R - random distribution with predefined min, max, mean, and sd values

I want to generate a random distribution of say 10,000 numbers with predefined min, max, mean, and sd values. I have followed this link setting upper and lower limits in rnorm to get random distribution with fixed min and max values. However, in doing so, mean value changes.

For example,

#Function to generate values between a lower limit and an upper limit.
mysamp <- function(n, m, s, lwr, upr, nnorm) {
set.seed(1)
samp <- rnorm(nnorm, m, s)
samp <- samp[samp >= lwr & samp <= upr]
if (length(samp) >= n) {
return(sample(samp, n))
}  
stop(simpleError("Not enough values to sample from. Try increasing nnorm."))
} 
Account_Value <- mysamp(n=10000, m=1250000, s=4500000, lwr=50000, upr=5000000, nnorm=1000000)
summary(Account_Value)

# Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
# 50060 1231000 2334000 2410000 3582000 5000000
#Note - though min and max values are good, mean value is very skewed for an obvious reason.
# sd(Account_Value) # 1397349

I am not sure whether we can generate a random normal distribution that meets all conditions. If there is any other sort of random distribution that can meet all conditions, please do share too.

Look forward to your inputs.

-Thank you.