### ** Spell Of Weakness**

### Problem Statement

Snuke is playing computer games again. He encounters *N* enemies in the game.

The i-th enemy has *A*_{i} HP (Health Points), and can take *A*_{i} points of damage before being defeated.

Snuke can do 1 point of damage to a single enemy in an attack. Snuke has *D* attacks. He can also cast *K* spells of weakness which will half the HP of one enemy (rounded down to the nearest integer).

**Each enemy can have at most one spell of weakness applied on it.**
Snuke wants to know the maximum number of enemies he can defeat.

### Constraints

- 1 ≤ K ≤ N ≤ 10
^{6}
- 1 ≤ D ≤ A
_{1}+A_{2}+...+A_{N}
- 0 ≤ A
_{i} ≤ 10^{9}

Subtask 1 (20%): K = 1

Subtask 2 (20%): 1 ≤ K ≤ N ≤ 2000

Subtask 3 (60%): No additional constraints.

Subtask 4 (0%): Sample Testcases

### Input

The input is given from Standard Input in the following format:

`N` `D` `K`
`A`_{1}` ``A`_{2} ... `A`_{N}

### Output

The output should contain a single integer, the number of enemies Snuke can defeat with K spells of weakness.

### Sample Input 1

3 5 2
2 4 7

### Sample Output 1

2

### Explanation

Snuke can cast the spells of weakness on the 2nd and 3rd enemies and deal 2+3 = 5 points of damage.

### Sample Input 2

3 5 2
1000 1000 1000

### Sample Output 2

0

### Explanation

No matter how Snuke casts the spells of weakness, he cannot defeat any of the enemies.