Paper Strip

Jasio found a very old roll of paper in the attic, on which his great-grandfather had written a sequence of integers. For a game he recently invented, Jasio needs a strip of the paper roll on which the sum of all the numbers is exactly $s$. He will cut away and throw out the parts he does not need.

However, he does not want to throw away too much of his great-grandfather's keepsake, so he wants the strip he keeps to be as long as possible.

Only numbers that lie next to each other on the roll can form a single strip. That is, a strip made of one number has length $1$, a strip made of two neighboring numbers has length $2$, and so on.

Find the length of the longest strip whose sum is exactly $s$.

The first line contains two integers $n$ and $s$ ($1 \le n \le 10^6$, $|s| \le 10^6$), the length of the roll and the sum the strip must have.

The second line contains the sequence of $n$ integers $x_1, x_2, \dots, x_n$ ($|x_i| \le 10^6$), separated by spaces, where $x_i$ is the value of the $i$-th number written on the paper.

Print a single integer, the length of the longest strip whose sum is exactly $s$. If no such strip exists, print the word BRAK instead.