Given an array A of n integers. Your task is to answer q queries. Each query consists of a number x, requiring you to find the length of the shortest contiguous subarray S of A such that all values in 1,2,…,x appear at least once in S.
### Input
- The first line contains two integers n,q.
- The second line contains n integers Ai.
- The next q lines each contain one integer x, representing a query.
### Output
- For each query, print the length of the shortest subarray that satisfies the condition. Print −1 if no such subarray exists.
### Constraints
- 1≤n,q≤2×105.
- 1≤Ai≤109.
- 1≤x≤109.
### Examples
Input:
5311243543
Output:
-144