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 <bits/stdc++.h>
using namespace std;
using ll = long long;

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);

    int N, K;
    cin >> N >> K;
    vector<int> a(N);
    for (int i = 0; i < N; i++) cin >> a[i];
    vector<int> cnt(K+1);
    int kind = 0;
    int t = 0, ans = N + 1;
    for (int s = 0; s < N; s++) {
        for (; t < N && kind < K; t++) {
            if (a[t] > K) continue;
            if (cnt[a[t]] == 0) kind++;
            cnt[a[t]]++;
        }
        if (kind < K) break;
        ans = min(ans, t - s);
        if (a[s] > K) continue;
        cnt[a[s]]--;
        if (cnt[a[s]] == 0) kind--;
    }
    if (ans <= N) cout << ans << endl;
    else cout << 0 << endl;
}