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)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
#![allow(non_snake_case)]
#![allow(unused_variables)]

use competitive_hpp::prelude::*;

fn solve(N: i64, A: i64, B: i64, C: i64, D: i64) -> i64 {
    let mut cost_map = hashmap! { N => 0 };
    let mut heap = BinaryHeap::new();
    heap.push((Reverse(0i64), N));

    while let Some((Reverse(cost), n)) = heap.pop() {
        let mut candedates = vec![];
        let ABC = vec![0, 0, A, B, 0, C];

        for i in vec![2i64, 3i64, 5i64] {
            let ceil_i = n.div_ceil(&i) * i;
            let ceil_i_cost = (ceil_i - n).abs() * D + ABC[i as usize] + cost;
            candedates.push((ceil_i / i, ceil_i_cost));

            let floor_i = n.div_floor(&i) * i;
            let floor_i_cost = (floor_i - n).abs() * D + ABC[i as usize] + cost;
            candedates.push((floor_i / i, floor_i_cost));
        }

        for &(next_n, next_cost) in candedates.iter() {
            if next_n == 0 {
                continue;
            }

            let tmp = cost_map.entry(next_n).or_insert(std::i64::MAX);
            if *tmp > next_cost {
                *tmp = next_cost;
                heap.push((Reverse(next_cost), next_n));
            }
        }

        let ans = cost_map.entry(0).or_insert(std::i64::MAX);
        if n < std::i64::MAX / D {
            if *ans > n * D + cost {
                *ans = n * D + cost;
            }
        }
    }

    *cost_map.get(&0).unwrap()
}

#[fastout]
fn main() {
    input! {
        T: i64,
        NABCD: [(i64, i64, i64, i64, i64); T]
    }

    for (N, A, B, C, D) in NABCD {
        println!("{}", solve(N, A, B, C, D))
    }
}
*/

fn main() {
    let exe = "/tmp/bin242E3BE3";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";