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;

int N;
int K;
vector<int> a(100001);

bool check(int x) {
    vector<int> cnt(100001, 0);
    set<int> all;
    for ( int i = 0; i < x; i++ ) {
        if ( a[i] <= K ) all.insert(a[i]);
        cnt[a[i]]++;
    }

    if ( all.size() >= K ) return true;
    for ( int i = 0; i < N-x; i++ ) {
        cnt[a[i]]--;
        if ( !cnt[a[i]] ) all.erase(a[i]);
        if ( a[i+x] <= K ) {
            all.insert(a[i+x]);
            cnt[a[i+x]]++;
        }
        if ( all.size() >= K ) return true;
    }

    return false;
}

int main() {
    cin >> N >> K;
    set<int> all;
    for ( int i = 0; i < N; i++ ) {
        cin >> a[i];
        if ( a[i] <= K ) all.insert(a[i]);
    }

    if ( all.size() < K ) {
        cout << 0 << endl;
        return 0;
    }

    int l = 0, r = N;
    while ( r-l > 1 ) {
        int mid = (l+r) / 2;
        if ( check(mid) ) r = mid;
        else l = mid;
    }

    cout << r << endl;
}