On cold winter days, Petriukas really likes tea, and today he wants to drink exactly n cups of tea. He would happily drink more, but he has exactly n tea bags, out of which a are green tea and b are black tea.

Petriukas doesn’t like drinking the same type of tea (either green or black) more than k times in a row.

Your task is to determine the order of tea bag usage so that Petriukas can drink n cups of tea without drinking the same type of tea more than k times in a row, or determine that it's impossible. Each tea bag can be used exactly once.

Four integers n, k, a, b (1 \le k \le n \le 10^{5}, 0 \le a, b \le n).
It is guaranteed that a + b = n.

If the answer is impossible, print "NEIMANOMA".
Otherwise, print a string of n characters consisting of 'Z' (green tea) and 'J' (black tea).
If there are multiple valid answers, print any of them.