A k-multiple free set is a set of integers where there is no pair of integers where one is equal to another integer multiplied by k. That is, there are no two integers x and y (x < y) from the set, such that y = x·k.

You're given a set of n distinct positive integers. Your task is to find the size of it's largest k-multiple free subset.

Input

The first line of the input contains two integers n and k (1 ≤ n ≤ 105, 1 ≤ k ≤ 109). The next line contains a list of n distinct positive integers a1, a2, ..., an (1 ≤ ai ≤ 109).

All the numbers in the lines are separated by single spaces.

Output

On the only line of the output print the size of the largest k-multiple free subset of {a1, a2, ..., an}.

Examples

Input

6 2
2 3 6 5 4 10


Output

3

Note

In the sample input one of the possible maximum 2-multiple free subsets is {4, 5, 6}.

var bsearch = function(A, x) { 
    var l = 0; 
    var r = A.length - 1; 
    while (l <= r) { 
        var m = Math.floor((r+l) / 2); 
        if (A[m] == x) { 
            return m; 
        }
        else if (A[m] < x) { 
            l = m + 1; 
        }
        else { 
            r = m - 1; 
        }
    }
    return -1; 
}

var main = function(n, k) { 
    if (k == 1) { 
        return n; 
    }
    A = readline().split(' ').map(Number); 
    A.sort(function(a, b) {
        return a - b;}); 

    var F = Array.apply(null, {length: n}).map(function(x) {return 0});

    var cnt = 0; 
    for (var i = n-1; i >= 0; i--) { 
        var m = bsearch(A, A[i] * k); 
        if (m >= 0 && F[m] == 0) { 
            F[i] = 1; 
        }
        else { 
            cnt += 1; 
        }
    }
    return cnt; 
}

print(main.apply(null, readline().split(' ').map(Number))); 
