As Close As You Can

Lili is now preparing the bonus point question for her Calculus class students. The bonus questions is explained below.

Lili will give data A, which contains N integers, to her class. Data A may not be sorted. Then, Lili will give them integer M. They will be asked to find the index from the data A such that if we sum all the elements from 1st index of A until Y th index, we will get a number that has the smallest difference with M and is less than or equal to M.

Lili as a kind teacher prepares several questions to the class to make sure that all of her students will get the bonus point. Unfortunately, Lili has a lot of work to do. So, Lili asked you to find the answer of the question she had prepared before. You should give Lili the answer based on the problem description above.

Format Input

Input consists of one integer N, size of data A and followed by a line consists of N integers, which is the data A. The next line contains an integer Q, number of test case and for each test case, given M, the number described on the problem description.

Format Output

Output should be expressed in format Case #X: Y where X is the number of test case, and Y the biggest index based on the problem description above. If no value exists, just print -1 as the value of Y .

Constraints

1 N 10^5

1 Q 30000

1 A i 10^9

1 M 10^15

Sample Input 1 (standard input)

4

3 2 7 6

3

8

20

12

Sample Output 1 (standard output)

Case #1: 2

Case #2: 4

Case #3: 3

Sample Input 2 (standard input)

5

2 9 5 5 7

6

11

12

16

17

22

3

Sample Output 2 (standard output)

Case #1: 2

Case #2: 2

Case #3: 3

Case #4: 3

Case #5: 4

Case #6: 1

PLEASE MAKE THE CODE USING C PROGRAMMING AND FOR THE HEADER USE INCLUDE STDIO.H

MAKE THE CODE AS SIMPLE AS U CAN

AND FOR THE CODE ALSO USE BINARY SEARCH CODE