D. Nightmare on 24th
time limit per test
1.3 seconds
memory limit per test
666 megabytes
input
standard input
output
standard output

It was the night before exams when all along 24th not a student was awake, as they wanted to be well rested. Freddy Krueger, dream visitor and altruist, thought this would be a good time to check in on students in their dreams before their exams. Freddy is playing with numbers in his head and is curious about how many buildings he'd have to visit to bless a given number of students.

There are $$$n$$$ buildings along 24th, with the $$$i$$$th building housing $$$a_i$$$ students. Freddy is curious about the logistics of $$$m$$$ possible quantities for the number of students he would visit, where the $$$j$$$th possible quantity is given by $$$q_j$$$. When meeting students, Freddy must visit the students' buildings in sequential order starting with the first building. For each number $$$q_j$$$ Freddy is curious about, please output the minimum number of buildings Freddy would have to visit to check that many students. If it's not possible to meet the requested number of students, please output -1.

Input

The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \leq n, m \leq 10^5$$$) — the number of buildings and number of quantities Freddy is curious about.

The second line contains $$$n$$$ integers $$$a_1, a_2, ... , a_n$$$ ($$$0 \leq a_i \leq 10^5$$$) — the number of students in each building.

The last line contains $$$m$$$ integers $$$q_1, q_2, ... , q_m$$$ ($$$0 \leq q_j \leq 10^9$$$) — where $$$q_i$$$ is the $$$i$$$th quantity Freddy is curious about.

Output

For each quantity, please output the minimum number of buildings Freddy would have to visit to check that many students, or -1 if it is not possible. Output each answer on its own line.

Example
Input
7 5
10 8 2 4 4 8 9
10 15 25 41 100
Output
1
2
5
7
-1