Divisible or Not#13059
Andrii and Taras are playing the following game.
Given two positive integers and , where is a prime number.
First, Andrii chooses any consecutive positive integers a_1, a_2, \ldots, a_n. That is, a_1 \ge 1 and a_{i+1} = a_i + 1 for all 1 \le i < n.
Then Taras chooses a non-empty subsegment of the array .
Taras wins if the sum of the numbers on the chosen subsegment is divisible by . Otherwise, Andrii wins.
Determine who wins under optimal play.
The only line contains two integers and (1 \le n, m \le 10^{18}).
It is guaranteed that is prime.
Print Andrii if Andrii can guarantee his victory.
Otherwise, print Taras.
Example 1
Example 2
In the first example, among any consecutive integers there is always a number divisible by . Taras can choose a subsegment consisting of only this number, so he can always win.
In the second example, Andrii can choose the numbers 1, 2, 3, 4. The sums of all non-empty subsegments of this array are 1, 2, 3, 4, 3, 5, 7, 6, 9, or . None of these numbers is divisible by , so Taras cannot win.
Subtask ( points): n \le 20, m \le 20.
Subtask ( points): n \le 2000, m \le 2000.
Subtask ( points): No additional constraints.