Problem: 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

Solution (in PYTHON3):

Solution:
if __name__ == "__main__":
    N, K = map(lambda x: int(x), input().split())
    a = list(map(lambda x: int(x), input().split()))

    ans = N + 1
    idx = 0
    num = 0
    values = [0] * K
    for s in range(N):
        while (idx < N and num < K):
            v = a[idx]
            if (v <= K):
                values[v - 1] += 1
                if (1 == values[v - 1]):
                    num += 1
            idx += 1
        if (K == num):
            ans = min(ans, idx - s)
        v = a[s]
        if (v <= K):
            values[v - 1] -= 1
            if (0 == values[v - 1]):
                num -= 1
    ans = ans if ans < N + 1 else 0
    print(ans)