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::min;
use std::cmp::Reverse;
use std::collections::BTreeSet;
use std::collections::BinaryHeap;

#[fastout]
fn main() {
    input! {
        t: usize,
    }
    for _ in 0..t {
        input! {
            n: u128, a: u128, b: u128, c: u128, d: u128,
        }
        let mut que = BinaryHeap::new();
        que.push(Reverse((0, n)));
        let mut used = BTreeSet::new();
        while let Some(Reverse((z, m))) = que.pop() {
            if used.contains(&m) {
                continue;
            }
            if m == 0 {
                println!("{}", z);
                break;
            }
            if m == 1 {
                println!("{}", z + d);
                break;
            }
            if m % 2 == 0 {
                que.push(Reverse((z + a, m / 2)));
            } else {
                que.push(Reverse((z + min(a + d, (m - m / 2 - 1) * d), m / 2 + 1)));
                que.push(Reverse((z + min(a + d, (m - m / 2) * d), m / 2)));
            }
            if m % 3 == 0 {
                que.push(Reverse((z + min(b, (m - m / 3) * d), m / 3)));
            } else {
                que.push(Reverse((
                    z + min(b + d * (3 - m % 3), (m - m / 3 - 1) * d),
                    m / 3 + 1,
                )));
                que.push(Reverse((z + min(b + d * (m % 3), (m - m / 3) * d), m / 3)));
            }
            if m % 5 == 0 {
                que.push(Reverse((z + min(c, (m - m / 5) * d), m / 5)));
            } else {
                que.push(Reverse((
                    z + min(c + d * (5 - m % 5), (m - m / 5 - 1) * d),
                    m / 5 + 1,
                )));
                que.push(Reverse((z + min(c + d * (m % 5), (m - m / 5) * d), m / 5)));
            }
            used.insert(m);
        }
    }
}