All binary numbers of length n that contain k 1s

Given two integers, N and K, your task is to generate all binary strings of length N that contain exactly K ones. The output should be in lexicographical order.

Input

You will receive two integers: N and K, where 0 ≤ K ≤ N and 0 ≤ N ≤ 100.

Output

Produce all binary strings of length N with exactly K ones, sorted in lexicographical order. The total size of the output will not exceed 10 megabytes.

Examples