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# 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]

Solution:

```class Solution {
public int findKthNumber(int m, int n, int k) {
int left=1,right=m*n;
while(left<right)
{
int mid=left+(right-left)/2;
if(smallest(mid,m,n,k))
right=mid;
else left=mid+1;

}
return left;
}

private boolean smallest(int num,int m,int n,int k)
{
int count=0;
for(int i=1;i<=m;i++)
{
count+=Math.min(num/i,n);
}
return count>=k;
}
}```