Problem Statement

Takahashi and Aoki will play a game against each other using $N$ piles of stones.

Initially, for each $i = 1, 2, \ldots, N$, the $i$-th pile is composed of $A_i$ stones. The players alternately perform the following action, with Takahashi going first.

• Choose a pile with at least one stone remaining, and remove one or more stones.

However, there are $M$ forbidden moves. For each $i = 1, 2, \ldots, M$, it is not allowed to remove exactly $Y_i$ stones from a pile composed of exactly $X_i$ stones.

The first player to become unable to perform the action loses, resulting in the other player's victory. Which player will win when both players employ the optimal strategy for the victory?

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $1 \leq M \leq 2 \times 10^5$
• $1 \leq A_i \leq 10^{18}$
• $1 \leq Y_i \leq X_i \leq 10^{18}$
• $i \neq j \Rightarrow (X_i, Y_i) \neq (X_j, Y_j)$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
A_1 A_2 \ldots A_N
X_1 Y_1
X_2 Y_2
\vdots
X_M Y_M

Output

If Takahashi will win when both players employ the optimal strategy for the victory, print Takahashi; if Aoki will win, print Aoki.