Exciting Startup

In the messaging app Alice built, one message is at most $n$ characters long.

Cathy, her first user, wants to send a single string of length $t$. Since $t$ is larger than $n$, the string does not fit in one message. She cuts it into $b$ pieces in order and sends the $a$-th piece as the $a$-th message. A piece may be empty.

So the messages can be read in order, Cathy appends an indicator of the exact form _a/b after the piece, where $a$ is the number of that message and $b$ is the total number of messages. Both numbers are written in decimal with no leading zeros. The indicator counts toward the limit of $n$ characters, so the length of the $a$-th message is (length of the piece) $+\ 2\ +$ (number of digits of $a$) $+$ (number of digits of $b$), and that length must not exceed $n$. All $b$ messages are sent, including any whose piece is empty.

For example, take $n = 7$ and the 29 character string floccinaucinihilipilification. At least 20 messages are needed: fl_1/20, oc_2/20, ci_3/20, ..., i_10/20, ..., n_20/20, where the first nine carry two characters each and the last eleven carry one each.

Given $n$ and $t$, find the minimum number of messages.

The first and only line contains two integers $n$ and $t$ separated by a space. ($5 \le n \le 100$, $n < t \le 10^6$)

$n$ is the maximum length of one message and $t$ is the length of the string Cathy wants to send.

Print the minimum number of messages Cathy has to send. If no number of messages can carry the string, print -1 instead.