MAXIMUM NUMBERS

Jojo gets a big challenge by Bibi to solve a game. The game description is explained below.

Given N integers and Jojo should determine the length of the longest segment such that if we add all the element of the segment, the result is less than or equal to M.

The definition of a segment is a set of consecutive elements in a part of an array. For example, given array with 5 element {2,3,4,1,5 }, then some valid segments are {2,3,4 } , {3,4,1,5 } , { 4 }, and etc.

Jojo is too lazy finish this game and he asks you to help him finish this game.

Format Input

Input consists of one integer T, number of test case given by Bibi. For each test case, there are N and M, length of the array (or number of element inside the array) and the limitation of the summation result of the segment. Next line contains N integers A which describe the element inside the array

Format Output

Output should be expressed in format Case #X: Y - X is the number of the test case, and followed by one integer Y , the length of the longest segment which the summation result (of all the elements inside it) less than or equal to M. If there is no solution exist, output -1.

Constraints

1 T 100 1 N 10⁴ 0 M 10⁹ 0 A_i 10⁹

Sample Input 1 (standard input)

2 5 6 1 2 3 4 5 4 3 4 1 3 8 Sample Output 1 (standard output)

Case #1: 3 Case #2: 1

Sample Input 2 (standard input)

3 3 10 2 9 2 4 11 2 9 1 1 3 2 2 2 2

Sample Output 2 (standard output)

Case #1: 1 Case #2: 3 Case #3: 1

Explanation

For Sample Input 1 test case 1, we can see that the longest segment which has the summation result less than or equal to 6 is the first 3 elements. If we sum all the first 3 elements, the result of the summation is 6. There is no other configuration which has length more than 3. Thus, the output is 3.

DO IN C++ LANGUAGE