Suppose you are in a 2-Dimensional world. Now, you are in a system of 'N' parallel zones of same or different speed, numbered from 0 to N-1. In each zone, you can move in some given constant speed (S_i amount per second in i^th zone) at any direction. Each zone is parallel to X axis, starting from the X axis (and then on the positive X and positive Y part only). Width of each zone is 100 (along the Y axis).

You are currently at the origin (0, 0). You need to reach (100*N, D) coordinate. But, you want to do that in minimum possible time (seconds).

Here is an example with N = 4, and D = 350. The arrows show a possible path from (0, 0) to (400, 350). Note that after the end of each zone (except the last one), it is possible that you may be at an non-integer 'X' coordinate.

Given N, D, and the speeds S₀, S₁, S₂, ..., S_N-1you will need to find the minimum possible time in seconds to reach the destination point.

Input starts with an integer T (≤ 50), denoting the number of test cases.

Each case contains two lines. In the first line you will be given two integers N (1 ≤ N ≤ 100) and D (0 ≤ D ≤ 10000). In the second line you will be given N integers, the speeds, in the order: S₀, S₁, S₂, ..., S_N-1. You can assume that 1 ≤ S_i ≤ 1000 for all 0 ≤ i < N.

For each case, print the case number and the minimum possible time in seconds. Error less than 10^-6 will be ignored.