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.

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.

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.

Sample Input 1

3 3
2 2 1

Sample Output 1

1 2 3 1 2

Two sequences x=(1,2,3,1,2),(2,1,3,2,1) satisfy the conditions. The lexicographically smaller one, (1,2,3,1,2), is the answer.

Sample Input 2

3 2
2 1 2

Sample Output 2

1 2 3 1 3

Sample Input 3

3 3
1 3 3

Sample Output 3

-1

见题面 Input 部分

见题面 Output 部分