Petya and Vasya are competing with each other in a new interesting game as they always do.

At the beginning of the game Petya has to come up with an array of $N$ positive integers. Sum of all elements in his array should be equal to $S$. Then Petya has to select an integer $K$ such that $0 \leq K \leq S$.

In order to win, Vasya has to find a non-empty subarray in Petya's array such that the sum of all selected elements equals to either $K$ or $S - K$. Otherwise Vasya loses.

You are given integers $N$ and $S$. You should determine if Petya can win, considering Vasya plays optimally. If Petya can win, help him to do that.