Boiled Eggs

Source: UVa

Version: Phuoc Hung OJ Extended

Problem Statement

There are $n$ eggs with weights $w_i$. At most $P$ eggs may be chosen and their total weight must not exceed $Q$. Find the maximum possible number of chosen eggs.

Input

The first line contains $n,P,Q$. The second line contains $n$ weights $w_i$.

Output

Print the maximum number of eggs that can be chosen.

Subtasks

General constraints:

• $1 \le n,P,Q \le 30$.

• $1 \le w_i \le 10$.

• Subtask 1 (20 points): $n \le 8$

• Subtask 2 (30 points): $n \le 15$

• Subtask 3 (50 points): No additional constraints.

Examples

Input

3 2 10
1 2 3

Output

2

Explanation

The eggs of weights $1$ and $2$ can be selected. The count limit $P=2$ prevents selecting a third egg.