B. Mr. Wow and Dislikes
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Mr. Wow doesn't like arrays which contain positive integers. He is allowed to do the following operation on a given array $$$c$$$ of length $$$n$$$ by using two positive integers $$$a$$$ and $$$b$$$ $$$(a \gt b)$$$ :

  1. Choose any $$$i(1 \le i \le n)$$$;
  2. Set $$$c_i := c_i-a$$$, and $$$c_j =: c_j-b$$$ for every $$$j(1 \le j \le n, j ≠ i)$$$.

Help Mr. Wow with the minimum number of operations required to change the array $$$c$$$, such that it doesn't contain positive integers.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 1000$$$). The description of the test cases follows.

The first line of each test case contains three space separated integers $$$n, a, b$$$ ($$$1 \le n \le 2 \cdot 10^5$$$, $$$1 \le b \lt a \le 10^9$$$) — the length of the array $$$c$$$ and variables required to do operations.

The second line of each test case contains $$$n$$$ space separated integers $$$c_{i}$$$ ($$$-10^9 \le c_{i} \le 10^9$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases doesn't exceed $$$2 \cdot 10^5$$$.

Output

For each test case, print a single integer — minimum number of operations required to change the array $$$c$$$, such that it doesn't contain positive integers.

Example
Input
5
3 2 1
1 2 2
4 3 1
4 -7 9 -10
5 8 3
3 6 9 6 10
6 11 6
100 43 34 4 56 89
6 12 6
-1 -2 -3 -4 0 -11
Output
2
4
2
12
0
Note

In the $$$3$$$-rd test case, Mr. Wow can do the following two operations:

  1. Choose $$$i=3$$$. After that, $$$c=[0, 3, 1, 3, 7]$$$;
  2. Choose $$$i=5$$$. After that, $$$c=[-3, 0, -2, 0, -1]$$$.

It can be proven $$$2$$$ reaches the minimum.