Justice

— Let's play a game. There are several heaps, each of them contains certain number of stones. In one move you can take any number of stonesfrom one of the heaps. If you cannot make a move - you lose. — Well OK, but I go first. — Okay, then I choose how much stones we have. — Okay, then I choose how much heaps we have. — Then I will divide stones into heaps. — Good luck.

Input

Two numbers N and K (1 ≤ N ≤ 10^9, 2 ≤ K ≤ 16) - the number of stones and the number of heaps.

Output

If you can not divide the N stones smoothly on K non-empty heaps, so that the optimal game of both players leads to win of a second player, print -1. Otherwise, print K positive integers a_i — the size of heaps.

Examples