Yunho and Donghyeok are at an algorithm camp. When a problem will not come out, they take a break and play a game.
The game is made of turns, and each turn is won by one of the two players. Turns are numbered from 1, and the winner of turn i earns 2i−1 points.
The total number of turns is not fixed. Any number of turns is possible, including zero.
You are given two integers x and y. Decide whether Yunho can end with x points and Donghyeok with y points. If that is possible, also find the smallest number of turns Yunho has to win.