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 proconio::marker::*;

#[fastout]
fn main() {
   input! {
      t: usize,
      nabcd: [(usize, usize, usize, usize, usize); t]
   }

   for (n, a, b, c, d) in nabcd {
      let mut m = std::collections::BTreeMap::new();
      m.insert(0, 0);
      m.insert(1, d);
      let ans = f(n, a, b, c, d, &mut m);
      println!("{}", ans);
   }
}

use std::cmp::min;
macro_rules !min {($a :expr $(,) *) =>{{$a } } ;($a :expr ,$b :expr $(,) *) =>{{std ::cmp ::min ($a ,$b ) } } ;($a :expr ,$($rest :expr ) ,+$(,) *) =>{{std ::cmp ::min ($a ,min !($($rest ) ,+) ) } } ;}

fn f(
   x: usize,
   a: usize,
   b: usize,
   c: usize,
   d: usize,
   m: &mut std::collections::BTreeMap<usize, usize>,
) -> usize {
   if let Some(&y) = m.get(&x) {
      y
   } else {
      let two = match x % 2 {
         0 => f(x / 2, a, b, c, d, m),
         _ => d + min(f(x / 2, a, b, c, d, m), f(x / 2 + 1, a, b, c, d, m)),
      } + a;
      let three = match x % 3 {
         0 => b + f(x / 3, a, b, c, d, m),
         i => min(
            i * d + f(x / 3, a, b, c, d, m) + if x / 3 == 0 { 0 } else { b },
            (3 - i) * d + f(x / 3 + 1, a, b, c, d, m) + b,
         ),
      };
      let five = match x % 5 {
         0 => c + f(x / 5, a, b, c, d, m),
         i => min(
            i * d + f(x / 5, a, b, c, d, m) + if x / 5 == 0 { 0 } else { c },
            (5 - i) * d + f(x / 5 + 1, a, b, c, d, m) + c,
         ),
      };
      let mut y = min!{two, three, five};
      if x <= y/d {
         y = min(y, d*x);
      }
      m.insert(x, y);
      y
   }
}