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 33 1 2

output

1

input

4 7 23 3 2 4

output

2

input

5 5 11 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.

解題說明：此題是把m個裝置藉助導線和過濾器（類似於接線板）通上電，這裡導線有k根，過濾器有n個，每個上面插孔數目都不一樣，問最少要用多少個過濾器。顯然，如果導線數目足夠的話，我們一個裝置分配一根導線，這樣不需要過濾器，但是導線數目不夠時，我們要先把導線接到過濾器上，然後把裝置通過過濾器接上電，這樣一個過濾器可以同時給多個裝置供電。求解過程為首先判斷導線和裝置的數目，在導線不夠時對過濾器進行排序，每次選擇介面最多的過濾器，然後再判斷裝置和導線的情況，直到所有裝置都通上電，或是過濾器全部用完。

#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;}