CF257A.Sockets

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 $a_{i}$ 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.

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 $a_{1},a_{2},...,a_{n}$ ( $1<=a_{i}<=50$ ) — number $a_{i}$ stands for the number of sockets on the $i$ -th supply-line filter.

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.

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.