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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <cassert>
#include <cmath>
#include <algorithm>
#include <iostream>
#include <iomanip>
#include <limits.h>
#include <map>
#include <queue>
#include <set>
#include <string.h>
#include <vector>

using namespace std;
typedef long long ll;

struct Node {
  ll n;
  ll cost;

  Node(ll n = -1, ll cost = -1) {
    this->n = n;
    this->cost = cost;
  }

  bool operator>(const Node &n) const {
    return cost > n.cost;
  }
};

int main() {
  ll N, T, A, B, C, D;

  cin >> T;

  for (int i = 0; i < T; ++i) {
    cin >> N >> A >> B >> C >> D;
    priority_queue <Node, vector<Node>, greater<Node>> pque;

    pque.push(Node(N, 0));
    map<ll, bool> memo;

    while (!pque.empty()) {
      Node node = pque.top();
      pque.pop();

      assert(node.n <= N);

      if (memo[node.n]) continue;
      memo[node.n] = true;

      if (node.n == 1) {
        cout << node.cost + D << endl;
        break;
      }

      if (node.n % 2 == 0) {
        ll diff = node.n - node.n / 2;

        if (A / (double) diff > D) {
          pque.push(Node(node.n / 2, node.cost + diff * D));
        } else {
          pque.push(Node(node.n / 2, node.cost + A));
        }
      } else {
        ll d1 = node.n - (node.n - 1) / 2;

        if (A / (double) d1 > D) {
          pque.push(Node((node.n - 1) / 2, node.cost + d1 * D));
        } else {
          pque.push(Node((node.n - 1) / 2, node.cost + A + D));
        }

        ll d2 = node.n - (node.n + 1) / 2;

        if (A / (double) d2 > D) {
          pque.push(Node((node.n + 1) / 2, node.cost + d2 * D));
        } else {
          pque.push(Node((node.n + 1) / 2, node.cost + A + D));
        }
      }

      if (node.n % 3 == 0) {
        ll diff = node.n - node.n / 3;

        if (B / (double) diff > D) {
          pque.push(Node(node.n / 3, node.cost + diff * D));
        } else {
          pque.push(Node(node.n / 3, node.cost + B));
        }
      } else {
        ll s1 = node.n - 3 * floor(node.n / 3.0);
        ll d1 = node.n - (node.n - s1) / 3;

        if (node.n - s1 >= 3) {
          if (B / (double) d1 > D) {
            pque.push(Node((node.n - s1) / 3, node.cost + d1 * D));
          } else {
            pque.push(Node((node.n - s1) / 3, node.cost + B + s1 * D));
          }
        }

        ll s2 = 3 * ceil(node.n / 3.0) - node.n;
        ll d2 = node.n - (node.n + s2) / 3;

        if (B / (double) d2 > D) {
          pque.push(Node((node.n + s2) / 3, node.cost + d2 * D));
        } else {
          pque.push(Node((node.n + s2) / 3, node.cost + B + s2 * D));
        }
      }

      if (node.n % 5 == 0) {
        ll diff = node.n - node.n / 5;

        if (C / (double) diff > D) {
          pque.push(Node(node.n / 5, node.cost + diff * D));
        } else {
          pque.push(Node(node.n / 5, node.cost + C));
        }
      } else {
        ll s1 = node.n - 5 * floor(node.n / 5.0);
        ll d1 = node.n - (node.n - s1) / 5;

        if (node.n - s1 >= 5) {
          if (C / (double) d1 > D) {
            pque.push(Node((node.n - s1) / 5, node.cost + d1 * D));
          } else {
            pque.push(Node((node.n - s1) / 5, node.cost + C + s1 * D));
          }
        }

        ll s2 = 5 * ceil(node.n / 5.0) - node.n;
        ll d2 = node.n - (node.n + s2) / 5;

        if (C / (double) d2 > D) {
          pque.push(Node((node.n + s2) / 5, node.cost + d2 * D));
        } else {
          pque.push(Node((node.n + s2) / 5, node.cost + C + s2 * D));
        }
      }
    }
  }

  return 0;
}