Minimum Cost of Rod Cuts

You are given n rods with various lengths. Your task is to determine the minimum number of cuts required to produce a rod (or multiple pieces from a single rod) of exactly length m.

If a rod's length is exactly m, then no cuts are needed. Otherwise, if a rod of length \(L\) is greater than m and can be evenly divided into pieces of length m (i.e. \(L \bmod m = 0\)), you can cut it into \(\frac{L}{m}\) pieces. In this case, the number of cuts needed is given by the formula: \[ \text{cuts} = \frac{L}{m} - 1 \] Your goal is to find the minimum number of cuts required among all rods that meet these criteria. If no rod can produce a piece of length m using the above rules, output -1.

Note: Only one rod is cut at a time and pieces from different rods cannot be combined.

inputFormat

The input is provided via standard input (stdin). The first line contains two space-separated integers, n and m, where n is the number of rods and m is the target length. The second line contains n space-separated integers representing the lengths of the rods.

outputFormat

Output a single integer to standard output (stdout): the minimum number of cuts required to obtain a rod (or pieces from one rod) of length m, or -1 if it is not possible.

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