Sockets

Description:

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, ..., a_n (1 ≤ a_i ≤ 50) — number a_i 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 Input:

3 5 3
3 1 2

Sample Output:

1

Sample Input:

4 7 2
3 3 2 4

Sample Output:

2

Sample Input:

5 5 1
1 3 1 2 1

Sample 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.