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 C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder2 {
	class Program {
		static void Main(string[] args) {

	var inputArray = retreiveLongArray();
			var inputCount = 1;

			// 不正な入力は処理しない
			if (inputArray.Length != inputCount) {
				Console.WriteLine("invalid input");
				return;
			}
			long T = inputArray[0];
			var ans = new List<long>();
			for (int i = 0; i < T; i++) {
				var s = Solve();
				ans.Add(s);
			}
			foreach (var item in ans) {
				Console.WriteLine(item);
			}
		}

		/// <summary>
		/// 1つのテストケースについて説く
		/// </summary>
		private static long Solve() {
			var input = retreiveLongArray();
			long N = input[0];
			two = input[1];
			three = input[2];
			five = input[3];
			plusOne = input[4];

			var minCost = long.MaxValue;
			_memoDic = new Dictionary<long, long>();
			//メモ付きDFSで解く
			minCost = DFS(N);
			return minCost;

		}

		private static long DFS(long n) {

			if (n == 1) {
				return plusOne;
			}
			if (n==0) {
				return 0;
			}

			if (_memoDic.ContainsKey(n)) {
				return _memoDic[n];
			}

			var cost2 = subDFS(n, two,2);
			var cost3 = subDFS(n, three, 3);
			var cost5 = subDFS(n, five, 5);

			var cost = Math.Min(Math.Min(cost2, cost3),cost5);
			_memoDic.Add(n, cost);
			return cost;

		}

		private static long subDFS(long n, long shoricost,long divide) {

			checked {
				//divideで割る場合
				var amari = n % divide;
				if (amari == 0) {
					var normal = DFS(n / divide) + shoricost;
					var Jimichi = long.MaxValue;
					if (n-n/divide < shoricost / plusOne + 1) {//オーバーフロー対策である程度まともな時しか計算しない
						Jimichi = DFS(n / divide) + (n - n / divide) * plusOne;
					}
					return Math.Min(normal, Jimichi);

				}
				else {
					var Normal =  shoricost + plusOne * amari;
					
					var costfloor = subDFS(n - amari,shoricost,divide) + plusOne * amari; 

					var costsail = subDFS(n + divide - amari, shoricost, divide) + plusOne * (divide - amari);

					return Math.Min(costfloor, costsail);
				}
			}

		}

		//計算用メモ
		private static Dictionary<long, long> _memoDic;
		//必要コイン
		private static long two;
		private static long three ;
		private static long five ;
		private static long plusOne ;

		/// <summary>
		/// スペースで区切られた文字列配列の入力を受け取る
		/// </summary>
		/// <returns></returns>
		private static string[] retreiveStringArray() {
			var inputArray = Console.ReadLine().Split(' ');
			return inputArray;
		}

		/// <summary>
		/// スペースで区切られた整数配列の入力を受け取る
		/// </summary>
		/// <returns></returns>
		private static long[] retreiveLongArray() {
			var inputArray = Console.ReadLine().Split(' ');
			var longArray = inputArray.Select(s => long.Parse(s));
			return longArray.ToArray();
		}
	}
}