Not so Diverse

Takahashi has N balls. Initially, an integer A_i is written on the i-th ball.

He would like to rewrite the integer on some balls so that there are at most K different integers written on the N balls.

Find the minimum number of balls that Takahashi needs to rewrite the integers on them.

Constraints

• 1 \leq K \leq N \leq 200000
• 1 \leq A_i \leq N
• All input values are integers.

Input

Input is given from Standard Input in the following format:

N K A_1 A_2 ... A_N

Output

Print the minimum number of balls that Takahashi needs to rewrite the integers on them.

Examples

Input

5 2 1 1 2 2 5

Output

1

Input

4 4 1 1 2 2

Output

0

Input

10 3 5 1 3 2 4 1 1 2 3 4

Output

3

inputFormat

input values are integers.

Input

Input is given from Standard Input in the following format:

N K A_1 A_2 ... A_N

outputFormat

Output

Print the minimum number of balls that Takahashi needs to rewrite the integers on them.

Examples

Input

5 2 1 1 2 2 5

Output

1

Input

4 4 1 1 2 2

Output

0

Input

10 3 5 1 3 2 4 1 1 2 3 4

Output

3

样例

4 4
1 1 2 2

0