Problem:
Score : 400 points

Problem Statement

Given are integers A, B, and N.

Find the maximum possible value of floor(Ax/B) - A × floor(x/B) for a non-negative integer x not greater than N.

Here floor(t) denotes the greatest integer not greater than the real number t.

Constraints

1 ≤ A ≤ 10^{6}

1 ≤ B ≤ 10^{12}

1 ≤ N ≤ 10^{12}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

A B N

Output

Print the maximum possible value of floor(Ax/B) - A × floor(x/B) for a non-negative integer x not greater than N, as an integer.

Sample Input 1

5 7 4

Sample Output 1

2

When x=3, floor(Ax/B)-A×floor(x/B) = floor(15/7) - 5×floor(3/7) = 2. This is the maximum value possible.

Sample Input 2

11 10 9

Sample Output 2

9

Solution in Python (3.8.2) (judge verdict: Wrong Answer)

from math import gcd
A,B,N = list(map(int,input().split()))
ans = 0
lcm = A*B//gcd(A,B)
if N < 2*10**6:
    for x in range(N+1):
        ans = max(ans,(A*x//B)-A*(x//B))
else:
    for x in range(10**6+2):
        ans = max(ans,(A*x//B)-A*(x//B))
    for x in range(N,N-10**6,-1):
        ans = max(ans,(A*x//B)-A*(x//B))
    if lcm <= N:
        ans = max(ans,(A*(lcm-1)//B)-A*((lcm-1)//B))
        tmp = (N//lcm)*lcm
        ans = max(ans,(A*(tmp-1)//B)-A*((tmp-1)//B))

print(ans)