A Strange Exhibit

A new exhibit recently arrived at the exhibition of strange devices. It generates a random permutation of the numbers from $1$ to $n$, scans it, and prints $n - k + 1$ numbers on its screen. The $i$-th of these numbers is the number of inversions in the segment of the generated permutation from position $i$ to position $i + k - 1$.

Recall that an inversion in a permutation $p$ is any pair of indices $i, j$ such that $1 \le i < j \le n$ and p\[i] > p\[j]\].

Besides the screen, the exhibit has two knobs. The first sets $n$, the length of the permutation, and the second sets $k$. A visitor named Vasya turned the knobs and saw numbers on the screen. Now he wants to figure out which permutation the strange device generated. Help him.

The first line contains two positive integers $n$ and $k$ ($2 \le n \le 10^5$, $2 \le k \le 5$, $n \ge k$). The second line contains the $n - k + 1$ numbers printed by the device. The device is guaranteed to work correctly, and at least one permutation can produce these numbers.

Print $n$ numbers separated by spaces: the permutation generated by the device. If several permutations are possible, print any one of them.