Nearly every one have used the Multiplication Table. But could you find out the k-th smallest number quickly from the multiplication table?

Given the height m and the length n of a m * n Multiplication Table, and a positive integer k, you need to return the k-th smallest number in this table.

Example 1:

Input: m = 3, n = 3, k = 5

Output:

Explanation:

The Multiplication Table:

1	2	3

2	4	6

3	6	9

The 5-th smallest number is 3 (1, 2, 2, 3, 3).

Example 2:

Input: m = 2, n = 3, k = 6

Output:

Explanation:

The Multiplication Table:

1	2	3

2	4	6

The 6-th smallest number is 6 (1, 2, 2, 3, 4, 6).

Note:

1. The m and n will be in the range [1, 30000].
2. The k will be in the range [1, m * n]

class Solution {

public:

    int findKthNumber(int m, int n, int k) {

        int l = 1, r = m * n;

        while (l < r) {

            int mid = l + (r - l) / 2;

            if (!bignums(mid, m, n, k)) l = mid + 1;

            else r = mid;

        }

        return l;

    }

private:

    bool bignums(int x, int m, int n, int k) {

        int count = 0;

        for (int i = 1; i <= m; ++i) {

            count += min(x/i, n);

        }

        return count >= k;

    }

};