You are given two arrays \(A\) and \(B\) of length \(N\).

For every index \(i\) in array \(A\), find the length of the smallest subarray starting from index \(i\) such that there exist at least \(B[i]\) elements with a value greater than or equal to \(A[i]\) in the subarray. If no such subarray exists, then print \(-1\).

Input format

• The first line contains an integer \(N\) denoting the number of elements in array \(A\) and \(B\).
• The second line contains space-separated integers denoting the array \(A\).
• The last line contains space-separated integers denoting the array.

Output format

Print \(N\) space-separated integers denoting the answer for every index in array \(A\).

Constraints

\(1 \le N \le 3 \times 10^5 \\ 1 \le A[i] \le 10^9 \\ 1 \le B[i] \le N\)