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;
#define Rep(i,n) for(int i=0;i<(int)(n);i++)
#define For(i,n1,n2) for(int i=(int)(n1);i<(int)(n2);i++)
#define REP(i,n) for(ll i=0;i<(ll)(n);i++)
#define RREP(i,n) for(ll i=((ll)(n)-1);i>=0;i--)
#define FOR(i,n1,n2) for(ll i=(ll)(n1);i<(ll)(n2);i++)
#define RFOR(i,n1,n2) for(ll i=((ll)(n1)-1);i>=(ll)(n2);i--)
#define all(a)  (a).begin(),(a).end()
#define SORT(a) sort((a).begin(),(a).end())
#define oorret 0
#define oor(x) [&](){try{x;} catch(const out_of_range& oor){return oorret;} return x;}()
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> P;
template<typename T1, typename T2> inline bool chmin(T1& a, T2 b) { if (a > b) { a = b; return 1; }return 0; }
template<typename T1, typename T2> inline bool chmax(T1& a, T2 b) { if (a < b) { a = b; return 1; }return 0; }
template<class Type>struct is_vector : std::false_type {};
template<class ValueType, class Alloc>struct is_vector<std::vector<ValueType, Alloc>> : std::true_type {};
template <typename T> inline ostream& operator << (ostream& out, const vector<T>& v) {
    if (v.empty())return out;
    constexpr bool is_vector_v = is_vector<T>::value;
    if (is_vector_v)for (auto itr = v.begin(); itr != v.end();)out << (*itr),out << ((++itr != v.end()) ? "\n" : "");
    else for (auto itr = v.begin(); itr != v.end();)out << (*itr),out << ((++itr != v.end()) ? " " : "");
    return out;
}
inline void put() {}
template<class T> inline void put(const T& first) { std::cout << first; printf("\n"); }
template<class T, class... N> inline void put(const T& first, const N& ... rest) { std::cout << first; printf(" "); put(rest...); }
inline void putn() {}
template<class T, class... N> inline void putn(const T& first, const N& ... rest) { std::cout << first; printf("\n"); putn(rest...); }

int n,k;

bool proc(vector<int>& a,int t){
    vector<int> c(k,0);
    int cnt = 0;
    REP(i,n){
        if(a[i]<=k){
            int temp = a[i]-1;
            if(c[temp]==0){
                cnt++;
            }
            c[temp]++;
        }
        if(i-t>=0){
            int temp = a[i-t]-1;
            if(temp<k){
                if(c[temp]==1){
                    cnt--;
                }
                c[temp] = max(c[temp]-1,0);
            }
            
        }
        if(cnt==k){
            return true;
        }
        
        
    }
    return false;
}

int main(){
    cin >> n >> k;
    vector<int> a(n);
    REP(i,n){
        cin >> a[i];
    }
    int lb = -1,ub = n+1;
    while(ub-lb>1){
        int mid = (lb+ub)/2;
        if(proc(a,mid)){
            ub = mid;
        }else{
            lb = mid;
        }
    }
    if(ub>n){
        put(0);
    }else{
        put(ub);
    }
    return 0;
}