Problem Statement

Given are a sequence of $N$ integers $A=(A_1,A_2,\cdots,A_N)$ and an integer $K$.

Consider making a sequence of integers $x$ that satisfies both of the following conditions.

• For each integer $i$ ($1 \leq i \leq N$), $x$ contains exactly $A_i$ occurrences of $i$. $x$ does not contain other integers.
• For every way of choosing $K$ consecutive elements from $x$, their values are all distinct.

Determine whether it is possible to make $x$ that satisfies the conditions. If it is possible, find the lexicographically smallest such $x$.

Constraints

• $2 \leq K \leq N \leq 500$
• $1 \leq A_i$
• $\sum_{1 \leq i \leq N} A_i \leq 200000$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
A_1 A_2 \cdots A_N

Output

If it is impossible to make a sequence $x$ that satisfies the conditions, print -1. If it is possible, print the lexicographically smallest such $x$.