A. Sockets

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Vasya has got many devices that work on electricity. He's got n supply-line filters to plug the devices, the i-th supply-line filter has ai sockets.

Overall Vasya has got m devices and k electrical sockets in his flat, he can plug the devices or supply-line filters directly. Of course, he can plug the supply-line filter to any other supply-line filter. The device (or the supply-line filter) is considered plugged to electricity if it is either plugged to one of k electrical sockets, or if it is plugged to some supply-line filter that is in turn plugged to electricity.

What minimum number of supply-line filters from the given set will Vasya need to plug all the devices he has to electricity? Note that all devices and supply-line filters take one socket for plugging and that he can use one socket to plug either one device or one supply-line filter.

Input

The first line contains three integers n, m, k (1 ≤ n, m, k ≤ 50) — the number of supply-line filters, the number of devices and the number of sockets that he can plug to directly, correspondingly. The second line contains n space-separated integersa1, a2, ..., an (1 ≤ ai ≤ 50) — number ai stands for the number of sockets on the i-th supply-line filter.

Output

Print a single number — the minimum number of supply-line filters that is needed to plug all the devices to electricity. If it is impossible to plug all the devices even using all the supply-line filters, print -1.

Sample test(s)

input

3 5 3
3 1 2

output

1

input

4 7 2
3 3 2 4

output

2

input

5 5 1
1 3 1 2 1

output

-1

Note

In the first test case he can plug the first supply-line filter directly to electricity. After he plug it, he get 5 (3 on the supply-line filter and 2 remaining sockets for direct plugging) available sockets to plug. Thus, one filter is enough to plug 5 devices.

One of the optimal ways in the second test sample is to plug the second supply-line filter directly and plug the fourth supply-line filter to one of the sockets in the second supply-line filter. Thus, he gets exactly 7 sockets, available to plug: one to plug to the electricity directly, 2 on the second supply-line filter, 4 on the fourth supply-line filter. There's no way he can plug 7 devices if he use one supply-line filter.

解题说明：此题是把m个设备借助导线和过滤器（类似于接线板）通上电，这里导线有k根，过滤器有n个，每个上面插孔数目都不一样，问最少要用多少个过滤器。显然，如果导线数目足够的话，我们一个设备分配一根导线，这样不需要过滤器，但是导线数目不够时，我们要先把导线接到过滤器上，然后把设备通过过滤器接上电，这样一个过滤器可以同时给多个设备供电。求解过程为首先判断导线和设备的数目，在导线不够时对过滤器进行排序，每次选择接口最多的过滤器，然后再判断设备和导线的情况，直到所有设备都通上电，或是过滤器全部用完。

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <cstring>
#include <string>
#include <algorithm>
using namespace std;

int main()
{
	int n,m,k;
	int i,a[51];
	int count;
	scanf("%d %d %d",&n,&m,&k);
	for(i=0;i<n;i++)
	{
		scanf("%d",&a[i]);
	}
	sort(a,a+n);
	if(k>=m)
	{
		printf("0\n");
	}
	else
	{
		count=0;
		for(i=n-1;i>=0;i--)
		{
			m=m-a[i];
			k--;
			count++;
			if(k>=m)
			{
				printf("%d\n",count);
				break;
			}
		}
		if(i<0)
		{
			printf("-1\n");
		}
	}
	return 0;
}