Every ladder row begins by squaring the prior result and reducing modulo m. The multiply choice happens after that.
Carry the prior result
Before this row, the prior result is 7.
rprior=7
Why squaring advances the scan
Reading one more exponent bit doubles the exponent value already represented. Squaring is the modular way to make that advance.
next bit starts with a square
Square and reduce
Squaring gives 7 times itself, reduced modulo 33 to 16.
7⋅7mod33=16
Square happens first
The square value 16 is computed before checking whether this bit multiplies by the base.
square=16
Carry the row result forward
After the multiply decision, this row result 13 becomes the next row's prior result 13.
Summary
Every ladder row starts with a square-and-reduce step, then carries one small remainder forward.
prior→square