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;
using UL = unsigned int;
using ULL = unsigned long long;
using LL = long long;
#define rep(i, n) for(UL i = 0; i < (n); i++)

struct Problem {

    void Solve() {
        UL N, K; scanf("%d%d", &N, &K);
        vector<UL> A(N); rep(i, N) { scanf("%d", &A[i]); A[i]--; }
        vector<UL> C(K);
        UL Z = 0; UL q = 0;
        UL ans = -1;
        rep(p, N) {
            if (A[p] < K) {
                if (!C[A[p]]) Z++;
                C[A[p]]++;
            }
            while (Z == K) {
                if (A[q] >= K) { q++; continue; }
                if (C[A[q]] != 1) { C[A[q]]--; q++; }
                else break;
            }
            if (Z == K) ans = min(ans, p - q + 1);
        }
        if (ans == -1) printf("0\n");
        else printf("%d\n", ans);
    }
};
int main() {
    unique_ptr<Problem> p(new Problem());
    //cout << fixed << setprecision(10);
    p->Solve();
    return 0;
}