Does touching the penis with desire, through a barrier, invalidate ablution?

Touching the male organ with desire from behind a barrier is a matter of disagreement among scholars:

Shafi'is and the preponderant opinion among Hanbalis: It does not invalidate ablution (Wudu). Malikis: It invalidates ablution. Hanafis: It does not invalidate ablution at all, whether there is a barrier or not.

Those who say it does not invalidate ablution argue that touching from behind a barrier is not considered actual touching. In contrast, those who say it invalidates ablution argue that it is a direct contact with desire.