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: Wrong Answer)

using System;
using System.Collections.Generic;
using static Assistant.Input;
using static Assistant.Debug;
using System.Linq;
using Assistant;

namespace AGC044A_2
{
    class Program
    {
        static void Main(string[] args)
        {
            var T = RInt;

            for (int i = 0; i < T; i++)
            {
                var N = RLong;
                A = RLong;
                B = RLong;
                C = RLong;
                D = RLong;
                memo = new Dictionary<long, long>();

                long ans = DFS(N);
                Console.WriteLine(ans);
            }

        }

        static long A;
        static long B;
        static long C;
        static long D;
        static Dictionary<long, long> memo;
        static long DFS(long N)
        {
            if (N == 1) return D;
            if (N == 0) return 0;
            if (memo.ContainsKey(N)) return memo[N];

            long cand = long.MaxValue;
            if (N % 2 == 0) cand = Math.Min(cand, DFS(N / 2) + A);
            else if (N % 2 == 1)
            {
                cand = Math.Min(cand, DFS((N + 1) / 2) + D + A);
                cand = Math.Min(cand, DFS((N - 1) / 2) + D + A);
            }

            if (N % 3 == 0) cand = Math.Min(cand, DFS(N / 3) + B);
            else
            {
                long k = N % 3;
                cand = Math.Min(cand, DFS((N - k) / 3) + k * D + B);
                cand = Math.Min(cand, DFS((N + 3 - k) / 3) + (3 - k) * D + B);
            }

            if (N % 5 == 0) cand = Math.Min(cand, DFS(N / 5) + C);
            else
            {
                long k = N % 5;
                cand = Math.Min(cand, DFS((N - k) / 5) + k * D + C);
                cand = Math.Min(cand, DFS((N + 5 - k) / 5) + (5 - k) * D + C);
            }
            if (N <= 1000000000) cand = Math.Min(cand, N * D);

            memo.Add(N, cand);
            return cand;
        }
    }


}

namespace Assistant
{
    static class Input
    {
        static List<string> line = new List<string>();
        static int index = 0;
        static String RNext()
        {
            if (line.Count <= index) line.AddRange(Console.ReadLine().Split());
            return line[index++];
        }
        public static int RInt => int.Parse(RNext());
        public static long RLong => long.Parse(RNext());
        public static int[] RInts => Console.ReadLine().Split().Select(int.Parse).ToArray();
        public static long[] RLongs => Console.ReadLine().Split().Select(long.Parse).ToArray();
        public static string RString => RNext();
        //以下未テスト
        public static int[] RIntsC(int c) => Enumerable.Repeat(0, c).Select(x => int.Parse(RNext())).ToArray();
        public static long[] RLongsC(int c) => Enumerable.Repeat(0, c).Select(x => long.Parse(RNext())).ToArray();
        public static char[][] RMap(int h) => Enumerable.Repeat(0, h).Select(x => Console.ReadLine().ToCharArray()).ToArray();
    }

    public struct Mlong
    {
        long _v;
        const long mod = 1000000007;
        public Mlong(long n = 0) : this() { _v = n >= mod ? n % mod : n; }

        public static implicit operator Mlong(long _x) => new Mlong(_x);
        public static implicit operator long(Mlong _x) => _x._v;
        public static Mlong operator +(Mlong m1, Mlong m2) { long m = m1._v + m2._v; return m >= mod ? m - mod : m; }
        public static Mlong operator -(Mlong m1, Mlong m2) { long m = m1._v - m2._v; return m >= 0 ? m : m + mod; }
        public static Mlong operator *(Mlong m1, Mlong m2) => m1._v * m2._v % mod;
        public static Mlong operator /(Mlong m1, Mlong m2) => m1._v * ModPow(m2._v, mod - 2) % mod;

        public static long ModPow(long a, long n)
        {
            if (n == 0) return 1;
            else if (n % 2 == 1) return a * ModPow(a, n - 1) % mod;
            else return ModPow(a * a % mod, n / 2);
        }

        static Mlong[] fac, finv, inv;
        public static void nCkInit(int max)
        {
            fac = new Mlong[max]; finv = new Mlong[max]; inv = new Mlong[max];
            fac[0] = fac[1] = 1;
            finv[0] = finv[1] = 1;
            inv[1] = 1;
            for (int i = 2; i < max; i++)
            {
                fac[i] = fac[i - 1] * i;
                inv[i] = mod - inv[mod % i] * (mod / i);
                finv[i] = finv[i - 1] * inv[i];
            }
        }

        public static Mlong nCk(int n, int k)
        {
            if (n < k) return 0;
            if (n < 0 || k < 0) return 0;
            return fac[n] * finv[k] * finv[n - k];
        }
    }

    static class Debug
    {
        static public void Draw2D<T>(T[,] map, int mode = 1)
        {
#if DEBUG
            int W = map.GetLength(0);
            int H = map.GetLength(1);

            string[,] map2 = new string[W + 1, H + 1];
            for (int i = 0; i < W + 1; i++)
            {
                for (int j = 0; j < H + 1; j++)
                {
                    if (i == 0 && j == 0) map2[i, j] = 0.ToString();
                    else if (i == 0) map2[i, j] = (j - 1).ToString();
                    else if (j == 0) map2[i, j] = (i - 1).ToString();
                    else map2[i, j] = map[i - 1, j - 1].ToString();
                }
            }

            for (int i = 0; i < W + 1; i++)
            {
                for (int j = 0; j < H + 1; j++)
                {
                    if (mode == 0) Console.Write(map2[i, j].Last());
                    if (mode == 1) Console.Write(map2[i, j] + " ");
                }
                Console.WriteLine();
            }
            Console.WriteLine();
#endif
        }

        public static void Draw1D<T>(T[] array, int mode = 0)
        {
#if DEBUG
            Console.WriteLine(string.Join(" ", array));
#endif
        }
    }
}