April Fools' Problem (hard)

The plans for HC2 are rather far-fetched: we are just over 500 000 days away from HC2 3387, for example, and accordingly we are planning to have a couple hundred thousand problems in that edition (we hope that programming contests will become wildly more popular). The marmots need to get to work, and they could use a good plan...

Input

Same as the medium version, but the limits have changed: 1 ≤ k ≤ n ≤ 500 000.

Output

Same as the medium version.

Example

Input

8 4 3 8 7 9 9 4 6 8 2 5 9 4 3 8 9 1

Output

32

inputFormat

Input

Same as the medium version, but the limits have changed: 1 ≤ k ≤ n ≤ 500 000.

outputFormat

Output

Same as the medium version.

Example

Input

8 4 3 8 7 9 9 4 6 8 2 5 9 4 3 8 9 1

Output

32

样例

8 4
3 8 7 9 9 4 6 8
2 5 9 4 3 8 9 1

                                                              32

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