Problem:
Score : 100 points

Problem Statement

You are parking at a parking lot. You can choose from the following two fee plans:

Plan 1: The fee will be A×T yen (the currency of Japan) when you park for T hours.

Plan 2: The fee will be B yen, regardless of the duration.

Find the minimum fee when you park for N hours.

Constraints

1≤N≤20

1≤A≤100

1≤B≤2000

All input values are integers.

Input

Input is given from Standard Input in the following format:

N A B

Output

When the minimum fee is x yen, print the value of x.

Sample Input 1

7 17 120

Sample Output 1

119

If you choose Plan 1, the fee will be 7×17=119 yen.

If you choose Plan 2, the fee will be 120 yen.

Thus, the minimum fee is 119 yen.

Sample Input 2

5 20 100

Sample Output 2

100

The fee might be the same in the two plans.

Sample Input 3

6 18 100

Sample Output 3

100

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < (n); i++)
using namespace std;

// 数字の各桁の和を返す
int sumDigits (int n) {
    int s;
    while (n > 0) {
        s += n % 10;
        n /= 10;
    }
    return s;
}

// 最大公約数を返す
int gcd (int x, int y) {
  if (y == 0) return x;
  return gcd(y, x%y);
}

int main () {
  int N; cin >> N;
  
  int f = sumDigits(N);
  if (N % f == 0) cout << "Yes" << endl;
  else cout << "No" << endl;
}