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 <cstdio>
using namespace std;

int A[100010], cnt[100010];
int main() {
    int N, K; scanf("%d%d", &N, &K);
    for(int i=0; i<N; i++) {
        scanf("%d", &A[i]);
    }

    int r = 0, sum = 0, ans = N+1;
    for(int l=0; l<N; l++) {
        while(sum < K && r < N) {
            if(!cnt[ A[r] ] && A[r] <= K) sum++;
            cnt[ A[r++] ]++;
        }
        
        while(l < r) {
            if(--cnt[ A[l] ] == 0 && A[l] <= K) break;
            l++;
        }
        if(sum == K && ans > r - l) ans = r - l;
        if(A[l] <= K) sum--;
    }
    printf("%d\n", (ans == N+1 ? 0 : ans));
    return 0;
}