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;
typedef long long int ll;
typedef vector<ll> vl;
typedef pair<ll, ll> PP;
#define rep(i, n) for (ll i = 0; i < ll(n); i++)
#define all(v) v.begin(), v.end()
bool chmin(ll& a, ll b) {
    if (b < a) {
        a = b;
        return 1;
    }
    return 0;
}
bool chmax(ll& a, ll b) {
    if (b > a) {
        a = b;
        return 1;
    }
    return 0;
}
const ll INF = 999999999999999;
const ll MOD = 1000000007;
const ll MAX_N = 500010;
ll a, b, c, d, e, f, p, t, x, y, z, q, m, n, r, h, k, w, l, ans;
int main() {
    cin >> n >> k;
    vl A;
    rep(i, n) {
        cin >> x;
        A.push_back(x);
    }

    ans = INF;
    set<ll> S;
    vl V(MAX_N, 0);

    for (ll l = 0, r = 0;; l++) {
        while (r < n && S.size() < k) {
            if (A[r] <= k) S.insert(A[r]);
            V[A[r]]++;
            r++;
        }
        if (S.size() < k) break;
        //[l,r)は条件を満たす。
        ans = min(ans, r - l);
        V[A[l]]--;
        if (V[A[l]] == 0) S.erase(A[l]);
    }

    if (ans == INF)
        cout << 0 << endl;
    else
        cout << ans << endl;
}