Make It Large

You are given two string $S$ and $T$ of length $n$ and $m$ respectively.

Find a strictly increasing array of $m$ integers $A_1, A_2, …, A_m$ where $A_i$ is the index of the character in $S$ that matches with $T_i.$ $i.e$ $S_{A_i} = T_i$.

Among all possible arrays find the one where the summation of the absolute difference between each adjacent element is maximum. $i.e$ $\displaystyle\sum_{i = 1}^{i < m} A_{i+1} - A_{i }$ is maximum. If there are multiple answers find the one where the summation of the elements in the array is maximum. $i.e$ $\displaystyle\sum_{i = 1}^{i \leq m} {A_i}$ is maximum.

If such an array does not exist, print $-1$.

Input

The first line of input will contain two integers $n$ and $m$ $(1 \leq n, m \leq 2 * 10^5)$.

The second line will contain a string $S$ of length $n$.

The third line will contain a string $T$ of length $m$.

Output

Print $m$ integers $A_1, A_2, …, A_m$ the array you have found. If such an array does not exist, print $-1$.

Samples

Input	Output
4 2 BABC AC	2 4

Input	Output
5 2 ABCBC BD	-1

Input	Output
6 3 AXZXYZ AXZ	1 4 6