Dominating Subarray

An array $x\_1, \ldots, x\_\ell$ is a subarray of an array $y\_1, \ldots, y\_m$ if there exists an integer $i$ from $1$ to $m-\ell+1$ such that the following equalities hold: $y\_i = x\_1$, $y\_{i+1} = x\_2$, $\ldots$, $y\_{i+\ell-1} = x\_{\ell}$.

A subarray $b\_1, \ldots, b\_k$ of $a$ is $k$-dominating if for any subarray $c\_1, \ldots, c\_k$ of $a$, the following inequalities hold: $b\_1 \ge c\_1$, $b\_2 \ge c\_2$, $\ldots$, $b\_k \ge c\_k$.

You are given an array $a\_1, \ldots, a\_n$. Find any occurrence of a $k$-dominating subarray of $a$ if it exists.

The first line contains two integers $n$ and $k$ ($1 \le k \le n \le 100\\,000$), the length of the array $a$ and the parameter. The second line contains $n$ integers $a\_1, \ldots, a\_n$ ($1 \le a\_i \le 10^6$), the elements of the array.

Print "-1" if there is no $k$-dominating subarray in $a$. Otherwise, print an integer $i$ from $1$ to $n-k+1$ such that $a\_i, \ldots, a\_{i+k-1}$ is a $k$-dominating subarray of $a$.