First and last attempt with a score

Problem

A mock-test app stores all your attempt scores, sorted from low to high. The same score can appear many times.

For a score t, print the index of its first copy and the index of its last copy, counting from 0. If t never appears, print -1 -1.

Input: The first line has two integers n and t. The second line has n integers: the scores, from low to high.
Output: Two integers separated by a space: the first and the last index of t, or -1 -1.
Constraints: 1 ≤ n ≤ 10^5
0 ≤ score, t ≤ 10^9
The scores are in non-decreasing order.

Example 1

Input

7 55
40 55 55 55 62 70 70

Output

1 3

55 appears at indices 1, 2 and 3.

Example 2

Input

4 50
10 20 60 80

Output

-1 -1

50 does not appear.

Try the problem first. Open one hint at a time.

Hint 1

Searching once and stopping at any copy of t is not enough. You need the two ends of the run.

Hint 2

Do two searches. The first one keeps going left after it finds t; the second keeps going right.

Hint 3

In the first search, when the middle equals t, save it and continue with hi = mid - 1.

Hint 4

Another way: the last copy of t is just before the first score that is at least t + 1.

Write your Java code, run it on the examples and submit it to hidden tests.