#P4101. Zealot Round-game Stones
Zealot Round-game Stones
Zealot Round-game Stones
Little Z is a true ZRP (Zealot Round-game Player) who loves turn‐based games. He recalls a childhood game played in the Jiangnan region. Initially, there are n piles of stones, each containing exactly 1 stone. Two players take turns (Little Z goes first). In each turn a player must choose any two piles and merge them into one pile. However, there is an important restriction: at any moment, the number of stones in any pile may not exceed m. In other words, if two piles have a and b stones respectively, they can only be merged if
\(a+b \le m\).
The game ends when no legal merge is possible; the player who is unable to make a move loses. Both players play optimally. Given the numbers n and m, determine who will win the game.
inputFormat
The input consists of two space‐separated integers n and m (1 ≤ n, m ≤ 109), where n is the number of piles initially (each with one stone) and m is the maximum allowed stones in any pile.
outputFormat
Output a single line containing Z
if Little Z (the first player) wins when both play optimally, or Friend
if his opponent wins.
sample
1 2
Friend