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 <set>
#include <map>
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;}
typedef long long ll;
const ll INF = 1LL << 60;
const ll MOD = 1e9 + 7;

int N,K;

int main() {
    cin.tie(0); ios_base::sync_with_stdio(false);
    cin >> N >> K;
    vector<int> a(N);
    REP(i,N) cin >> a[i];
    map<int,int> m;
    int l = 0, r = 0, cnt = 0, ans = N+1;
    for(;;){
        while(r < N && cnt != K){
            if(a[r] <= K){
                if(m[a[r]]++==0) ++cnt;
            }
            ++r;
        }
        if(cnt!=K) break;
        chmin(ans,r-l);
        if(l==r) ++r;
        if(--m[a[l++]] == 0) --cnt;
    }
    cout << (ans==N+1 ? 0 : ans) << '\n';
    return 0;
}