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 aisockets.

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 integers a1, 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.

 

水题，每加一个拖线板要占掉一个插头，把拖线板的插头书都减一，再排序就可以了。

 

附代码：

 1 #include<iostream>
 2 #include<cstdlib>
 3 using namespace std;
 4 int cmp( const void *a, const void *b)
 5 {
 6     return *(int*) b-*(int*)a;
 7 }
 8 
 9 int arr[50]={0};
10 
11 int main(void)
12 {
13     int n, m, k, ans=0, sum=0;
14     int i;
15 
16     cin>>n>>m>>k;
17     for( i=0; i<n; i++)
18     {
19         cin>>arr[i];
20     }
21     qsort( arr, n, sizeof( int), cmp);
22     sum+=k;
23     i=0;
24     while( sum<m)
25     {
26         if( i==n)
27         {
28             ans=-1;
29             break;
30         }
31         sum+=arr[i];
32         sum-=1;
33         i++;
34         ans++;
35     }
36     cout<<ans<<endl;
37 
38     return 0;
39 }