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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

import math

a, b, n = map(int, input().split())
def f(x):
    return math.floor(a * x / b) - a * math.floor(x / b)

left, right = 0, n
while right > left + 10:
    mid1 = (right * 2 + left) / 3
    mid2 = (right + left * 2) / 3
    if f(mid1) <= f(mid2):
        # 上限を下げる（最小値をとるxはもうちょい下めの数だな）
        right = mid2
    else:
        # 下限を上げる（最小値をとるxはもうちょい上めの数だな）
        left = mid1
listalt = []
for i in range(int(left), int(right) + 1):
    listalt.append(f(i))
listalt.append(f(0))
listalt.append(f(n))
print(max(listalt))