## 题目描述：

LeetCode 668. Kth Smallest Number in Multiplication Table

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]

## 解题思路：

若count >= k，则令hi = mid - 1

否则，令lo = mid + 1

## Python代码：

``````class Solution(object):
def findKthNumber(self, m, n, k):
"""
:type m: int
:type n: int
:type k: int
:rtype: int
"""
count = lambda t: sum(min(m, t / x) for x in range(1, n + 1))
lo, hi = 1, k
while lo <= hi:
mid = (lo + hi) / 2
if (count(mid)) >= k:
hi = mid - 1
else:
lo = mid + 1
return lo
``````

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