Farmer John owes Bessie NN gallons of milk (1≤N≤10121≤N≤1012). He has to give her the milk within KK days. However, he doesn't want to give the milk away too quickly. On the other hand, he has to make forward progress on the loan, so he must give Bessie at least MM gallons of milk each day (1≤M≤10121≤M≤1012).Here is how Farmer John decides to pay back Bessie. He first picks a positive integer XX. He then repeats the following procedure every day:

1. Assuming that Farmer John has already given Bessie GG gallons, compute N−GXN−GX rounded down. Call this number YY.
2. If YY is less than MM, set YY to MM.
3. Give Bessie YY gallons of milk.

Determine the largest XX such that if Farmer John follows the above procedure, Farmer John gives Bessie at least NN gallons of milk after KK days (1≤K≤10121≤K≤1012).

SCORING:

• Test cases 2-4 satisfy K≤105**.**K≤105.
• Test cases 5-11 satisfy no additional constraints.

INPUT FORMAT (file loan.in):

The only line of input contains three space-separated positive integers NN, KK, and MM satisfying K⋅M<NK⋅M<N.

OUTPUT FORMAT (file loan.out):

Output the largest positive integer XX such that Farmer John will give Bessie at least NN gallons using the above procedure.

SAMPLE INPUT:

10 3 3

SAMPLE OUTPUT:

2

For the first test case, when X=2X=2 Farmer John gives Bessie 55 gallons on the first day and M=3M=3 gallons on each of the next two days.

Note that the large size of integers involved in this problem may require the use of 64-bit integer data types (e.g., a "long long" in C/C++).