#000131

z-01seq

You are given a sequence of length N containing only 0s and 1s. You should find exactly 2 * K different indices ai among which there must be exactly K indices of 1s and exactly K indices 0s in the given sequence (the indices are 0-based, and you should output them in increasing order - such that for each j < k, aj < ak) .

In the case of multiple solutions return the set of indices such that Sum of (aj + 1 - aj), 0 < j < 2K, is minimal. If there are still multiple solution, return the lexicographically smallest set of indices.



InputThe first line of the standard input contains two space-separated integers N (2 <= N <= 800 000) and K (2 <= 2 * K <= N). The next line contains sequence of 0s and 1s of length N.


OutputTo the first line of the standard output you should print 2 * K indices (separated by a single space). If such set does not exist, you should print only one integer -1.

Input:
8 2
00100100

Output:
2 3 4 5

Explanation:
At position 2 and position 5 we have 1s. Note that indices are 0-based.

Input:
10 3
1000100000

Output:
-1


Input:
8 2
01111101

Output:
0 1 2 6


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