I was going through problem E editorial . As per my understanding if make matrix for "16" ,
then initially I will construct matrix for "1" and then "6" and then "16" ,
normally according to segment tree merge operation.

Now "1"'s matrix (as per my understanding of your state diagram) should look like :


__|_____________
  |  0 0 0 0 0
  |  0 0 0 0 0
  |  0 0 1 0 0
  |  0 0 0 0 0
  |  0 0 0 0 0

and "6"'s matrix should look like :
__|_____________
  |  0 0 0 0 0
  |  0 0 0 0 0
  |  0 0 0 0 0
  |  0 0 0 1 0
  |  0 0 0 0 1
and "16"'s matrix should look like :

__|_____________
  |  0 0 0 0 0
  |  0 0 0 0 0
  |  0 0 1 1 1
  |  0 0 0 1 1
  |  0 0 0 0 1
Now my main problem is understanding merge operation , will matrix be multiplied
 during concatenation or simply added . Now for that I tried both adding and multiplication .
Multiplication is leading to definite null matrix . However adding is not leading to "16"'s matrix as
you can see.
So which operation is to be applied ?