Igor reads a news feed in his favorite social network, which consists of n successive entries. Each entry in the feed has its own characteristic — the positivity of a
i , given by a natural number. After reading the i-th entry, Igor's mood improves by a
i .
Igor reads the entries in the order in which they are shown, without skipping any of them. The social network application is designed so that after viewing the last entry, Igor moves to the beginning of the feed and sees the first entry. Igor can start viewing the news feed from any of the entries and read any number of entries in a row, not exceeding n .
Igor feels happy if his mood improved by at least p after reading the news. He wants to feel happy by reading as few entries as possible, because he is already late for the Olympiad! Help him decide which post to start watching and the number of posts to watch, or determine that there aren't enough posts in his feed to make him happy.
Input
The first line contains two numbers n and p ( 1 ≤ n ≤ 1000 , 1 ≤ p ≤ 10
7 ) — the number of entries in the news feed and the amount by which Igor wants to increase his mood.
The second line contains n non-negative integers a i ( 1 ≤ a
i ≤ 10
4 ) — positivity of entries in the tape. Neighboring numbers are separated by exactly one space.
Imprint
If Igor can become happy, print two numbers — the number of the record k to start browsing, and the number of records c to look at. If there are several possible answers with minimal
c, print the one with minimal k.
If there is no solution, print - 1.
Examples
| # |
Input |
Output |
| 1 |
9 10
1 2 3 4 5 4 3 2 1
| 3 3 |
| 2 |
5 6
3 1 1 1 4
| 5 2 |
| 3 |
3 100
10 10 10
| -1 |