G. Game of Cards
time limit per test
1.5 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

Rami and Yessine were learning some advanced data structures. Eventually, they got tired from writing code so they decided to take a break and play a game.

Rami told Yessine about a game of cards he has invented. In this game, each player will get $$$N$$$ cards. Each card has a number written on it and both players can see each other's cards.

They will take turns to play. At each turn, a player must choose a prime number $$$P,$$$ then, the other player must find a card in his hands with a number $$$C$$$ divisible by $$$P$$$, then change the number written on that paper to $$$\frac{C}{P}$$$. The chosen prime number $$$P$$$ should be less than or equal to $$$L$$$, where $$$L$$$ is a number they agree on before the game starts. The player who can't make a move loses.

Rami will start first. Assuming both players will play optimally, determine who will win at each game .

Input

- Ths first line contains $$$2$$$ integers $$$1\leq N \leq 10^5$$$ and $$$2\leq L \leq 10^6$$$.

- The second line contains N space separated integers $$$1 \leq A_1,\dots,A_N \leq 10^6$$$ denoting the numbers written on Rami's cards

- The third line contains N space separated integers $$$1 \leq B_1,\dots,B_N \leq 10^6$$$ denoting the numbers written on Yessine's cards.

Output

Rami if Rami will win. Otherwise Yessine if he will win.

Examples
Input
3 3
6 3 4
1 2 3
Output
Rami
Input
5 7
2 3 4 5 6
2 3 5 7 2
Output
Yessine
Note
  • It is guaranteed that the game will always have a winner.
  • For the first test case, Rami can force a win by choosing $$$3,2,3$$$ on this order.
  • For the second test case, whatever Rami will play on his first turn, Yessine can win instantly by choosing $$$7$$$