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 Python (3.8.2) (judge verdict: Time Limit Exceeded)

import sys
from math import ceil, floor, sqrt, sin, cos, pi, log
from itertools import accumulate, permutations, combinations
from fractions import gcd # 最大公約数
from collections import deque, Counter
from operator import itemgetter
from heapq import heappop,heappush
from copy import deepcopy
sys.setrecursionlimit(10**7)
def lcm(x, y): return ((x * y) // gcd(x, y)) # 最小公倍数
# list(map(int, input().split()))

t = int(input())
for _ in range(t):
    n, a, b, c, d = map(int, input().split())
    now = {2: min(a+d, d+d), 3: b+d, 5: c+d}
    mae = {2: min(a+d, d+d), 3: b+d, 5: c+d, 1: d}
    for z in [2, 3, 5]:
        x, y = 1, d
        while True:
            x *= z
            if x in mae:
                mae[x] = min(mae[x], y)
            else:
                mae[x] = y
            if x > n:break
    sep = min(d*n, floor(log(n, 2))*a+(n + 1 - 2**floor(log(n, 2)))*d, floor(log(n, 3))*b+(n + 1 - 3**floor(log(n, 3)))*d, floor(log(n, 5))*c+(n + 1 - 5**floor(log(n, 5)))*d)
    while True:
        if len(now) == 0: break
        dic = {}
        for k, v in now.items():
            if k == 0: continue
            if k == 1: continue
            if v >= sep: continue
            if k > n:
                sep = min(sep, v+d*abs(k - n))
                continue
            # a
            tugi = k * 2
            cost = v + a
            if tugi == n:
                sep = min(sep, cost)
            elif tugi in mae:
                if mae[tugi] > cost:
                    dic[tugi] = cost
                    mae[tugi] = cost
            else:
                dic[tugi] = cost
                mae[tugi] = cost
            # b
            tugi = k * 3
            cost = v + b
            if tugi == n:
                sep = min(sep, cost)
            elif tugi in mae:
                if mae[tugi] > cost:
                    dic[tugi] = cost
                    mae[tugi] = cost
            else:
                dic[tugi] = cost
                mae[tugi] = cost
            # c
            tugi = k * 5
            cost = v + c
            if tugi == n:
                sep = min(sep, cost)
            elif tugi in mae:
                if mae[tugi] > cost:
                    dic[tugi] = cost
                    mae[tugi] = cost
            else:
                dic[tugi] = cost
                mae[tugi] = cost
            # d
            tugi = k + 1
            cost = v + d
            if tugi == n:
                sep = min(sep, cost)
            elif tugi in mae:
                if mae[tugi] > cost:
                    dic[tugi] = cost
                    mae[tugi] = cost
            else:
                dic[tugi] = cost
                mae[tugi] = cost
            # e
            tugi = k - 1
            cost = v + d
            if tugi == n:
                sep = min(sep, cost)
            elif tugi in mae:
                if mae[tugi] > cost:
                    dic[tugi] = cost
                    mae[tugi] = cost
            else:
                dic[tugi] = cost
                mae[tugi] = cost
        now = deepcopy(dic)
    print(sep)