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::io;
use std::str::FromStr;
use std::collections::HashMap;
use std::cmp::min;


static INF: u128 = 1_000_000_000_000;

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

fn input_tuple() -> (u128, u128, u128, u128, u128) {
    let mut line: String = String::new();
    io::stdin().read_line(&mut line);
    let vec: Vec<u128> = line.split_whitespace().map(|s| s.parse().unwrap()).collect();
    (vec[0], vec[1], vec[2], vec[3], vec[4])
}

fn dfs(i: u128, a: u128, b: u128, c: u128, d:u128, memo: &mut HashMap<u128, u128>) -> u128 {
    if i == 1 {
        return d;
    }
    if i == 0 {
        return 0;
    }
    if memo.contains_key(&i) {
        return *memo.get(&i).unwrap();
    }

    let mut min_count = INF;
    if i % 2 == 0 {
        let tmp: u128;
        if a / d <= i / 2 {
            tmp = dfs(i / 2, a, b, c, d, memo) + min(a, i / 2 * d);
        } else {
            tmp = dfs(i / 2, a, b, c, d, memo) + a;
        }
        min_count = min(tmp, min_count);
    } else {
        let tmp = dfs((i + 1) / 2, a, b, c, d, memo) + min(a, (i + 1) / 2 * d) + d;
        min_count = min(tmp, min_count);
        let tmp = dfs((i - 1) / 2, a, b, c, d, memo) + min(a, (i - 1) / 2 * d) + d;
        min_count = min(tmp, min_count);
    }

    if i % 3 == 0 {
        let tmp = dfs(i / 3, a, b, c, d, memo) + min(b, 2 * i / 3 * d);
        min_count = min(tmp, min_count);
    } else if i % 3 == 1 {
        let tmp = dfs((i - 1) / 3, a, b, c, d, memo) + min(b, 2 * (i - 1) / 3 * d) + d;
        min_count = min(tmp, min_count);
        let tmp = dfs((i + 2) / 3, a, b, c, d, memo) + min(b, 2 * (i + 2) / 3 * d) + d * 2;
        min_count = min(tmp, min_count);
    } else {
        let tmp = dfs((i - 2) / 3, a, b, c, d, memo) + min(b, 2 * (i - 2) / 3 * d) + d * 2;
        min_count = min(tmp, min_count);
        let tmp = dfs((i + 1) / 3, a, b, c, d, memo) + min(b, 2 * (i + 1) / 3 * d) + d;
        min_count = min(tmp, min_count);
    }
    
    if i % 5 == 0 {
        let tmp = dfs(i / 5, a, b, c, d, memo) + min(c, 4 * i / 5 * d);
        min_count = min(tmp, min_count);
    } else if i % 5 == 1 {
        let tmp = dfs((i - 1) / 5, a, b, c, d, memo) + min(c, 4 * (i - 1) / 5 * d) + d;
        min_count = min(tmp, min_count);
        let tmp = dfs((i + 4) / 5, a, b, c, d, memo) + min(c, 4 * (i + 4) / 5 * d) + d * 4;
        min_count = min(tmp, min_count);
    } else if i % 5 == 2 {
        let tmp = dfs((i - 2) / 5, a, b, c, d, memo) + min(c, 4 * (i - 2) / 5 * d) + d * 2;
        min_count = min(tmp, min_count);
        let tmp = dfs((i + 3) / 5, a, b, c, d, memo) + min(c, 4 * (i + 3) / 5 * d) + d * 3;
        min_count = min(tmp, min_count);
    } else if i % 5 == 3 {
        let tmp = dfs((i - 3) / 5, a, b, c, d, memo) + min(c, 4 * (i - 3) / 5 * d) + d * 3;
        min_count = min(tmp, min_count);
        let tmp = dfs((i + 2) / 5, a, b, c, d, memo) + min(c, 4 * (i + 2) / 5 * d) + d * 2;
        min_count = min(tmp, min_count);
    } else {
        let tmp = dfs((i - 4) / 5, a, b, c, d, memo) + min(c, 4 * (i - 4) / 5 * d) + d * 4;
        min_count = min(tmp, min_count);
        let tmp = dfs((i + 1) / 5, a, b, c, d, memo) + min(c, 4 * (i + 1) / 5 * d) + d;
        min_count = min(tmp, min_count);
    }
    memo.insert(i, min_count);

    min_count
}

fn main() {
    let t: usize = input();
    for _ in 0..t {
        let (n, a, b, c, d) = input_tuple();
        let mut memo: HashMap<u128, u128> = HashMap::new();
        println!("{}", dfs(n, a, b, c, d, &mut memo));
    }
}