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 bisect  # 二分探索の公式のライブラリをimportする
# A, B, N = map(int, input().split())
# ans = (int(A*N/B) - A*int(N/B))
# # シミュレーション
# for i in range(max(N-1000005, 0), N+1):
#     ans = max(ans, int(A*i/B)-A*int(i/B))
# print(ans)


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

l = 0  # 最初の下界
r = N+1  # 最初の上界
ans = 0
while r - l > 1:  # rとlが交わることがあれば終了
    mid = (l+r) // 2  # 中央値, 選ぶ候補になっている値
    tmp = int(A*mid/B) - A*int(mid/B)
    if tmp >= ans:
        ans = tmp
        l = mid  # 下界をあげる
    else:
        r = mid  # 上界を下げる
    # print(l, r)
# print(l, r)
ans = max(ans, int(A*min(N, B-1)/B)-A*int(min(N, B-1)/B))
print(max(ans, int(A*N/B)-A*int(N/B), int(A*l/B)-A*int(l/B), int(A*min(N, r)/B)-A*int(min(N, r)/B)))