【CF Edu 28 B. Math Show】

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Polycarp takes part in a math show. He is given n tasks, each consists of k subtasks, numbered 1 through k. It takes him t_j minutes to solve the j-th subtask of any task. Thus, time required to solve a subtask depends only on its index, but not on the task itself. Polycarp can solve subtasks in any order.

By solving subtask of arbitrary problem he earns one point. Thus, the number of points for task is equal to the number of solved subtasks in it. Moreover, if Polycarp completely solves the task (solves all k of its subtasks), he recieves one extra point. Thus, total number of points he recieves for the complete solution of the task is k + 1.

Polycarp has M minutes of time. What is the maximum number of points he can earn?

Input

The first line contains three integer numbers n, k and M (1 ≤ n ≤ 45, 1 ≤ k ≤ 45, 0 ≤ M ≤ 2·10⁹).

The second line contains k integer numbers, values t_j (1 ≤ t_j ≤ 1000000), where t_j is the time in minutes required to solve j-th subtask of any task.

Output

Print the maximum amount of points Polycarp can earn in M minutes.

Examples

input

3 4 11
1 2 3 4

output

6

input

5 5 10
1 2 4 8 16

output

7

Note

In the first example Polycarp can complete the first task and spend 1 + 2 + 3 + 4 = 10 minutes. He also has the time to solve one subtask of the second task in one minute.

In the second example Polycarp can solve the first subtask of all five tasks and spend 5·1 = 5 minutes. Also he can solve the second subtasks of two tasks and spend 2·2 = 4 minutes. Thus, he earns 5 + 2 = 7 points in total.

【翻译】有n个一样的套题，每套题包含k个题，每个题的解决时间ai可能不同(输入)。做一道题得到1分，做完一套题另外加一分，询问m时间内最多得到多少分。

题解：

     ①直接贪心写很麻烦，但是观察到对于一套题只有两种状态：做完,没做完。

     ②由于每套题是完全相同的，所以暴力枚举做完了的套题数，剩下的没做完就排序贪心完成。

#include<stdio.h>
#define S(x,y) (x^=y^=x^=y)
#define go(i,a,b) for(int i=a;i<=b;i++)
int n,k,a[50];long long Time,sum,Score,ans,m;
int main()
{
	scanf("%d%d%d",&n,&k,&m);
	go(i,1,k)scanf("%d",a+i),sum+=a[i];
	go(i,1,k)go(j,i,k)if(a[i]>a[j])S(a[i],a[j]);

	go(i,0,n){Score=(k+1)*i;if((Time=sum*i)>m)break;
	go(j,1,k)Time+(n-i)*a[j]>=m?Score+=(m-Time)/a[j],j=k:(Time+=(n-i)*a[j],Score+=n-i);
		Score>ans?ans=Score:1;}printf("%I64d\n",ans);return 0;
}//Paul_Guderian

天空升起紫色的烟花,眼前是一片辉煌

我迎着风向前狂奔,这速度远不能抛开忧伤。————汪峰《十二月的泪》