Spam Filter

Goo works at a well known Slovak antivirus company that cannot be named here. Besides antivirus software, the company develops a spam filter. Goo has improved the filter recently and wants to show the progress to his boss. Listing the low level details of the implementation will not convince anyone, so Goo decided to prepare a presentation full of graphs of the filtering results.

The company keeps a huge database of e-mails, and every e-mail carries a mark saying whether it is spam or ham (an e-mail that is not spam). People wrote all of those marks by hand and every mark is correct. Whenever someone in the company receives an e-mail, that person marks it as spam or ham and adds it to the database.

The quality of Goo's program is easy to measure. Goo ran the program on every e-mail in the database and wrote down, for each message, whether the program decided correctly. The messages were processed from the oldest one to the newest one. To leave a good impression on the boss, Goo wants to pick the e-mails of one period of time and compute the success rate of that period only. A period that holds a single e-mail convinces nobody, so the period has to be long enough.

You are given the sequence of results and an integer $k$. Find a contiguous subsequence of length at least $k$ whose success rate is the highest possible. The success rate of a subsequence is the number of correctly classified e-mails divided by the length of the subsequence.

The first line contains the minimum length $k$ of the subsequence ($1 \le k \le 100$).

The second line contains a string made of the characters 0 and 1. The $i$-th character of the string tells how the program judged the $i$-th e-mail. A 1 means the program answered correctly and a 0 means it failed. The length of the string is at least $k$ and at most $100\,000$.

Print two integers $f$ and $\ell$ on one line, separated by a single space. $f$ is the position of the first element of the chosen subsequence, counted from 1, and $\ell$ is its length.

If several subsequences reach the best success rate, print the one with the smallest $f$. If several of those remain, print the shortest one among them.