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;

constexpr int INF = 1 << 30;

void solve(){
    int N, K;
    cin >> N >> K;
    vector<int> A(N);
    for(int i=0;i<N;i++){
        cin >> A[i];
    }
    vector<int> cnt(K+1);
    int ans = INF, s=0;
    for(int l=0,r=0;l<N;l++){
        while(r<N && s<K){
            if(A[r]<=K){
                if(cnt[A[r]]==0) s++;
                cnt[A[r]]++;
            }
            r++;
        }
        if(s==K){
            ans = min(ans, r-l);
        }
        if(A[l]<=K){
            cnt[A[l]]--;
            if(cnt[A[l]]==0) s--;
        }
    }    
    cout << (ans<INF ? ans : 0) << endl;
}

int main() {
    solve();
    return 0;
}