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;

int main() {
    int N, K; cin >> N >> K;
    vector<int> A(N);
    for(int i=0; i<N; ++i) cin >> A[i];

    map<int, int> cnt;
    int right = 0;
    int res = N + 1;
    for(int left = 0; left < N; ++left) {
        while(right < N && cnt.size() < K) {
            if(A[right] >= 1 && A[right] <= K) cnt[A[right]] += 1;
            ++right;
        }

        if(cnt.size() < K) break;
        else res = min(res, right - left);

        if(left == right) {
            ++right;
        } else if(A[left] >= 1 && A[left] <= K) {
            cnt[A[left]] -= 1;
            if(cnt[A[left]] == 0) cnt.erase(A[left]);
        } 
    }
    
    cout << (res < N + 1 ? res : 0) << endl;
}