Longest block with a given total

Problem

Find the length of the longest block of consecutive items whose sum is exactly k. Print 0 if there is none. Items can be negative.

Example

Input

5 3
1 -1 5 -2 3

Output

The first four items add to 3.

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

Hint 1

Use prefix sums again, but store where each prefix first appeared.

Hint 2

Never overwrite a stored index. The earliest start gives the longest block.

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