Implement the following function $$\texttt{find_k}$$ :

$$\texttt{int find_k(int A[], int N, int k);}$$

where $$\texttt{A}$$ is an array of distinct positive numbers, $$\texttt{N}$$ the dimension of the array, and $$\texttt{k} > 0$$. The function calculates the k$$^{th}$$ smallest element in the array and returns this element or -1 if it doesn't exist.

Use $$\texttt{QuickSort}$$ in searching for this element without sorting the entire array.

Example : In the following array [11, 4, 7, 8, 2, 9, 23, 30, 10, 14]

The first smallest element is 2, the 2nd smallest element is 4, the 3rd smallest element is 7, $$\cdots$$

int place(int tab[], int i, int j)
{
	int k,l, Aux;
	l=i+1;
	k=j;
	while (l<=k)
	{
		while (tab[k]>tab[i]  && k>=l )
			k--;
		/*now, tab[k]<=tab[i]*/
		while (tab[l]<=tab[i]  && l<=k)
			l++;
		/*now, tab[l]>tab[i]*/
		if (l<k)
		{
			Aux = tab[l];
			tab[l] = tab[k];
			tab[k] = Aux;
			l++;
			k--;
		}
	}
	/* place pivot tab[i] at k */
	Aux = tab[i];
	tab[i] = tab[k];
	tab[k] = Aux;
	return k;
}

int find_k(int tab[],int N,int k)
{
	int start=0, end=N-1, j;
	if (k>N || k<1)
		return -1;
	do 
	{
		j=place(tab,start,end);
		if (j>k-1)
			end=j-1;
		else 
			if (j<k-1)
				start=j+1;
			else
				return(tab[j]);
	}
	while (1);
}