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)

import math

def bisearch(function, ok, ng):
    tmp = 0
    while abs(ok-ng) > 1:
        mid = (ok + ng)//2
        ans = function(mid)
        if ans > tmp:
            ok = mid
        else:
            ng = mid
        print("mid:{}".format(mid))
        tmp = ans
    return ok

def calc(x):
    return (math.floor(A*x/B) - A*math.floor(x/B))

A, B, N = map(int, input().split())
ok = N
ng = 0

# print(bisearch(calc, ok, ng))
ans = 0
for i in range(min(N+1, 100000)):
    ans = max(calc(i), ans)
print(ans)