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 <algorithm>
#include <vector>
#include <queue>
#include <map>
#include <cmath>
#include <iomanip>
using namespace std;
#define REP(i,n) for (int i=0;i<(n);++i)
#define rep(i,a,b) for(int i=a;i<(b);++i)
template<class T> inline bool chmin(T &a, T b){ if(a > b) { a = b; return true;} return false;}
template<class T> inline bool chmax(T &a, T b){ if(a < b) { a = b; return true;} return false;}
using ll = long long;
constexpr long long INF = 1LL << 62;
constexpr int MOD = 1e9 + 7;
constexpr double EPS = 1e-10;

int main() {
    cin.tie(0); ios_base::sync_with_stdio(false);
    int n,k; cin >> n >> k;
    vector<int> a(n);
    REP(i,n) cin >> a[i];

    int l = 0, r = 0, num = 0, ans = 101010;
    int cnt[101010];
    while(true) {
        while(num != k && r < n) {
            if(a[r] <= k) {
                if(cnt[a[r]]++==0) ++num;
            }
            ++r;
        }
        if(num != k) break;

        ans = min(ans, r - l);
        if(--cnt[a[l++]]==0) --num;
    }

    if(ans==101010) ans = 0;
    cout << ans << endl;

    return 0;
}