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"

#define REP(i,num) for(int i=0;i<(num);++i)
#define LOOP(i) while(i--)
#define ALL(c) c.begin(),c.end()
#define PRINTALL(c) for(auto& x:c){cout<<x<<' ';}cout<<endl;
#define PAIRCOMP(c,comp) [](const pair<ll,ll>& lhs,const pair<ll,ll>& rhs){return lhs.c comp rhs.c;}

using namespace std;
using ll = long long;

constexpr ll atcoder_mod = 1e9+7;

template<typename T=int>
T in(){T x; cin >> x; return (x);}
template<typename T=int,typename C=vector<T>>
C vecin(int N){C x(N);REP(i,N){x[i]=in<T>();}return move(x);}

void vout(){cout << endl;}
template<typename Head,typename... Tail>
void vout(Head&& h,Tail&&... t){cout << ' ' << h;vout(forward<Tail>(t)...);}
void out(){cout << endl;}
template<typename Head,typename... Tail>
void out(Head&& h,Tail&&... t){cout << h;vout(forward<Tail>(t)...);}

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

	auto N=in(),S=in();
	vector<ll> A=vecin<ll>(N);
	map<int,int> M;

	int ans = 1<<30;
	int left = 0,right = 0,find = 0;
	while(true){
		while(right<N && find<S){
			if(A[right]<=S && !(M[A[right]]++)){
				find++;
			}
			right++;
		}
		if(find==S){
			while(left<right && find==S){
				if(A[left]<=S && !(--M[A[left]])){
					find--;
				}
				ans = min(ans,right-left);
				left++;
			}
		}
		else break;
	}
	
	out(ans==1<<30 ? 0 : ans);
	return 0;
}