INVERSE OF CDF OF LOG PEARSON TYPE III DISTRIBUTION

Could someone kindly tell me how to calculate the inverse of the CDF of a log Pearson type III distribution?

In fact, I need to use Monte Carlo sampling to generate samples for certain log Pearson type III distributed data. I should be able to take the inverse of the CDF of a log Pearson type III distribution for this.

I have some data with me with that data I already know all three parameter(given below a, b, m i.e. shape, scale and location parameter) and clearly I can take scaled value(log values) of all these. The question now revolves around the data provided as well as the three parameters that I have. I need to generate as many samples as I like using the same method, so let's say 1e7 (number of sample want to generate).

I simply needed those 1e7 samples using the inverse CDF of the log Pearson type III distribution, which will obviously be in the range of 23.81-543.68

Can you consider the below data and help me with this

Data : 23.81, 33.98, 62.01, 140.45, 184.91, 257.97, 325.64, 410.59, 543.68

b =12.4640; a = 0.3161; m =1.0202