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)]
// Thanks to @hamadu for referring to code
use proconio::{input, fastout};
use proconio::marker::*;
use nalgebra::min;
use std::collections::HashMap;

fn dfs(r: usize, a: usize, b: usize, c: usize, d: usize, m: &mut HashMap<usize, usize>) -> usize {
    let mut res = if let Some(k) = r.checked_mul(d){ k } else { std::usize::MAX };
    if r == 0 { return 0; }
    if r == 1 { return d; }
    if m.contains_key(&r) {
        return *m.get(&r).unwrap();
    }
    res = min(res, dfs(r / 2, a, b, c, d, m) + a + d * (r % 2));
    res = min(res, dfs((r + 1) / 2, a, b, c, d, m) + a + d * (r % 2));
    res = min(res, dfs(r / 3, a, b, c, d, m) + b + d * (r % 3));
    res = min(res, dfs((r + 2) / 3, a, b, c, d, m) + b + d * (3 - r % 3));
    res = min(res, dfs(r / 5, a, b, c, d, m) + c + d * (r % 5));
    res = min(res, dfs((r + 4) / 5, a, b, c, d, m) + c + d * (5 - r % 5));
    m.insert(r, res);
    res
}

#[fastout]
fn main() {
    input! {
    t: usize,
    nabcds: [[usize; 5]; t]
    }
    for nabcd in nabcds {
        let mut m = HashMap::new();
        let (r, a, b, c, d) = (nabcd[0], nabcd[1], nabcd[2], nabcd[3], nabcd[4]);
        let ans = dfs(r, a, b, c, d, &mut m);
        println!("{}", ans);
    }
}