Count Powers of k in Readings

Given an array of positive integers and k, count the elements equal to a non-negative integer power of k, such as k⁰, k¹, k², and so on; duplicates are counted separately. The original site's answer to the first example is wrong, and this site has corrected it.

输入格式

The first line contains n k (1≤n≤100000, 2≤k≤10⁹), and the second line contains n positive integers (1..10⁹).

输出格式

Output the answer as described; separate multiple results with spaces in order, and output an empty line for an empty array.

样例 1

输入：

7 2
1 2 3 8 16 10 120

输出：

4

样例 2

输入：

6 10
10000 100 1000000 101 1010 1010000

输出：

3

样例 3

输入：

3 3
1 1 3

输出：

3

样例说明

Example 1: the non-negative integer powers of 2 are 1, 2, 8, and 16, for 4 items in total; 3, 10, and 120 are not.