TCHS-9-1000

Problem Statement
	Consider a square n x n matrix A. The cell Ai,j is equal to the product i * j (i, j are 1-based). Let's create a one-dimensional array which contains all the elements of the matrix A. The length of this array will be equal to n2. Sort this array and return the element which will be in the k-th position (k is a 1-based index).
Definition
	Class: ProductsMatrix Method: nthElement Parameters: int, int Returns: long Method signature: long nthElement(int n, int k) (be sure your method is public)
Constraints
-	n will be between 1 and 10^5, inclusive.
-	k will be between 1 and min(10^9, n^2), inclusive.
Examples
0)
	3 7 Returns: 6 The matrix will be: 1 2 3 2 4 6 3 6 9 The array after sorting will be: {1, 2, 2, 3, 3, 4, 6, 6, 9}.
1)
	2 4 Returns: 4 k is 1-based.
2)
	3 8 Returns: 6
3)
	1 1 Returns: 1
4)
	4 4 Returns: 3

public class ProductsMatrix {

	long N;
	
	public long nthElement(int n, int k) {
		N = n;
		long low = 1L, high = (n + 0L) * n;
		while (low < high) {
			long mid = low + (high - low) / 2;
			if (indexOf(mid) < k)
				low = mid + 1;
			else
				high = mid;
		}
		return low;
	}
	
	private long indexOf(long x) {
		long sum = 0;
		for (long i = 1; i <= N; i++)
			sum += (i * N <= x) ? N : x / i;
		return sum;
	}

}