You are given S - a sequence of n integers S = s₁, s₂ ... s_n, Q - a sequence of n integers Q = q₁, q₂ ... q_n and a nonnegative parameter x.

Please print in ascending order all such i, that s_i = q_i+y, where -x <= y <= x.

Input data specification

In the first line you are given two integers 2 <= n <= 100, 0 <= x < n and in the following two lines n integers in each of the line:
-100 <= s_i, q_i <= 100

Output data specification

The sequence of requested integers separated by spaces.

Example 1

Input:
5 2
-1 2 -1 1 -1
3 -2 -1 1 2

Output:
1 3 4 5

Example 2

Input:
6 4
-1 2 2 2 2 -2
3 -2 3 3 3 -1

Output:
6

Example 3

Input:
6 0
-1 2 10 12 6 -2
2 -2 10 21 6 -1
 
Output:
3 5