The Smallest Window II

For a given array $a_1, a_2, a_3, ... , a_N$ of $N$ elements and an integer $K$, find the smallest sub-array size (smallest window length) where the elements in the sub-array contains all integers in range [$1, 2, ..., K$]. If there is no such sub-array, report 0.

Constraints

• $1 \leq N \leq 10^5$
• $1 \leq K \leq 10^5$
• $1 \leq a_i \leq 10^5$

Input

The input is given in the following format.

$N$ $K$ $a_1$ $a_2$ ... $a_N$

Output

Print the smallest sub-array size in a line.

Examples

Input

6 2 4 1 2 1 3 5

Output

2

Input

6 3 4 1 2 1 3 5

Output

3

Input

3 4 1 2 3

Output

0

inputFormat

Input

The input is given in the following format.

$N$ $K$ $a_1$ $a_2$ ... $a_N$

outputFormat

Output

Print the smallest sub-array size in a line.

Examples

Input

6 2 4 1 2 1 3 5

Output

2

Input

6 3 4 1 2 1 3 5

Output

3

Input

3 4 1 2 3

Output

0

样例

3 4
1 2 3

0