We have a directed graph with $N$ vertices, called Vertex $1$, Vertex $2$, $\ldots$, Vertex $N$.
For each pair of integers such that $1 \leq i, j \leq N$ and $i \neq j$, there is a directed edge from Vertex $i$ to Vertex $j$ of weight $(A_i + B_j) \bmod M$. (Here, $x \bmod y$ denotes the remainder when $x$ is divided by $y$.)
There is no edge other than the above.
Print the shortest distance from Vertex $1$ to Vertex $N$, that is, the minimum possible total weight of the edges in a path from Vertex $1$ to Vertex $N$.

Input is given from Standard Input in the following format:
$N\ M$
$A_1\ A_2\ \ldots\ A_N$
$B_1\ B_2\ \ldots\ B_N$

Print the minimum possible total weight of the edges in a path from Vertex $1$ to Vertex $N$.

$2≤N≤2×10^5$
$2 \leq M \leq 10^9$
$0 \leq A_i, B_j < M$
All values in input are integers.

3

Below, $i \rightarrow j$ denotes the directed edge from Vertex $i$ to Vertex $j$.
Let us consider the path $1 \rightarrow 3 \rightarrow 2 \rightarrow 4$.

• Edge $1\rightarrow 3$ weighs $(A_1 + B_3) \bmod M = (10 + 4) \bmod 12 = 2$,
• Edge $3 \rightarrow 2$ weighs $(A_3 + B_2) \bmod M = (6 + 7) \bmod 12 = 1$,
• Edge $2\rightarrow 4$ weighs $(A_2 + B_4) \bmod M = (11 + 1) \bmod 12 = 0$.

Thus, the total weight of the edges in this path is $2 + 1 + 0 = 3$.
This is the minimum possible sum for a path from Vertex $1$ to Vertex $N$.