401908: GYM100571 A Cursed Query

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 a_i seconds, and then it turns itself off (if it is turned on, in time t, in time t + a_i - 1 it will be turned on, but on time t + a_i 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.

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

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

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

1 ≤ n, q ≤ 10⁵

1 ≤ a_i ≤ 10⁹

1 ≤ t ≤ 10¹⁸

For each query, print the answer in one line.

5 7
1 2 3 4 5
1
2
3
7
14
15
16

2
2
3
4
5
1
2