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A. Sockets

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputVasya 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.

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 *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.

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.

Examples

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.

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