# Eating Queries solution codeforces

## Eating Queries solution codeforces

Timur has nn candies. The ii-th candy has a quantity of sugar equal to aiai. So, by eating the ii-th candy, Timur consumes a quantity of sugar equal to aiai.

Timur will ask you qq queries regarding his candies. For the jj-th query you have to answer what is the minimum number of candies he needs to eat in order to reach a quantity of sugar greater than or equal to xjxj or print -1 if it’s not possible to obtain such a quantity. In other words, you should print the minimum possible kk such that after eating kk candies, Timur consumes a quantity of sugar of at least xjxj or say that no possible kk exists.

Note that he can’t eat the same candy twice and queries are independent of each other (Timur can use the same candy in different queries).

Input

## Eating Queries solution codeforces

The first line of input contains a single integer tt (1t10001≤t≤1000)  — the number of test cases. The description of test cases follows.

The first line contains 22 integers nn and qq (1n,q1.51051≤n,q≤1.5⋅105) — the number of candies Timur has and the number of queries you have to print an answer for respectively.

The second line contains nn integers a1,a2,,ana1,a2,…,an (1ai1041≤ai≤104) — the quantity of sugar in each of the candies respectively.

Then qq lines follow.

Each of the next qq lines contains a single integer xjxj (1xj21091≤xj≤2⋅109) – the quantity Timur wants to reach for the given query.

It is guaranteed that the sum of nn and the sum of qq over all test cases do not exceed 1.51051.5⋅105.

Output

## Eating Queries solution codeforces

For each test case output qq lines. For the jj-th line output the number of candies Timur needs to eat in order to reach a quantity of sugar greater than or equal to xjxj or print -1 if it’s not possible to obtain such a quantity.

Example

input

Copy
3
8 7
4 3 3 1 1 4 5 9
1
10
50
14
15
22
30
4 1
1 2 3 4
3
1 2
5
4
6


output

Copy
1
2
-1
2
3
4
8
1
1
-1

Note

## Eating Queries solution codeforces

For the first test case:

For the first query, Timur can eat any candy, and he will reach the desired quantity.

For the second query, Timur can reach a quantity of at least 1010 by eating the 77-th and the 88-th candies, thus consuming a quantity of sugar equal to 1414.

For the third query, there is no possible answer.

For the fourth query, Timur can reach a quantity of at least 1414 by eating the 77-th and the 88-th candies, thus consuming a quantity of sugar equal to 1414.

For the second test case:

For the only query of the second test case, we can choose the third candy from which Timur receives exactly 33 sugar. It’s also possible to obtain the same answer by choosing the fourth candy.

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