Mapping between natural numbers and permutation in O(n)

public static int[] perm(int n, int k)
{
    int i, ind, m=k;
    int[] permuted = new int[n];
    int[] elems = new int[n];

    for(i=0;i<n;i++) elems[i]=i;

    for(i=0;i<n;i++)
    {
        ind=m%(n-i);
        m=m/(n-i);
        permuted[i]=elems[ind];
        elems[ind]=elems[n-i-1];
    }

    return permuted;
}

public static int inv(int[] perm)
{
    int i, k=0, m=1;
    int n=perm.length;
    int[] pos = new int[n];
    int[] elems = new int[n];

    for(i=0;i<n;i++) {pos[i]=i; elems[i]=i;}

    for(i=0;i<n-1;i++)
    {
        k+=m*pos[perm[i]];
        m=m*(n-i);
        pos[elems[n-i-1]]=pos[perm[i]];
        elems[pos[perm[i]]]=elems[n-i-1];
    }

    return k;
}