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)

A, B, N = map(int, input().split())

lo = 1
hi = N

def f(x):
    return int(A*x/B)-A*int(x/B)

ans = 0
if B-1<=N:
    ans = f(B-1)

while hi > lo :
    if f(lo) <= f(hi):
        mid = (lo + hi) // 2
        if f(mid)<=f(mid+1):
            lo = mid+1
        else:
            lo = mid
    else:
        mid = -(-(lo + hi) // 2)
        hi = mid

ans = max(ans,f(lo),f(N-1),f(B*N//B-1),f(B-1),f(A),f(N))

print(ans)