PROGRAM

문제

Mirko is trying to debug a piece of his code. First he creates an array of N integers and fills it with zeros. Then he repeatedly calls the following procedure (he is such a good coder he coded it in both C++ and Pascal):

void something(int jump) {
    int i = 0;
    while (i < N) {
        a[i] = a[i] + 1;
        i = i + jump;
    }
}

As you can see, this procedure increases by one all elements in the array whose indices are divisible by jump.

Mirko calls the procedure exactly K times, using the sequence X₁ X₂ X₃... X_k as arguments.

After this, Mirko has a list of Q special parts of the array he needs to check to verify that his code is working as it should be. Each of this parts is defined by two numbers, L and R (L ≤ R) the left and right bound of the special part. To check the code, Mirko must compute the sum of all elements of seq between and including L and R. In other words seq[L] + seq[L+1] + seq[L+2] + ... + seq[R]. Since he needs to know the answer in advance in order to check it, he asked you to help him.

입력

The first line of input contains two integers, N (1 ≤ N ≤ 10⁶), size of the array, and K (1 ≤ K ≤ 10⁶), number of calls to something Mirko makes.

The second line contains K integers: X₁X₂X₃ ... X_k, arguments passed to the procedure. (1 ≤ X_i < N).

Next line contains one integer Q (1 ≤ Q ≤ 10⁶), number of special parts of the array Mirko needs to check.

Next Q lines contain two integers each L_i and R_i(0 ≤ L_i≤ R_i < N), bounds of each special part.

출력

The output should contain exactly Q lines. The i^th line should contain the sum of elements seq[L_i] + seq[L_i+1] + seq[L_i+2] + ... + seq[R_i].

10 4
1 1 2 1
3
0 9
2 6
7 7

35
18
3

11 3
3 7 10
3
0 10
2 6
7 7

8
2
1

1000000 6
12 3 21 436 2 19
2
12 16124
692 29021

16422
28874