Problem Statement

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 $N$.

Constraints

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

Input

Input is given from Standard Input in the following format:

$N$ $M$ $A_1$ $A_2$ $\\ldots$ $A_N$ $B_1$ $B_2$ $\\ldots$ $B_N$

Output

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

Sample Input 1

4 12
10 11 6 0
8 7 4 1

Sample Output 1

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 $N$.

Sample Input 2

10 1000
785 934 671 520 794 168 586 667 411 332
363 763 40 425 524 311 139 875 548 198

Sample Output 2

462