CF251B Playing with Permutations

Little Petya likes permutations a lot. Recently his mom has presented him permutation $ q_{1},q_{2},...,q_{n} $ of length $ n $ . A permutation $ a $ of length $ n $ is a sequence of integers $ a_{1},a_{2},...,a_{n} $ $ (1

The first line contains two integers $ n $ and $ k $ ( $ 1

If the situation that is described in the statement is possible, print "YES" (without the quotes), otherwise print "NO" (without the quotes).

In the first sample Masha's permutation coincides with the permutation that was written on the board before the beginning of the game. Consequently, that violates the condition that Masha's permutation never occurred on the board before $ k $ moves were performed. In the second sample the described situation is possible, in case if after we toss a coin, we get tails. In the third sample the possible coin tossing sequence is: heads-tails-tails. In the fourth sample the possible coin tossing sequence is: heads-heads.