Tennis Tournament

1000ms

262144K

Description:

A tennis tournament with n participants is running. The participants are playing by an olympic system, so the winners move on and the losers drop out.

The tournament takes place in the following way (below, m is the number of the participants of the current round):

let k be the maximal power of the number 2 such that k ≤ m,
k participants compete in the current round and a half of them passes to the next round, the other m - k participants pass to the next round directly,
when only one participant remains, the tournament finishes.

Each match requires b bottles of water for each participant and one bottle for the judge. Besides p towels are given to each participant for the whole tournament.

Find the number of bottles and towels needed for the tournament.

Note that it's a tennis tournament so in each match two participants compete (one of them will win and the other will lose).

Input:

The only line contains three integers n, b, p (1 ≤ n, b, p ≤ 500) — the number of participants and the parameters described in the problem statement.

Output:

Print two integers x and y — the number of bottles and towels need for the tournament.

Sample Input:

5 2 3

Sample Output:

20 15

Sample Input:

8 2 4

Sample Output:

35 32

Note:

In the first example will be three rounds:

in the first round will be two matches and for each match 5 bottles of water are needed (two for each of the participants and one for the judge),
in the second round will be only one match, so we need another 5 bottles of water,
in the third round will also be only one match, so we need another 5 bottles of water.

So in total we need 20 bottles of water.

In the second example no participant will move on to some round directly.

Informação

Provedor Codeforces

Código CF628A