Description

You are a magician in a high-dimensional space, and you have an initial $n$-dimensional hypercube with edge lengths $a_1, a_2, \dots, a_n$. For a $d$-dimensional hypercube, the edge length sum is defined as $\sum_{i=1}^d a_i$, and its hypervolume is $\prod_{i=1}^d a_i$.

You want to obtain a hypercube with edge length sum $S$ and hypervolume $M$. To achieve this, you can perform both dimensional reduction and dimensional expansion operations on the current hypercube.

• Dimensional Reduction: Remove a dimension.
• Dimensional Expansion: Add a new dimension, with its edge length being any positive integer.

Both operations are very exhausting, so you want to determine the minimum number of operations required to obtain a hypercube with edge length sum $S$ and hypervolume $M$.

Input Format

The first line contains three integers $n, S, M$ ($1\le n \le 10^5$, $1 \le S, M \le 10^{10}$).

The second line contains $n$ integers, representing the initial edge lengths $a_i$ of the hypercube ($1 \le a_i \le 10^{10}$).

Output Format

Output a single integer representing the minimum number of operations required. If it is impossible to obtain a hypercube that meets the conditions, output $-1$.

2 5 6
1 2

2

3 6 5
1 2 3

3

2 114514 735134400
114 514

20

2 4 7
1 3

-1

Hint

For the first sample, one possible approach: first delete the dimension with edge length $1$, and then add a dimension with edge length $3$.