Predict Answer

For each 1-based query day i, find among the other days the nearest day j whose price is strictly lower than that day's; if two days are equally near, choose the smaller day number. If there is no strictly cheaper day, output −1. Each query is independent and does not change the prices.

输入格式

The first line contains n q, the second line contains n stockData values, and the third line contains q 1-based days. The original bounds are 1≤n,q≤100000, 1≤stockData[i]≤10^9, 1≤query≤n. The raw restores the conditions stockData[j]<stockData[i] and j≠i, which the HTML had swallowed.

输出格式

Output the q answers in query order, separated by spaces.

样例 1

输入：

10 3
5 6 8 4 9 10 8 3 6 4
6 5 4

输出：

5 4 8

样例 2

输入：

3 2
1 2 1
2 1

输出：

1 -1

样例 3

输入：

2 2
3 3
1 2

输出：

-1 -1

样例说明

The answers are 5 4 8; 1 −1; and −1 −1. An equal price is not lower, and at equal distance the left day wins.