A11696. Watering System

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?

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.

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

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.