Wearing shoes while in a state of ritual impurity, wiping over them, and then praying: Does one have to repeat the prayer?

The questioner : This is something that has happened to me personally more than once. I would perform wudu, put on my socks and sandals, and then take off the sandals. My wudu would be broken, and then I would put on the sandals or shoes, perform wudu, and forget that I had put on the shoes while in a state of ritual impurity. So I performed wudu and wiped over the shoes, and then I remembered, perhaps after I had already prayed. Do I have to repeat the prayer?

The Shaykh : You must, you must.

The questioner : May Allah reward you with good.