Problem:
Score : 100 points

Problem Statement

Alice and Bob are playing One Card Poker.

One Card Poker is a two-player game using playing cards.

Each card in this game shows an integer between 1 and 13, inclusive.

The strength of a card is determined by the number written on it, as follows:

Weak 2 < 3 < 4 < 5 < 6 < 7 < 8 < 9 < 10 < 11 < 12 < 13 < 1 Strong

One Card Poker is played as follows:

Each player picks one card from the deck. The chosen card becomes the player's hand.

The players reveal their hands to each other. The player with the stronger card wins the game.

If their cards are equally strong, the game is drawn.

You are watching Alice and Bob playing the game, and can see their hands.

The number written on Alice's card is A, and the number written on Bob's card is B.

Write a program to determine the outcome of the game.

Constraints

1≦A≦13

1≦B≦13

A and B are integers.

Input

The input is given from Standard Input in the following format:

A B

Output

Print Alice if Alice will win. Print Bob if Bob will win. Print Draw if the game will be drawn.

Sample Input 1

8 6

Sample Output 1

Alice

8 is written on Alice's card, and 6 is written on Bob's card.
Alice has the stronger card, and thus the output should be Alice.

Sample Input 2

1 1

Sample Output 2

Draw

Since their cards have the same number, the game will be drawn.

Sample Input 3

13 1

Sample Output 3

Bob

Solution in PHP (5.6.30) (judge verdict: Runtime Error)

<?php
error_reporting(0);
$stdin = file_get_contents('php://stdin');
$line = explode("\n",$stdin);
$fi = 0;
$cnt = 0;
$list = array();
$key = new stdclass();
foreach($line as $l) {
  if (strlen($l)==0) continue;
  if ($fi == 0) {
    $a = explode(" ",$l);
    $key->A = $a;
    $fi++;
    continue;
  }
  if ($fi > 0) {
    $a = explode(" ",$l);
    $key->X[] = $a;
  }
}
//N頂点
$N = $key->A[0];
//M辺
$M = $key->A[1];
//https://book.mynavi.jp/manatee/detail/id=65960
//頂点フラグ
$used = new SplFixedArray($N);
//接続状態を保存する
$connected = new SplFixedArray($N);
//初期化
for($i=0;$i<$N;$i++) {
  $used[$i]=0;
  //接続状態はconnected[頂点数=N][頂点数=N]
  $connected[$i]=new SplFixedArray($N);
  for($j=0;$j<$N;$j++) {
    $connected[$i][$j]=0;
  }
}
//つながっているところを1にする
//頂点1-2がつながっているなら
// connected[0][1]=1
// connected[1][2]=1になるようにする
for($i=0;$i<$M;$i++) {
  $a = $key->X[$i][0]-1;
  $b = $key->X[$i][1]-1;
  $connected[$a][$b] = 1;
  $connected[$b][$a] = 1;
}
printf("%d\n",dfs(0,1));

function dfs($now,$depth) {
  global $used,$connected,$M,$N;
  if ($used[$now]) return 0;
  if ($depth == $N) return 1;
  $used[$now]=1;
  $ans  = 0;
  for($i=0;$i<$N;$i++) {
    if ($connected[$now][$i]) {
      $ans += dfs($i,$depth+1);
    }
  }
  $used[$now]=0;
  return $ans;
}