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 CPP):

Solution:
#include <iostream>
#include <vector>

const int INF = 1 << 25;

int main() {
    int N, K;
    std::cin >> N >> K;
    std::vector<int> A(N);
    for (auto& a : A) {
        std::cin >> a;
        --a;
    }

    std::vector<int> cnt(K, 0);
    int unfill = K, r = 0;
    int ans = INF;
    for (int l = 0; l < N; ++l) {
        while (r < N && unfill > 0) {
            if (A[r] < K) {
                if (cnt[A[r]] == 0) --unfill;
                ++cnt[A[r]];
            }
            ++r;
        }

        if (unfill == 0) ans = std::min(ans, r - l);

        if (A[l] < K) {
            --cnt[A[l]];
            if (cnt[A[l]] == 0) ++unfill;
        }
    }

    std::cout << (ans == INF ? 0 : ans) << std::endl;
    return 0;
}