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:
#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define all(x) x.begin(),x.end()
const long double PI = acos(-1.0L);
const long long MOD = 1000000007LL;
//const long long MOD = 998244353LL;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<long long, long long> pll;
template<class T> inline bool chmax(T &a, T b) { if (a < b) { a = b; return true;} return false; }
template<class T> inline bool chmin(T &a, T b) { if (a > b) { a = b; return true;} return false; }
///////////////////////////////////////////////////////////////////////////////////////////////////

int main() {
    ios::sync_with_stdio(false); cin.tie(nullptr);
    ll N,K; cin >> N >> K;
    vector<int> A(N);
    rep(i,N) cin >> A[i];

    vector<int> B(K+1);
    set<int> dic;
    int ans = 1e9;
    int right = 0;
    rep(left,N) {
        while (right < N && dic.size() < K) {
            if (A[right] <= K) {
                B[A[right]]++;
                dic.emplace(A[right]);
            }
            right++;
        }
        if (dic.size() == K) chmin(ans,right-left);
        if (left == right) right++;
        if (A[left] <= K) {
            B[A[left]]--;
            if (B[A[left]] == 0) dic.erase(A[left]);
        }
    }

    cout << (ans==1e9 ? 0 : ans) << endl;
}