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 JavaScript (Node.js 12.16.1) (judge verdict: Runtime Error)

function Main(input) {
	var str = input;
	str = str.split("\n");
	var t =[];
	var ans = 0;
	var n= Number((str[0].split(" ")[0]));
	for (var i = 1;i<str.length;i++){
		t[i-1] = str[i].split(" ");
		t[i-1] = t[i-1].map(Number);
		}
// 		console.log(t);
	var tlen = t.length;
	var cost =Array(tlen);
	for (var k = 0;k<tlen; k++){
		target = t[k];
		var nk = target[0];
		var ak = target[1];
		var bk = target[2];
		var ck = target[3];
		var dk = target[4];
		cost[k] = mod(nk,ak,bk,ck,dk);
		console.log(cost[k]);
	}
}
		function mod(n,a,b,c,d){
			var mod2 =0;
			var mod3 =0;
			var mod5 =0;
			var n2 = 0;
			var n3 = 0;
			var n5 = 0;
			var m = 0;	
			if(n%2===0){
					n = n/2;
					mod2++;
			}if(n%3===0){
					n = n/3;
					mod3++;	
			}if(n%5===0){
					n = n/5;
					mod5++;						
			}
			if(mod2===0&&mod3===0&&mod5===0){//われなかった
				return Math.min(mod(n+1,a,b,c,d),mod(n-1,a,b,c,d))+d;
			}else{//われた
				m += mod2*a+mod3*b+mod5*c;
				if(n===1){
					return m+d;
				}else{
					return (m+mod(n,a,b,c,d));
				}
			}
		}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));