Watering System

1000ms

262144K

Description:

Arkady wants to water his only flower. Unfortunately, he has a very poor watering system that was designed for $$$n$$$ flowers and so it looks like a pipe with $$$n$$$ holes. Arkady can only use the water that flows from the first hole.

Arkady can block some of the holes, and then pour $$$A$$$ liters of water into the pipe. After that, the water will flow out from the non-blocked holes proportionally to their sizes $$$s_1, s_2, \ldots, s_n$$$. In other words, if the sum of sizes of non-blocked holes is $$$S$$$, and the $$$i$$$-th hole is not blocked, $$$\frac{s_i \cdot A}{S}$$$ liters of water will flow out of it.

What is the minimum number of holes Arkady should block to make at least $$$B$$$ liters of water flow out of the first hole?

Input:

The first line contains three integers $$$n$$$, $$$A$$$, $$$B$$$ ($$$1 \le n \le 100\,000$$$, $$$1 \le B \le A \le 10^4$$$) — the number of holes, the volume of water Arkady will pour into the system, and the volume he wants to get out of the first hole.

The second line contains $$$n$$$ integers $$$s_1, s_2, \ldots, s_n$$$ ($$$1 \le s_i \le 10^4$$$) — the sizes of the holes.

Output:

Print a single integer — the number of holes Arkady should block.

Sample Input:

4 10 3
2 2 2 2

Sample Output:

Sample Input:

4 80 20
3 2 1 4

Sample Output:

Sample Input:

5 10 10
1000 1 1 1 1

Sample Output:

Note:

In the first example Arkady should block at least one hole. After that, $$$\frac{10 \cdot 2}{6} \approx 3.333$$$ liters of water will flow out of the first hole, and that suits Arkady.

In the second example even without blocking any hole, $$$\frac{80 \cdot 3}{10} = 24$$$ liters will flow out of the first hole, that is not less than $$$20$$$.

In the third example Arkady has to block all holes except the first to make all water flow out of the first hole.

Informação

Provedor Codeforces

Código CF967B