Source

This problem is adapted from Long Long OJ. All rights reserved.

Description

Given $n,k$, and sequences $a,b$, find the shortest interval $[i,j]$ such that:

Output the length of the interval.

Output $-1$ if no interval is found.

Input

The first line consists of two integers $n$ and $k$.

The second line consists of $n$ integers $a_1,a_2,\ldots,a_n$.

The third line consists of $n$ integers $b_1,b_2,\ldots,b_n$.

Output

An integer that represents the minimum length of interval.

Output $-1$ if no interval is found.

Samples

5 10
8 7 14 8 3
4 2 5 8 2

-1

5 14
11 22 3 15 6
21 20 17 22 136

1

Tips

Sample Explanation 2:

The interval is $[3,3]$ or $[5,5]$, because $a_3+k=3+14=17$ and $a_5+k=6+14=20\lt136$.

• $1\le n\le 10^5$.
• $1\le k,a_i,b_i\le 10^6$.