Heidi and Library (medium)

Whereas 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

inputFormat

Input

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

outputFormat

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

样例

4 100
1 2 2 1

2

</p>