Sum of values in column V1 based on conditions set in V2 in R

I want to create the sum of a number of values in a column, based on following conditions:

Say I have following data

Z <- matrix(c(1,2,3,4,5,6,7,8,9,10,0,0,1,1,0,0,0,0,0,1), nrow = 10, ncol = 2)

giving me

V1   V2
1    0
2    0
3    1
4    1
5    0
6    0
7    0
8    0
9    0
10   1

Now I only want to sum of values in V1 between the first 1 in V2 and the first value in V2 that is followed by four zeroes. In this example this would be the sum of [3,1] and [4,1] since [3,2] contains the first zero and [4,2] is the first value that is followed by four zeroes in resp. [5,2], [6,2], [7,2] and [8,2].

I tried following loop and variations on it but it keeps giving errors.

for(j in 1:10){
  ifelse(V2(j) == 1,
         (for i in (j:(10-j+1)){
           ifelse (V2(i+1) == 0 & V2(i+2) == 0 & V2(i+3) == 0 & V2(i+4) == 0, total <- sum(V1(c(j:i))), next)})
         , next)
}