Karl has 11 cups of sugar, and he wants to make 2 batches of his famous triple chocolate cookies, and 1 batch of sugar cookies. Each batch of triple chocolate cookies takes $2\frac{1}{3}$ cups of sugar, and each batch of sugar cookies takes $3\frac{2}{5}$ cups of sugar. After Karl makes his cookies, how many cups of sugar will he have left? Express your answer as a mixed number.