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: Time Limit Exceeded)

import sys
a, b, n = map(int, input().split())

if n < b:
    ans = a * n // b  
    print(ans)
    sys.exit()  
elif n == b:
    ans = a * (b-1) // b
    print(ans)
    sys.exit()

# n == 1のときは0 問題なし
r = n // b
ans = 0
for i in range(1, r + 1):
    t = i * b - 1
    ans_t = a * t // b - (a * (i - 1))
    ans = max(ans, ans_t) 
    # print(i, t, ans)

t = r * b - 1
ans_t = a * t // b - (a * (r - 1))
ans = max(ans, ans_t) 

ans_t = a * n // b - (a * (n // b))
ans = max(ans, ans_t) 

print(ans)