Count Powers of K (MLE)

Given an integer array arr and an integer k, count how many numbers in the array are powers of k, that is, numbers that can be written as k^e for a positive integer e.

输入格式

The first line contains two integers n and k; the second line contains n integers arr[0..n−1]. 1≤n≤200000, 2≤k≤10^18, 2≤arr[i]≤10^18.

输出格式

Output one integer: the number of elements that are powers of k.

样例 1

输入：

3 11
11 121 10

输出：

2

样例 2

输入：

5 2
2 4 6 8 1024

输出：

4

样例 3

输入：

3 5
10 20 30

输出：

0

样例说明

Example 1: arr=[11,121,10], k=11. 11=11^1 and 121=11^2, but 10 is not, so the answer is 2. Example 2: 2, 4, 8, and 1024 are all powers of 2, but 6 is not, so the answer is 4. Example 3: none of 10, 20, 30 is a power of 5, so the answer is 0.