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B. Heidi and Library (medium)

time limit per test

10 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputWhereas humans nowadays read fewer and fewer books on paper, book readership among marmots has surged. Heidi has expanded the library and is now serving longer request sequences.

Input

Same as the easy version, but the limits have changed: 1 ≤ *n*, *k* ≤ 400 000.

Output

Same as the easy version.

Examples

Input

4 100

1 2 2 1

Output

2

Input

4 1

1 2 2 1

Output

3

Input

4 2

1 2 3 1

Output

3

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

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