Sockets

题意翻译

Vasya 有 $m$ 个电器需要用电， 他有 $n$ 个插线板， 第 $i$ 个插线板有 $a_i$ 个插口， 每个插口可以插入另一个插线板或一个电器 他的公寓一共有 $k$ 个插座， 每个插座可以插入一个插线板或一个电器， 求他最少需要多少个插线板， 才可以让所有电器都通电。 若无论如何都无法让所有电器通电， 就输出 $-1$ 。

题目描述

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.

输入输出格式

输入格式

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.

输出格式

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.

输入输出样例

输入样例 #1

3 5 3
3 1 2

输出样例 #1

1

输入样例 #2

4 7 2
3 3 2 4

输出样例 #2

2

输入样例 #3

5 5 1
1 3 1 2 1

输出样例 #3

-1

说明

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.