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 = [int(i) for i in input().split(" ")]
ans = 0
idx = 0
for x in range(1, min(A+1,N+1)):
    #print(x, A*x//B, A*(x//B), A*x//B-A*(x//B))
    if ans < A*x//B-A*(x//B):
        idx = x
    ans = max(ans, A*x//B-A*(x//B))

for x in range(N, N-A-1, -1):
    if x < 0:
        break
    #print(x, A*x//B, A*(x//B), A*x//B-A*(x//B))
    if ans < A*x//B-A*(x//B):
        idx = x
    ans = max(ans, A*x//B-A*(x//B))

print(ans)