how to coerce part of each column of a matrix to a vector and merge them

Hello

Suppose I have a matrix mat=(1:16,2)
    [,1] [,2] [,3] [,4]
[1,]    1    5    9   13
[2,]    2    6   10   14
[3,]    3    7   11   15
[4,]    4    8   12   16

there is a vector end=c(2,3,1,3)

#coerce the 1st 2 numbers of the 1st column to a vector  [1]  1  2
#coerce the 1st 3 numbers of the 2nd column and append it to the previous vector  [1]  1  2  5  6  7
#coerce the 1st number of the 3rd column and append it to the previous vector  [1]  1  2  5  6  7  9
#coerce the 1st 3 numbers of the 4th column and append it to the previous vector  [1]  1  2  5  6  7  9 13 14 15
#they are specified by vector end
a for loop
mat<-matrix(1:16,4)
end<-c(2,3,1,3)
vec<-numeric()
for (i in 1:4)
       {vec<-c(vec,mat[1:end[i],i])
       }
#the result

 > vec

[1]  1  2  5  6  7  9 13 14 15

 but when I want to do it to a large dataset, it's inefficiency becomes a problem, so need vectorization

 Thank you in advance
 Yours sincerely

ZhaoXing
Department of Health Statistics
West China School of Public Health
Sichuan University
No.17 Section 3, South Renmin Road
Chengdu, Sichuan 610041
P.R.China