Generating A Permutation

For a permutation \( P = (p_1, p_2, \dots, p_N) \) of numbers \([1, 2, \dots, N]\), we define the function \( f(P) = \max(p_1, p_2) + \max(p_2, p_3) + \dots + \max(p_{N-1}, p_N) \). You are given \( N \) and an integer \( K \). Find and report a permutation \( P \) of \([1, 2, \dots, N]\) such that \( f(P) = K \), if such a permutation exists. Note \( f([1]) = 0 \). ### Input - The first line o