Challenge 3: Exact In Swap Quote

Now compute the output amount for an exact-in swap.

Formula

Starting from:

x * y = k

After adding x_in to the X reserve:

new_x = x + x_in
new_y = k / new_x
y_out = y - new_y

Task

Implement quote_exact_in.

Requirements

• Do intermediate math in u128.
• Return the final output as u64.
• Round down naturally through integer division.

For the sample:

x = 1000
y = 2000
x_in = 100
k = 2_000_000
new_x = 1100
new_y = 1818
y_out = 182