A. Cursed Query
time limit per test
1 second
memory limit per test
256 megabytes
input
стандартный ввод
output
стандартный вывод

De Prezer loves movies and series. He has watched the Troy for like 100 times and also he is a big fan of Supernatural series.So, he did some researches and found a cursed object which had n lights on it and initially all of them were turned off.Because of his love to the Troy, he called that object Troy.

He looked and saw a note on it in Khikulish (language of people of Khikuland): "Ma in hame rah umadim, hala migi ... ? ... Mage man De Prezer am k mikhay mano ... ? .... Man se sale ... To boro .... beshur manam miram ... o mishuram".

He doesn't know Khikulish, so just ignored the note and tested the Troy.

He realized that the light number i stays turned on for exactly ai seconds, and then it turns itself off (if it is turned on, in time t, in time t + ai - 1 it will be turned on, but on time t + ai it won't be) and the next light will be turned on (if i < n, next light is the light number i + 1, otherwise it is light with number 1).

For example if n = 2 and we turn on the first light in time 0, it will be turned on in hole interval [0, a1) and in hole interval [a1, a1 + a2) the second light will be turned on and so on.

In time 0 he turns on the light number 1.

De Prezer also loves query.So he gives you q queries.In each query he will give you integer t (the time a revengeful ghost attacked him) and you should print the number of the light that is turned on, in time t.

Input

The first line of input contains two integers n and q.

The second line contains n space separated integers, a1, a2, ..., an .

The next q lines, each line contains a single integer t .

1 ≤ n, q ≤ 105

1 ≤ ai ≤ 109

1 ≤ t ≤ 1018

Output

For each query, print the answer in one line.

Examples
Input
5 7
1 2 3 4 5
1
2
3
7
14
15
16
Output
2
2
3
4
5
1
2