Problem I. Item enhancement ≡

Statement

Petya likes to play MMORPG and wants to beat everyone in PvP.

He just bought a cool weapon and wants to enhance it.

Initially enhancement level of the weapon is zero.

Petya has N enhancement stones of different levels in his inventory.

To raise enhancement level by 1, you need K stones of a higher level than the current level of the weapon, after this operation the stones disappear.

It is also possible to create a stone of one level higher from M stones of the same level.

What is the maximum enhancement level of the weapon Petya can reach?

Input format

First line contains 3 integers: N, K and M.

N - number of enhancement stones.

K - number of stones to raise enhancement level of the weapon by 1.

M - number of stones to craft a stone of a level higher by 1.

Second line contains an array A from N integers - levels of enhancement stones.

Output format

One integer - maximum enhancement level of the weapon that Petya can reach.

Constraints

1 ≤ N ≤ 10⁵

1 ≤ K ≤ 10⁹

1 ≤ M ≤ 10⁹

1 ≤ A_i ≤ 10⁹

Notes on samples

1-st: Petya crafts 3 stones of level 3 and uses it in any order.

2-nd: uses stones in order 2, 3, 4, 5.

3-rd: uses 2 stones of level 1, crafts stone of level 2 and uses 2 stones of level 2.

4-th: uses 1 stone of level 1.

5-th: uses two stones one time.

Sample tests

3 1 1
1 1 1

3

4 1 1
5 2 4 3

4

5 2 2
1 1 1 1 2

2

2 1 100
1 1

1

2 2 100
1 3

1