Source

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

Problem 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 Format

The first line consists of two integers $n, k (1 \le n \le 10^5, 1 \le k \le 10^6)$.

The second line consists of $n$ integers $a_1,a_2,\ldots,a_n\ (1 \le a_i \le 10^6)$.

The third line consists of $n$ integers $b_1,b_2,\ldots,b_n\ (1 \le b_i \le 10^6)$.

Output Format

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

Sample 2 Explanation

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