2015 CIMC keystage2-EMIC team Question 3

There is a machine with five slots. Each slots can receive two cards as input and in most cases will produce a new card as output. All cards have positive integers on them. The output from the $+,-,\times$ or $\div$ slots is the sum, the difference, the product or the quotient. If the difference or the quotient is not a positive integer, there is no output. The output from the $\sim$ slot is a number obtained by writing the second input immediately after the first input. For example, we get $102$ if we input $10$ and $2$, or $210$ if we input $2$ and $10$. All input cards are returned. Starting with two cards with the numbers $1$ and $2$, find a way of getting a card with the number $2015$, using the machine only five times. Every time we use a slot it counts as a separate operation.

For each of the five response rows, record the two input cards, the slot and the output card.