M. Nomad
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Due to the high rent prices in Shanghai, Kai, of the Yafa clan, has become homeless. Fortunately, he has already found a new place! However, he will need to wait for exactly $$$D$$$ days until he can move in.

In the meantime, he has evaluated his options and found $$$N$$$ places, represented by indices from $$$1$$$ to $$$N$$$, where he can spend the night. Each place, however, has a tolerance limit: after a certain number of consecutive days, Kai will be kicked out.

For each of the $$$N$$$ places, an integer $$$d_i$$$ has been determined, representing the maximum number of consecutive days he can sleep at the $$$i$$$-th location before being expelled. It is possible that $$$d_i = 0$$$; in this case, it means Kai cannot spend even a single night at that location.

Your goal is to create an accommodation plan for Kai to get through the $$$D$$$ days by alternating between these places, without exceeding the consecutive day limit of any of them. Kai can return to a place later, as long as each new consecutive stay respects the limit.

Write a program that determines if it is possible to create such a plan. If so, produce a sequence of places (indices from $$$1$$$ to $$$N$$$), indicating where Kai should sleep on each of the $$$D$$$ days. Otherwise, print $$$-1$$$.

Input

The first line contains two integers $$$N$$$ and $$$D$$$ ($$$1 \leq N, D \leq 10^5$$$), representing the number of available places and the number of days Kai needs to wait, respectively.

The second line contains $$$N$$$ integers $$$d_1, d_2, \ldots, d_N$$$ ($$$0 \leq d_i \leq 10^5$$$), where $$$d_i$$$ is the tolerance limit of the $$$i$$$-th place.

Output

Print $$$D$$$ integers, the sequence of places representing the accommodation plan. If it is not possible to create a plan, print $$$-1$$$.

Examples
Input
3 5
0 1 3
Output
2 3 3 3 2
Input
10 1
0 0 0 0 0 0 0 0 0 0
Output
-1