Simulation of random variables X and Y

I have the following algorithm to generate values for X and Y.

Step 1. Generate U1,U2~U(0,1)

Step 2. t=-beta*log(U1*U2)

Step 3. Generate U3~U(0,1)

Step 4. X=t*U3, Y=t-X

---

Notice you can compare the way to generate X and Y by generating U1 and U2 and defining X=-beta * log(U1) and Y=-beta * log(U2)

---

Here is my approach to implement this algorithm in R:

f<-function(alpha,beta){ # alpha=2, beta=3 for example

  N<-1000
  t<-rep(0,N)
  X<-rep(0,N)
  Y<-rep(0,N)

  for(j in 1:N) 
  {
    u<-runif(alpha)

    t[j]<- -beta*log(prod(u)) 

    U3<-runif(1)

    X[j]<-t[j]*U3
    Y[j]<-t[j]-X[j]

  }

  c<-list(X,Y)

  return(c)
}
alpha<-2
beta<-3
y1<-f(alpha,beta)


hist(y1,freq=F,nclass=10,col="gray")

---

#COMPARISON, defining x and y directly as -beta*ln(u):

u1<-runif(1)
u2<-runif(1)
betaa<-2
x<- -betaa*log(u1)
y<- -betaa*log(u2)
x
y

---

The code works only in the numerical part, generates the 1000 values for both 'X' and 'Y'. Where I am having problems is in the part of the histogram because it does not show anything, marks an error

hist(y1,freq=F,nclass=10,col="gray") Error in hist.default(y1, freq = F, nclass = 10, col = "gray") : 'x' must be numeric

I don't understand why, how can I fix this?

Could someone please help?