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 <bits/stdc++.h>

using namespace std;

#define sz(c) (int)c.size()
#define	pb push_back

typedef long long ll;
typedef pair<ll, ll> state;
typedef pair<int,int> ii;
typedef pair<int,ii> iii;
typedef vector<int> vi;
typedef vector<ii> vii;

constexpr int MAX_N = 510;
constexpr ll INF = 8'000'000'000'000'000'000;
constexpr ll P = 9'982'443'53;
constexpr int SIGMA = 28;
constexpr double PI = 3.14159265359;
constexpr double toRad = PI/180.;

struct Edge {
	ll np, cost;

	bool operator<(const Edge & o)const{
		if(cost != o.cost){
			return cost < o.cost;
		}
		return np < o.np;
	}
};

ll N, D;
map<ll,ll> costs;
ll dijkstra(){
	set<Edge> q;
	set<ll> vis;
	q.insert(Edge({N,0}));
	while(q.size()){
		auto e = q.begin();
		if(e->np == 0) return e->cost;
		
		if(vis.find(e->np) != vis.end()) {
			q.erase(e); 
			continue;	
		}

		vis.insert(e->np);		

		if(D < INF / e->np){
			q.insert(Edge({
				0,
				e->cost + e->np*D
			}));
		}
		
		for(auto c : costs){
			ll r = e->np % c.first;
			q.insert(Edge({
				(e->np + r) / c.first,
				e->cost + c.second + r*D
			}));

			ll r2 = c.first - r;
			if(r2){
				q.insert(Edge({
					(e->np - r2) / c.first,
					e->cost + c.second + r2*D
				}));
			}
		}
		q.erase(e); 
	}
	return -1;
}

int main(){
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	int T;
	cin >> T;
	while(T--){
		cin >> N >> costs[2] >> costs[3] >> costs[5] >> D;
		cout << dijkstra() << "\n";
	}
	
	return 0;
}