Ryu, a literal street fighter is about to take on $N$ opponents (numbered from $0$ to $N-1$) on Wah Yan Street, each rival has a fighting style denoted by an integer $S_i$ _{$(0\le i\le N-1)$}.
Ryu has already taken down the first opponent (opponent $0$) of fighting style $S_0$ to initiate the battle, and he plans to take down the rest of the opponents in order, from opponent $1$ to opponent $N-1$.

However, Ryu can only defeat opponent $j$ if he has previously defeated an opponent of "similar" fighting style. Two fighting styles are considered similar if they differ by at most $k$, where $k$ is Ryu's skill level.

Formally, he can defeat an opponent $j$ if and only if he has previously defeated some opponent $i$ _{$(i\lt j)$} such that $|S_i-S_j|\le k$.

Help deduce whether Ryu can defeat all $N$ opponents in order, or otherwise deduce which opponent he would be defeated by.

Input

The first line contains two integers, $N$ and $k$.
The next line contains $N$ integers, where the $i$-th integer is $S_i$, the fighting style of the $i$-th opponent.

Output

Output Winner if he defeats all $N$ opponents, or output an integer $x$, the index of the opponent he is defeated by.

Constraints

For all cases, $2\le N\le 2 \cdot 10^5, 1\le k,S_i\le 10^9$
Subtask 1 (40%): $N\le1000$
Subtask 2 (60%): No additional constraints