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:
N, K = map(int, input().split())
*A, = map(int, input().split())

ans = N+1
t = 0; u = [0]*K; c = 0
for s in range(N):
    while t < N and c < K:
        v = A[t]
        if v <= K:
            u[v-1] += 1
            if u[v-1] == 1:
                c += 1
        t += 1
    if c == K:
        ans = min(ans, t-s)
    v = A[s]
    if v <= K:
        u[v-1] -= 1
        if u[v-1] == 0:
            c -= 1
print(ans if ans < N+1 else 0)