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,
   marker::{Bytes, Chars, Isize1, Usize1},
};

use std::collections::HashMap;

fn func(a: u128, b: u128, c: u128, d: u128, k: u128, memo: &mut HashMap<u128, u128>) -> u128 {
   if memo.contains_key(&k) {
      return memo[&k];
   }

   if k == 0 {
      return 0;
   }
   if k == 1 {
      return d;
   }

   let mut cost = k * d;

   cost = std::cmp::min(
      cost,
      (k - (k / 5) * 5) * d + c + func(a, b, c, d, k / 5, memo),
   );
   cost = std::cmp::min(
      cost,
      (k - (k / 3) * 3) * d + b + func(a, b, c, d, k / 3, memo),
   );
   cost = std::cmp::min(
      cost,
      (k - (k / 2) * 2) * d + a + func(a, b, c, d, k / 2, memo),
   );

   cost = std::cmp::min(
      cost,
      (((k + 5 - 1) / 5) * 5 - k) * d + c + func(a, b, c, d, (k + 5 - 1) / 5, memo),
   );
   cost = std::cmp::min(
      cost,
      (((k + 3 - 1) / 3) * 3 - k) * d + b + func(a, b, c, d, (k + 3 - 1) / 3, memo),
   );
   cost = std::cmp::min(
      cost,
      (((k + 2 - 1) / 2) * 2 - k) * d + a + func(a, b, c, d, (k + 2 - 1) / 2, memo),
   );

   memo.insert(k, cost);

   return cost;
}

#[fastout]
fn main() {
   input! {
      t:u128
   }
   for _ in 0..t {
      input! {
         n:u128,a:u128,b:u128,c:u128,d:u128
      }
      let mut memo = HashMap::new();
      let buf = std::cmp::min(d * n, func(a, b, c, d, n, &mut memo));
      println!("{}", buf);
   }
}