C. Two players, two numbers
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Arthur and Nikita, tired of playing chess, came up with a new game. Each player starts with a number, $$$a$$$ and $$$b$$$ respectively. First, Arthur appends $$$n$$$ digits to the right of his number $$$a$$$, then Nikita appends $$$m$$$ digits to the right of his number $$$b$$$. The winner is the player whose resulting number is greater. Your task is to determine the outcome of the game given the numbers $$$a$$$, $$$b$$$, $$$n$$$, and $$$m$$$, assuming that both players follow an optimal strategy.

Input

The input consists of a single line containing four integers $$$a$$$, $$$b$$$, $$$n$$$, and $$$m$$$ $$$(1 \le a, b, n, m \le 10^9)$$$.

Output

Output the word "Arthur" if Arthur wins, "Nikita" if Nikita wins, and "Draw" if the game ends in a tie.

Examples
Input
1 2 3 4
Output
Nikita
Input
54 54 54 54
Output
Draw
Input
11 10 2 2
Output
Arthur