Understanding Uniswap's Constant Product Market Maker Model

Uniswap uses x * y = k where x and y represents the quantity of each token.

I can understand that when a trader is trading token A against token B, the formula determines the price (rate) as it ensures k value remains the same. But when a liquidity provider provies two tokens, doesn't that change the k?

Let's say Token A / Token B is in the liquidity pool, with 100 Token A and 50 Token B meaning k is 5000. When a liquidity provider comes in and deposits 20 Token A and 10 Token B, that means the liquidity pool now has 120 Token A and 60 Token B. Now, the value of k is 7200 ?

Is the constant k supposed to change every time a liquidity provider comes in? This seems like a very nooby question but I don't get why people call it the "constant" when it changes everytime with change in liquidity...