {
            if next_x == 0 {
                continue;
            }

            let cur = dist.entry(next_x).or_insert(INF);
            if *cur > next_cost + cost {
                *cur = next_cost + cost;
                heap.push((Reverse(next_cost + cost), next_x));
            }
        }

        if x < INF / d {
            let cur = dist.entry(0).or_insert(INF);
            if *cur > x * d + cost {
                *cur = x * d + cost;
            }
        }
    }

    dist[&0]
}

pub struct IO<R, W: std::io::Write>(R, std::io::BufWriter<W>);

impl<R: std::io::Read, W: std::io::Write> IO<R, W> {
    pub fn new(r: R, w: W) -> Self {
        Self(r, std::io::BufWriter::new(w))
    }
    pub fn write<S: ToString>(&mut self, s: S) {
        use std::io::Write;
        self.1.write(s.to_string().as_bytes()).unwrap();
    }
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .0
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n' || b == b'\r' || b == b'\t')
            .take_while(|&b| b != b' ' && b != b'\n' && b != b'\r' && b != b'\t')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}