Hanger Hanger Hanger

You need to tidy up your closet, but there are too many clothes and they are spilling onto the closet floor. There are $N$ spots where you can hang a hanger, and you have $M$ hangers. Then you realize something remarkable: when you have more hangers than the closet can hold, hanging hangers on a hanger lets you hang more clothes!

Instead of hanging clothes on a hanger, you can hang hangers on both sides of it to hold more clothes, but to keep the hanger balanced you must build a complete binary hanger where the total number of hangers on both sides is the same. Naturally, you can hang clothes only on the bottommost hangers that have no hangers hanging from them.

Call a single hanger a hanger tree of height 1. Hanging one hanger on each side of a hanger gives a hanger tree of height 2. Repeating this, hanging a hanger tree of height $i$ on each side of a hanger gives a hanger tree of height $i+1$. The closet is short, so you can hang clothes only on hanger trees of height 3 or less. A hanger tree of height 4 fits in the closet but is too tall to hang clothes below it, and a hanger tree of height 5 or more does not fit in the closet. You have nowhere else to put hangers, so you must use every hanger, and you do not need to place a hanger tree at every spot where a hanger can be hung.

Find the maximum number of clothes you can hang while placing hanger trees so that the conditions hold.

The first line gives the number of spots where a hanger can be hung and the number of hangers, $N$ and $M$. ($1\leq N \leq5,000, 1\leq M \leq 10,000$)

On the first line, print the maximum number of clothes you can hang. If there is no way to hang $M$ hangers at $N$ or fewer spots while satisfying the conditions above, print $-1$.

If you place hanger trees of heights 1, 2, 2, 3 in that order, you can hang 1, 2, 2, 4 clothes on them respectively.