Having a Solana program mint tokens while a user pays the fee

Question

I'm trying to have a Solana Anchor program mint tokens to a user's token account (so the program or its PDA should be the authority for the mint), while the owner of the token account that's receiving the tokens should pay the fee.

This is what I have right now:

use anchor_lang::prelude::*;
use anchor_spl::token;
use anchor_spl::token::{Token, MintTo};

declare_id!("EcFTDXxknt3vRBi1pVZYN7SjZLcbHjJRAmCmjZ7Js3fd");
//token HKTPz1skkSNAC8TXJiYvPyYtMCQDHtAheCL4FrBArCDJ
//program EcFTDXxknt3vRBi1pVZYN7SjZLcbHjJRAmCmjZ7Js3fd
//account GHQMHrt4j8i6bBaVhpMCLP8uoFfWUrLZsQtWCWqSJKA6
#[program]
pub mod solana_ubi {
    use super::*;

    pub fn mint_token(ctx: Context<MintToken>,) -> Result<()> {
        // Create the MintTo struct for our context
        let cpi_accounts = MintTo {
            mint: ctx.accounts.mint.to_account_info(),
            to: ctx.accounts.token_account.to_account_info(),
            authority: ctx.accounts.owner.to_account_info(),
        };

        //need to make pda. see cookbook: sign a transaction with a pda.

        let cpi_program = ctx.accounts.token_program.to_account_info();
        // Create the CpiContext we need for the request
        let cpi_ctx = CpiContext::new(cpi_program, cpi_accounts);

        // Execute anchor's helper function to mint tokens
        token::mint_to(cpi_ctx, 10_000_000_000)?;

        Ok(())
    }
}

#[derive(Accounts)]
pub struct MintToken<'info> {
    /// CHECK: This is the token that we want to mint
    #[account()]
    pub mint: UncheckedAccount<'info>,
    pub token_program: Program<'info, Token>,
    /// CHECK: This is the token account that we want to mint tokens to
    #[account(mut)]
    pub token_account: UncheckedAccount<'info>,
    /// CHECK: ugh
    #[account(signer)]
    pub owner: AccountInfo<'info>,
}

this does mint the tokens, if I pass the mint's authority (any account holding SOL) as owner. Again for clarity: I want this program to be the mint authority for the token, but the user receiving the tokens to pay the fee. how should I change the code to make it work as described above? Please provide a code answer.