Seán 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 which he has written in C++:</p>

void something( int jump ) {
 int i = 0;
 while( i < N ) {
   seq[i] = seq[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.

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

After this, Seán 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, Seán 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 형식

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 Seán makes.The second line contains K integers: X₁ X₂ X₃ ... X_k , arguments passed to the procedure. (1 ≤ X_i < N).</p>

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

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

출력 형식

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

예제 입력 1

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

예제 출력 1

35
18
3

예제 입력 2

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

예제 출력 2

8
2
1

예제 입력 3

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

예제 출력 3

16422
28874

힌트

Example 1 description: The procedure is called with arguments 1, 1, 2, 1. After that the array contains values {4, 3, 4, 3, 4, 3, 4, 3, 4, 3}. Sum of indices 2 to 6 (inclusive) is 4+3+4+3+4 = 18.</p>

Example 2 description: After the procedure calls, the array is {3, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1}.