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)]
use std::cmp::*;
use std::collections::*;
use itertools::Itertools;
use num::clamp;
use proconio::{input, marker::*, fastout};
use superslice::*;

#[fastout()]
fn main() {
    input! {
        t: usize
    }
    for _ in 0..t {
        input!(n: usize, abcd: (usize, usize, usize, usize));

        let mut memo = HashMap::new();
        println!("{}", rec(n, abcd, &mut memo));
    }
}

fn rec(n: usize, abcd: (usize, usize, usize, usize), memo: &mut HashMap<usize, usize>) -> usize {
    let (a, b, c, d) = abcd;
    if n == 0 {
        return 0;
    } else if n == 1 {
        return d;
    }
    if let Some(&res) = memo.get(&n) {
        return res;
    }

    let mut res = Vec::new();
    res.push(rec(n/2, abcd, memo) + d*(n - n/2*2) + a);
    res.push(rec((n+1)/2, abcd, memo) + d*((n+1)/2*2 - n) + a);
    res.push(rec(n/3, abcd, memo) + d*(n - n/3*3) + b);
    res.push(rec((n+2)/3, abcd, memo) + d*((n+2)/3*3 - n) + b);
    res.push(rec(n/5, abcd, memo) + d*(n - n/5*5) + c);
    res.push(rec((n+4)/5, abcd, memo) + d*((n+4)/5*5 - n) + c);
    res.push(n.saturating_mul(d));
    let res = res.into_iter().min().unwrap();
    memo.insert(n, res);
    res
}