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.

瓦西娅有许多需要用电的设备。他有 $n$ 个电源排插（供电线路滤波器）用于连接这些设备，其中第 $i$ 个电源排插有 $a_i$ 个插孔。

瓦西娅总共有 $m$ 个设备，以及房间内原有的 $k$ 个电源插座。他可以直接将设备或电源排插插入这 $k$ 个插座中。当然，他也可以将一个电源排插插入另一个电源排插。当一个设备（或一个电源排插）直接插入这 $k$ 个原始插座中的任意一个，或者插入了一个本身已通电的电源排插时，该设备（或电源排插）即被视为已接入电力。

问：瓦西娅至少需要从给定的 $n$ 个电源排插中选用多少个，才能使他全部 $m$ 个设备都通电？注意：每个设备和每个电源排插在插入时均占用一个插孔；且每个插孔只能插入一个设备或一个电源排插。

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.

第一行包含三个整数 $n$、$m$、$k$（$1 ≤ n, m, k ≤ 50$），分别表示电源排插的数量、设备的数量以及他可以直接插入的插座数量。
第二行包含 $n$ 个用空格分隔的整数 $a_1, a_2, ..., a_n$（$1 ≤ a_i ≤ 50$），其中 $a_i$ 表示第 $i$ 个电源排插上的插座数量。

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.

输出一个整数——即插满所有设备所需的供电线滤波器的最小数量。如果即使使用所有供电线滤波器也无法插满所有设备，则输出 -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.

在第一个测试用例中，他可以将第一个插线板滤波器直接接入电源。接入后，他获得 5 个可用插座（插线板滤波器自身提供 3 个插座，外加 2 个剩余的直连插座）用于插入设备。因此，仅需一个插线板滤波器即可插入 5 台设备。

第二个测试样例的一种最优方案是：将第二个插线板滤波器直接接入电源，并将第四个插线板滤波器接入第二个插线板滤波器的某个插座中。这样，他总共可获得恰好 7 个可用插座用于插入设备：1 个用于直接接入电源，2 个位于第二个插线板滤波器上，4 个位于第四个插线板滤波器上。若仅使用一个插线板滤波器，则无法插入 7 台设备。